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27 4.1 Introduction This chapter presents information on the analytical tech- niques used in various components of conventional travel demand models and on parameters for these models obtained from typical models around the United States and from the 2009 NHTS. These parameters can be used by analysts for urban areas with insufficient local data with which to esti- mate model parameters. They may also be used, in areas that have already developed model parameters, to check these parameters for reasonableness. Chapter 5 discusses the use of the parameters presented in this chapter for model valida- tion and reasonableness checking. 4.1.1 Information Sources There are two primary sources of information in this chapter: 1. The NHTS is administered by the FHWA. It provides information to assist transportation planners and pol- icy makers who need comprehensive data on travel and transportation patterns in the United States. The 2009 NHTS updates information gathered in the 2001 NHTS and in prior Nationwide Personal Transportation Surveys (NPTS) conducted in 1969, 1977, 1983, 1990, and 1995. Data were collected from a nationwide sample of house- holds on trips taken within a 24-hour period and include: â¢ Trip purpose (work, shopping, etc.); â¢ Means (mode) of transportation used (car, bus, light rail, walk, etc.); â¢ How long the trip took, i.e., travel time; â¢ Time of day and day of week when the trip took place; and â¢ If a private vehicle trip: â Number of people in the vehicle, i.e., vehicle occu- pancy; â Driver characteristics (age, sex, worker status, educa- tion level, etc.); and â Vehicle attributes (make, model, model year, amount of miles driven in a year). The 2009 NHTS was used to obtain selected parameters including trip generation rates, average trip lengths, and time-of-day percentages. The information included in this report from the NHTS uses the weekday sample only. This information was estimated by urban area population range, using the urbanized area identifier in the data set. The population ranges available in the NHTS data set are as follows: â¢ Over 1 million population with subway/rail; â¢ Over 1 million population without subway/rail; â¢ 500,000 to 1 million population; â¢ 200,000 to 500,000 population; â¢ 50,000 to 200,000 population; and â¢ Not in an urban area. It was found that many of the parameters estimated from NHTS data did not vary by population range, varied only between some ranges, or had only minor fluctuations that showed no trends and appeared to be related to survey sampling. In these cases, parameters are presented for aggregated population ranges and, in cases where there was no variation among population ranges or only minor fluctuations, for all areas together. 2. A database of information from model documenta- tion from 69 MPOs4 was used to obtain information on selected model parameters. While all of the documents did not include information on every parameter of inter- est, information was again summarized by urban area population range where sufficient data were available. C h a p t e r 4 Model Components 4 While the term âMPOsâ is used here for convenience to describe the agencies maintaining travel models, it is recognized that some agencies maintaining models are not actually metropolitan planning organizations.
28 This database is referred to throughout the chapter as the âMPO Documentation Database.â The metropolitan areas are organized by population range, as follows: â¢ Over 1 million population; â¢ 500,000 to 1 million population; â¢ 200,000 to 500,000 population; and â¢ 50,000 to 200,000 population. The areas included in the MPO Documentation Data- base are shown in Table 4.1, organized by population category. Again, some parameters did not vary by popula- tion range, varied only between some ranges, or had only minor fluctuations. For some parameters, there was insuf- ficient information for some population ranges. In these cases, parameters are presented for aggregated population ranges and for all areas together, in cases where there was no variation among population ranges, or only minor fluctuations. A few supplementary sources were used to fill gaps where neither of the primary sources could be used. These sources are identified where they are used throughout the chapter. 4.1.2 Chapter Organization This chapter comprises 12 sections. The first section after this introduction is a brief description of the logit model, a formulation that is used in several of the model compo- nents described later in the chapter. Each of the remaining 10 sections corresponds to a specific model component and includes the following subsections: â¢ Model FunctionâA brief summary of the function of the model component and how it fits into the overall model- ing process. â¢ Best PracticesâA brief description of the typical method(s) representing best practice. This subsection may include alternative methods that may be appropriate in differ- ent contexts. For example, trip generation might include methods to estimate total person trips, total motorized person trips, or total vehicle trips. This subsection does not include a complete discussion of the theory behind the methods and the model estimation procedures; rather, references to the already extensive existing literature doc- umenting these items are provided. â¢ Basis for Data DevelopmentâThe basis for the develop- ment of the data presented in the subsection and in typical modeling practice. â¢ Model ParametersâModel parameters classified by urban area category (including tables and figures as appropri- ate), with explanations of how they can be used in model estimation, validation and reasonableness checking, and parameter transfer. Model Components The methods presented in this chapter follow the con- ventional sequential process for estimating transportation demand. It is often called the âfour-stepâ process where the principal steps are: â¢ Step 1âTrip Generation; â¢ Step 2âTrip Distribution; â¢ Step 3âMode Choice; and â¢ Step 4âAssignment. This chapter discusses the following components of con- ventional travel modeling: â¢ Vehicle Availability (Section 4.3)âEstimating the number of automobiles available to households; â¢ Trip Generation (Section 4.4)âEstimating the number of passenger trips that are made from origin zones and to destination zones, classified as trip productions and trip attractions; â¢ Trip Distribution (Section 4.5)âEstimating the number of passenger trips that are made between origins and des- tinations; â¢ External Travel (Section 4.6)âEstimating the travel that has at least an origin or a destination external to the area being covered by the transportation model; â¢ Mode Choice (Section 4.7)âEstimating the mode to be used for passenger travel between origins and destinations; â¢ Automobile Occupancy (Section 4.8)âEstimating the number of vehicles required to accommodate passenger trips by automobile between origins and destinations; â¢ Time-of-Day Characteristics (Section 4.9)âEstimating the time of the day during which passenger trips are made; â¢ Freight/Truck Modeling (Section 4.10)âEstimating the number of freight and other trucks that travel in addition to passenger trips between origins and destinations; â¢ Highway Assignment (Section 4.11)âEstimating the vol- ume of trips on the highway segments that result from accommodating the passenger automobile and truck trips between origins and destinations; and â¢ Transit Assignment (Section 4.12)âEstimating the vol- ume of trips on transit vehicles and lines that result from accommodating the passenger transit trips between ori- gins and destinations. One of the primary reasons for the development of this report is the presentation of transferable parameters for use in urban areas where there is insufficient local data with which to estimate models. In such cases it has been common practice to transfer parameters from other models or data sets. In preparing this report, a literature review of trans- ferability of model parameters was undertaken (the results
29 Metropolitan Planning Organization Region Served MPOs with Population greater than 1,000,000 (25 MPOs) Atlanta Regional Commission Atlanta, Georgia Baltimore Regional Transportation Board Baltimore, Maryland Capital Area Metropolitan Planning Organization Austin, Texas Central Transportation Planning Staff Boston, Massachusetts Chicago Area Transportation Study Chicago, Illinois Denver Regional Council of Governments Denver, Colorado Durham-Chapel Hill-Carrboro MPO Durham, North Carolina Greater Buffalo/Niagara Falls Regional Transportation Council Buffalo/Niagara Falls, New York Hampton Roads MPO Hampton Roads, Virginia Maricopa Association of Governments Phoenix, Arizona Mecklenburg-Union MPO Charlotte, North Carolina Metropolitan Council of the Twin Cities Minneapolis-St. Paul, Minnesota Metropolitan Transportation Commission San Francisco, California Mid-America Regional Council Kansas City, Missouri Metropolitan Washington Council of Governments Washington, D.C. North Central Texas Council of Governments Dallas-Fort Worth, Texas Puget Sound Regional Council Seattle, Washington Regional Transportation Commission of Southern Nevada Las Vegas, Nevada Sacramento Area Council of Governmentsa Sacramento, California San Diego Association of Governments San Diego, California Shelby County MPO Memphis, Tennessee Southeast Michigan Council of Governments Detroit, Michigan Southeastern Wisconsin Regional Planning Commission Milwaukee, Wisconsin Southern California Association of Governments Los Angeles, California Wasatch Front Regional Council Salt Lake City, Utah MPOs with Population between 500,000 and 1,000,000 (8 MPOs) Akron Metropolitan Area Transportation Study Akron, Ohio Capital District Transportation Committee Albany, New York Capitol Region Council of Governments Hartford, Connecticut Council of Fresno County Governments Fresno County, California Genesee Transportation Council Rochester, New York Kern County Council of Governments Bakersfield, California Mid-Region Council of Governments Albuquerque, New Mexico Nashville Metropolitan Planning Organization Nashville, Tennessee MPOs with Population between 200,000 and 500,000 (18 MPOs) Brown County Planning Commission Green Bay, Wisconsin Chatham Urban Transportation Study Savannah, Georgia Chattanooga-Hamilton County Regional Planning Agency Chattanooga, Tennessee Des Moines MPO Des Moines, Iowa East Central Wisconsin Regional Planning Commission Appleton-Oshkosh, Wisconsin Knoxville Regional Transportation Planning Organization Knoxville, Tennessee Lane Council of Governments Eugene, Oregon Madison Area MPO Madison, Wisconsin Mid-Willamette Valley Council of Governments Salem, Oregon Table 4.1. MPOs classified using year 2000 population. (continued on next page)
30 of this review are presented in Appendix B). This review found mixed results: while transferability was valid in some studies, its validity could not be demonstrated in oth- ers. In general, transferability was demonstrated for trip generation and mode choice in some cases but not others while the literature on transferability of other parameters, including trip distribution, time of day, and freight/truck modeling, was insufficient to draw any conclusions. More research into model transferability, the conditions under which transferability is most likely to be valid, and ways in which the validity of transferred parameters could be improved, is needed. While the literature to date has not provided conclu- sive guidelines for transferability across geographic areas, it appears that transferability would be improved with a transfer approach that involves transfer scaling of coeffi- cients using limited data from the application context (the area to which parameters are to be transferred). Appen- dix B includes several references that describe methods for scaling that could be used if the limited data (possibly from Metropolitan Planning Organization Region Served North Front Range Metropolitan Planning Organization Fort Collins, Colorado Pima Association of Governments Tucson, Arizona Poughkeepsie-Dutchess County Transportation Council Poughkeepsie, New York San Joaquin Council of Governments Stockton, California Spokane Regional Transportation Council Spokane, Washington Stanislaus Council of Governments Modesto, California Syracuse Metropolitan Transportation Council Syracuse, New York Tri-County Regional Planning Commission Harrisburg, Pennsylvania Tulare County Association of Governments Visalia, California MPOs with Population between 50,000 and 200,000 (31 MPOs) Adirondack-Glens Falls Transportation Council Glens Falls, New York Association of Monterey Bay Area Governments Monterey, California Bay-Lake Regional Planning Commission Sheboygan, Wisconsin Binghamton Metropolitan Transportation Study Binghamton, New York Bristol Metropolitan Planning Organization Bristol, Tennessee Butte County Association of Governments Chico, California Chittenden County Metropolitan Planning Organization Burlington, Vermont Clarksville-Montgomery County Regional Planning Agency Clarksville, Tennessee Cleveland Area MPO Cleveland, Tennessee Columbus-Phenix City Metropolitan Planning Organization Muscogee, Georgia - Russell, Alabama Elmira-Chemung Transportation Council Elmira, New York Fond du Lac MPO Fond du Lac, Wisconsin Grand Valley MPO Grand Junction, Colorado Herkimer-Oneida County Transportation Study Utica, New York Ithaca Tompkins County Transportation Council Ithaca, New York Jackson Municipal Regional Planning Commission Jackson, Tennessee Janesville MPO Janesville, Wisconsin Johnson City Metropolitan Planning Organization Johnson City, Tennessee Kings County Association of Governments Lemoore, California Kingsport Transportation Department Kingsport, Tennessee La Crosse Area Planning Committee La Crosse, Wisconsin Lakeway Area Metropolitan Transportation Planning Organization Morristown, Tennessee Madera County Transportation Commission Madera, California Merced County Association of Governments Merced, California San Luis Obispo Council of Governments San Luis Obispo, California Santa Barbara County Association of Governments Santa Barbara, California Shasta County Regional Transportation Planning Agency Redding, California Siouxland Interstate Metropolitan Planning Council Sioux City, Iowa Thurston Regional Planning Council Olympia, Washington Ulster County Transportation Council Kingston, New York West Central Wisconsin Regional Planning Commission Eau Claire, Wisconsin aThe documentation reviewed for the Sacramento Area Council of Governments was for its trip-based model, not its current activity-based model. Table 4.1. (Continued).
31 a small household activity/travel survey or NHTS samples in the model region) were available. However, it is recognized that many areas, especially smaller urban areas, will not have even the limited data needed, or the required resources and expertise, to perform scaling of trans- ferred parameters. In such cases, the parameters presented in this chapter, or parameters from specific models that could provide estimation contexts, will serve as the best available parameters to use in the local models. Regardless of the transfer approach used, validation and rea- sonableness testing of results based on the transferred models should be performed. Validation and reasonableness testing are described in Chapter 5 and in the Travel Model Valida- tion and Reasonableness Checking Manual, Second Edition (Cambridge Systematics, Inc., 2010b). It will be particularly important to perform validations for two points in time, if possible, and to apply reasonableness tests to travel forecasts. While models based on transferred parameters may be vali- dated to base year conditions, the transferred models may have different sensitivities to changed conditions and scenarios than might be expected in an area. Trip Purposes In four-step travel models, the unit of travel is the âtrip,â defined as a person or vehicle traveling from an origin to a destination with no intermediate stops. Because people trav- eling for different reasons behave differently, four-step mod- els segment trips by trip purpose. The number and definition of trip purposes in a model depends on the types of informa- tion the model needs to provide for planning analyses, the characteristics of the region being modeled, and the avail- ability of data with which to obtain model parameters and the inputs to the model. Trip purposes are defined by the type of activity tak- ing place at each end of the trip (home, work, school, etc.). Because most trips begin or end at home, many trip purposes are defined as âhome basedâ (e.g., home-based work, which would include trips from home to work and from work to home). Nonhome-based trips are most often not segmented further, but some models further categorize these as work based or nonwork based (âother basedâ). The minimum number of trip purposes in most mod- els is three: home-based work, home-based nonwork, and nonhome based. In this report, these three trip purposes are referred to as the âclassic threeâ purposes. Other commonly used home-based trip purposes are school, shopping, social- recreational, escorting (pickup/dropoff), and university. Models use a âhome-based otherâ trip purpose to represent home-based trips not to or from an activity type defined by one of the other trip purposes. While the convention varies for different model documents, in this report âhome-based nonworkâ is used rather than âhome-based otherâ for mod- els that have only one home-based trip purpose besides work. Throughout this chapter, model parameters and other data are presented for the classic three trip purposes. In some cases, where the data are sufficient, figures for the home- based school purpose are presented separately because of the unique nature of school travel, which is mainly made by children. In these cases, a home-based other trip purpose that represents all home-based nonwork and nonschool trips is included. To clarify, âhome-based otherâ represents all home-based trips except work and school trips, and âhome- based nonworkâ represents all home-based trips except work trips. Depending on whether the analyst is including a separate home-based school purpose, he or she should use the information stratified by trip purpose in one of the fol- lowing ways: â¢ For the classic three purposes (home-based work, home- based nonwork, and nonhome based) or â¢ For the following four purposes: home-based work, home- based school, home-based other, and nonhome based. Throughout Chapter 4, tables of transferable parameters are presented. The longer tables can be found in Appendix C and are referred to in the text of this chapter by table number (e.g., Table C.1). 4.2 The Logit Model This section describes the logit model, the most com- monly used discrete choice analysis method in travel fore- casting. This background is provided for understanding the parameters of logit models described in this chapter, rather than to provide a detailed discussion of logit model estima- tion, validation, and application. The principles and the basic mathematical formulation are presented, and the ways it can be used for choice analysis in travel demand modeling are discussed. For more detailed information about logit mod- els, the reader may wish to consult Ben-Akiva and Lerman (1985) and Koppelman and Bhat (2006). The basic idea underlying modern approaches to travel demand modeling is that travel is the result of choices made by individuals or collective decision-making units such as households. Individuals choose which activities to do during the day and whether to travel to perform them, and, if so, at which locations to perform the activities, when to perform them, which modes to use, and which routes to take. Many of these choice situations are discrete, meaning the individual has to choose from a set of mutually exclusive and collectively exhaustive alternatives.
32 The presentation of discrete choice analysis uses the princi- ple of utility maximization. Briefly, a decision maker is mod- eled as selecting the alternative with the highest utility among those available at the time a choice is made. An operational model consists of parameterized utility functions in terms of observable independent variables and unknown parameters. The utility represents the individualâs value for each option, and its numerical value depends on attributes of the available options and the individual. In practice, it is not unusual for apparently similar individuals (or even the same individual, under different conditions) to make different choices when faced with similar or even identical alternatives. Models in practice are therefore random utility models, which account for unexplained (from the analystâs perspective) variations in utility. The utility function, U, can be written as the sum of the deterministic (known) utility function specified by the ana- lyst, V, and an error term, e. That is: U = V + e. An analyst never knows the true utility function. In effect, the analyst always measures or estimates utility with error, and an error term of unknown size is always present in the analystâs speci- fication of the utility function. This error term accounts for variables that are not included in the data set, or that the ana- lyst chooses to omit from the model (e.g., because he cannot forecast them well), or that are completely unknown to the analyst. When the true utilities of the alternatives are random vari- ables, it is not possible to state with certainty which alterna- tive has the greatest utility or which alternative is chosen. This inability is because utility and choice depend on the random components of the utilities of the available alternatives, and these components cannot be measured. The most an analyst can do is to predict the probability that an alternative has the maximum utility and, therefore, the probability that the alternative is chosen. Accordingly, the analyst must represent travel behavior as being probabilistic. In logit formulations used in most travel demand models, the utility function for each alternative is a linear combina- tion of variables affecting the choice. The utility equations have the form: V xn n nk kk= + âÎ² Î²0 (4-1) where: n = Alternative number; Vn = (Deterministic) utility of alternative n; bn0 = The statistically estimated constant associated with alternative n, essentially the effects of variables that influence the choice that cannot be included in the model due to inability to quantify or forecast, lack of data from the surveys used in model estimation, etc.; bnk = The statistically estimated coefficient indicating the relative importance of variable xk on choice n; and xk = The value of decision variable k. Variables in utility functions may be alternative specific, meaning that the coefficients must be different in each utility function (i.e., the values of bnk cannot be equal for all values of n), or they may be generic, meaning that bnk is the same for each alternative. In a logit model, the utility of one alterna- tive matters only in terms of its value relative to the utilities of other alternatives. Logit is the most widely used mathematical model for making probabilistic predictions of mode choices. The sim- plest function used is the multinomial logit formulation. In the multinomial logit model, the probability of each alterna- tive is expressed as: P V V n n n Alternatives n = ( ) ( )â² â² â exp exp _ (4-2) where: Pn = The probability that alternative n is chosen; exp() = The exponential function; and Vn = (Deterministic) utility of alternative n (from Equa- tion 4-1). Another logit model form that is often used for mode choice is the nested logit model. Under a nested structure, the model pools together alternatives that share similarities, and the choice is represented as a multistep decision. Consider an example with three alternatives, labeled 1A, 1B, and 2, where 1A and 1B are more similar to each other than either is to alternative 2. In the upper level of the nested model, the prob- ability that an individual would choose alternative 1 (one of alternative 1A or alternative 1B) is given by Equation 4-3. P V V V 1 1 1 2 = ( ) ( ) + ( ) exp exp exp (4-3) The probability of choosing alternative 1A conditional on choosing 1 is equal to: P V V V A A A B 1 1 1 1 1 = ( ) ( ) + ( ) exp exp exp (4-4) Thus, the probability of choosing alternative 1A is equal to: P P PA A1 1 1 1= Ã (4-5) In a nested model, the utility of an alternative in an upper level is a function of the utilities of its subalternatives. The utility for a nest m includes a variable that represents the
33 expected maximum utility of all of the alternatives that com- pose the nest. This variable is known as the logsum and is given by the formula: Logsum = ln (4-6nest m M All M in nest m Uexp( ) _ _ _ _ â ) As an example, consider a model with a simple nest with two alternatives. If the utility of each alternative is the same, say 3.00 (indicating the choice probability of each is 50 per- cent), then the logsum is equal to ln [exp(3.00) + exp(3.00)] = 3.69, higher than the utility of either alternative. But if the utilities are, say, 5.00 for one alternative and 0.05 for the other (indicating a choice probability for the first alterna- tive of over 99 percent), the logsum is equal to ln [exp(5.00) + exp(0.05)] = 5.01, only slightly higher than the utility of the superior alternative. Thus, the inclusion of a competitive alter- native in a nest increases the expected maximum utility of all alternatives while the inclusion of a substantially inferior alter- native has little effect on the logsum value. Note that the logsum is equal to the natural logarithm of the denominator of the logit probability function (Equa- tion 4-2) for the alternatives in nest m. A ânesting coefficientâ of the logsum term is used in the utility function for nest m. This coefficient must be between zero and one and should be statistically significantly different from zero and one. The primary advantage of nested logit models over (non- nested) multinomial logit models is that nested logit models enable one to reduce the intensity of the âindependence of irrelevant alternativesâ (IIA) assumption by nesting related choices. The IIA assumption, which is characteristic of all multinomial logit models as well as the lowest level nests in nested logit models, states that the probability of choices does not depend on alternatives that are not relevant. For example, assume in a mode choice model that there are three alternativesâcar, red bus, and blue busâwith equal utilities. Most people would choose between car and any bus, not dis- tinguishing between the bus choices simply due to their color (i.e., they would be perfect substitutes for one another). But, given equal utility for all three of these choices, in a multi- nomial logit model framework the choice probabilities for each of the three choices would calculate as equal (Â¹âÂ³), lead- ing to a greater probability of choosing any bus than the car alternative simply because the choice is being made among three equal alternatives rather than two (i.e., respecting the IIA assumption means one must not construct such choice sets with irrelevant alternatives). 4.3 Vehicle Availability The number of motor vehicles available to a household has a major impact on the travel behavior of the members of the household. As a result, some travel demand models have incorporated components modeling household vehicle availability or automobile ownership. Vehicle availability models estimate the number of vehicles available to house- holds based on characteristics of the households themselves, the areas in which they are located, and the accessibilities of those areas via various transportation modes. These models are most commonly used in larger urban areas and often are not used in small or mid-size regions. While the estimation of vehicle availability is not one of the four âclassicâ steps of tra- ditional travel demand models, the availability of vehicles to households can influence trip generation, trip distribution, and mode choice. The advantage of modeling vehicle availability, rather than simply estimating it from trends or assuming that vehi- cle availability levels remain constant across scenarios and forecast years, is to consider the effects of changes in demo- graphics, such as household size and income, on vehicle own- ership. Furthermore, accessibility by various transportation modes and changes in land use patterns, both of which can be affected by transportation planning policies, have been shown to affect vehicle availability, and these effects can be included in vehicle availability models. To produce credible forecasts of travel demand, it is therefore desirable not only to have accu- rate estimates of the households and employment for traffic analysis zones, but also to have accurate estimates of the num- ber of autos (vehicles) available to these households. 4.3.1 Model Function The function of a vehicle availability model is to estimate the number of households with zero, one, two, etc., vehicles. In the context of a four-step travel demand model, this esti- mate is done through an aggregate process where the shares of households for each vehicle availability level are applied to the total households in each zone. These shares may be obtained from a disaggregately estimated model (i.e., a logit model). The reason to have the households in each zone seg- mented into vehicle availability levels based on the number of vehicles is to allow later steps in the modeling process to use different parameters for market segments based on these levels. These segments may be based solely on the number of vehicles (zero, one, two, etc.) or on variables that incorpo- rate interactions between the number of vehicles and another variable, such as the number of persons or number of work- ers in the household. Examples of these types of interactions include the following: â¢ For trip productions, model parameters representing the number of person trips per household (as discussed in Section 4.4) are applied for combinations of two or three input variables, such as number of persons by number of
34 vehicles. If one of the variables is the number of vehicles, the segmentation of households may be achieved through a vehicle availability model, assuming that the segmenta- tion of the other variable(s) is performed through another means. â¢ For trip distribution and mode choice, models may be applied separately for household market segments defined simply by the number of vehicles (zero, one, two, etc.) or for segments defined by combinations of two or three input variables. Examples include households where the number of vehicles is less than, equal to, or greater than the number of workers. The use of such segmentation requires that the information needed to define the segmentation levels is available from the trip generation model. For example, segmentation comparing the number of vehicles to the number of workers could be used if the trip produc- tion model uses a cross-classification of number of vehicles by number of workers. It is not necessary that the segmentation scheme be the same for every trip purpose. In some models, segmentation might be used only for some trip purposes such as home- based work. Some aggregate models compute the shares for each vehi- cle availability level from curves fitted against observed data and do not base these shares on household, area, or accessi- bility characteristics. On the other hand, a logit vehicle avail- ability model might include such variables, as discussed in Section 4.3.2. 4.3.2 Best Practices There are two commonly used approaches in vehicle availability modeling: aggregate approaches and discrete choice models (Cambridge Systematics, Inc., 1997b). Both approaches estimate the number of households owning zero, one, two, etc., vehicles. Aggregate approaches estimate the percentage of households in each vehicle availability category while discrete choice (i.e., logit) models estimate the probabilities of having zero, one, two, etc., vehicles. These probabilities are used either as aggregate percentages applied to different segments of households or as probabili- ties used in simulation models. The most common num- ber of vehicle availability categories is four (i.e., zero, one, two, or three or more vehicles), although some models have three or five categories. Aggregate approaches estimate the percentages of house- holds for each vehicle ownership category at the zonal level, sometimes for segments of households within zones (such as income levels). In these approaches, curves are fitted to match distributions of households by number of vehicles available. The observed distributions that the curves attempt to match usually come from U.S. Census data. These models do not necessarily use mathematical formulas; rather, points on the curves can be determined, and âsmoothâ curves fitting the points are derived. There are therefore no mathematical parameters to derive or transfer for these types of models. Logit models of vehicle availability have been in use for some time. In these models, a utility function for each vehicle availability level is developed, including variables that affect vehicle availability. Examples of the decision variables in the utility functions include the following: â¢ Household characteristics: â Persons per household; â Workers per household; â Household income; and â Single or multifamily dwelling. â¢ Geographic (zone) characteristics: â Urban area type; â Residential and/or commercial density; and â Pedestrian environment. â¢ Transportation accessibility: â Accessibility via highway; â Accessibility via transit; and â Accessibility via walking/bicycling. Accessibility may be expressed as the amount of activity (for example, trip attractions) within a certain travel time by the corresponding mode or may be a more sophisticated variable that does not depend on a defined travel time cutoff. An example of the latter is provided in Figure 4.1. A multinomial logit formulation is commonly used for vehicle availability models, although ordered response and nested models are sometimes used. Variables in vehicle availability models are alternative specific (see Section 4.2). For simplicity, therefore, the coefficient for one alternative is set to zero for each variable. It is most efficient (and easiest to interpret the results) if this is the same alternative for each variable and for the alternative-specific constant bn0. So, typi- cally, the entire utility for one alternative, most often the zero-vehicle alternative, is set to zero (i.e., all coefficients and constants for this alternative are equal to zero). 4.3.3 Basis for Data Development When sufficient local data are available, best practice for vehicle availability models is to estimate the models from local household activity/travel survey data. Data on vehicle availability are required for model validation and usually are obtained from U.S. Census data for the urban area. Because there are only a few alternatives (three to five) and, usually, several thousand households in the sample, typical
35 urban area household surveys include sufficient data for esti- mation of logit vehicle availability models. It might also be possible to estimate these models using data from the NHTS, although sample sizes for urban areas that are not included in NHTS add-on areas are probably insufficient. Usually, the main issue is whether the survey data set con- tains sufficient samples of zero-vehicle households, which are the smallest category in nearly all U.S. urban areas. According to data from the ACS, the percentage of zero-vehicle house- holds in U.S. metropolitan statistical areas (MSAs) ranges from about 3 to 14 percent, with areas in Puerto Rico having 20 to 24 percent zero-vehicle households and the New York area having about 30 percent (U.S. Census Bureau, 2011a). The percentages of households with zero, one, two, and three or more vehicles from the ACS are presented in Table C.1. Another possible source for vehicle availability model estimation data is the U.S. Census PUMS. This data source, which is now based on the ACS, can provide household-level records that include most household and person character- istics that would be used in vehicle availability models. The main limitation of PUMS data is that geographic resolution is only to the PUMA, an area of approximately 100,000 in population. These areas contain many travel analysis zones and are too large to estimate accessibility, pedestrian envi- ronment, or area-type variables. There are relatively few U.S. urban area models for which vehicle availability model documentation is available, and most of those that have been documented are for larger urban areas. Nor have there been studies of transferabil- ity of vehicle availability model parameters. Ryan and Han Source: This function was recommended by a Travel Model Improvement Program Peer Review Panel and was successfully implemented for the Southern California Association of Governments. Ai = Auto accessibility during the peak hours for zone TSZi. )exp1ln( /2 iij TT j ji TotEmpA where: TotEmpj = Total employment in TSZj; Tij = Peak non-HOV auto travel time from TSZi to TSZj; and JTT j iji /)( where J = Total number of TSZi to TSZj pairs. TRi = Transit accessibility during the peak hours for TSZj. )exp1ln( /2 iij SSij j ji RTotEmpTR where: TotEmpj = Total employment in TSZj. Rij = 1 if TSZi to TSZj has transit access, 0 otherwise. Sij = Peak non-park-and-ride transit total travel time from TSZi to TSZj. KSRS j ijiji /)( where K = Total number of TSZi to TSZj pairs having transit access. Acci = Ratio of auto accessibility during the peak hours to transit accessibility during the peak hours. )1/( iii TRAAcc Figure 4.1. Example accessibility variable.
36 (1999) compared parameters estimated using PUMS data for the same model specification across seven large urban areas in the United States. They concluded that transfer- ability was likely due to similarity in the estimated param- eters but did not test specifically for transferability. Given the lack of information on transferability, it therefore is preferable not to transfer vehicle availability models if local data (i.e., household travel/activity survey) to estimate models are available. However, if an area does not have the necessary local data and wishes to take advantage of the benefits of model- ing vehicle availability, transferring an existing model from another location may be considered. Section 4.3.4 presents parameters from four models as examples that could be con- sidered in urban areas where the survey data to estimate such a model is unavailable. 4.3.4 Model Parameters Tables C.2 through C.4 in Appendix C show parameters for four U.S. urban area vehicle availability models, for the one-vehicle, two-vehicle, and three-or-more-vehicle utilities respectively. The urban areas for which these models were developed are summarized as follows: â¢ Model 1âWestern metro area, 1 to 2 million population range, about 1.9 vehicles per household; â¢ Model 2âSouthern metro area, over 3 million population range, about 1.8 vehicles per household; â¢ Model 3âSouthern metro area, 1 to 2 million population range, about 1.7 vehicles per household; and â¢ Model 4âEastern metro area, 1 to 2 million population range, about 1.5 vehicles per household. In these specifications, the parameters are presented as the zero-vehicle alternative having a total utility of zero. These four models were chosen for the following reasons: â¢ All are multinomial logit models with four alternatives: zero, one, two, and three or more vehicles; â¢ All are associated with four-step models (activity-based models usually have household and person variables not usually available in four-step models); â¢ All were estimated since 2000 using household activity/ travel survey data; and â¢ The variable specifications are somewhat similar. Some important points to note regarding the variable defi- nitions in these tables: â¢ The variables representing the number of persons, num- ber of workers, and income levels are indicator variables, taking a value of one if the household has the indicated characteristic and zero otherwise. For example, when the model is applied to two-person, one-worker, high-income households, the values of the two-person, one-worker, and high-income variables would be equal to one, and the values of the other person, worker, and income indicator variables would be zero. â¢ The income groups are intended to represent quartiles, but the income-level definitions are different for every model. Because they were estimated in various places at different times, they are not directly comparable. â¢ The accessibility ratio for Model 2 is the same as the one shown in Figure 4.1. The columns in Tables C.2 through C.4 correspond to the parameters bnk in the utility functions (see Equation 4-1) of the four models (bn0 represents the alternative-specific con- stants). So, for example, in Model 2, the utility function for the one-vehicle alternative is: U = 1.58 1.84 Low-medium income 2.54 Hig 1 + + h-medium income 0.72 High income 0.06 Ac + + cessibility ratio A low-mediumâincome household in a zone with an acces- sibility ratio of 2.0 would therefore have a utility of owning one vehicle of 1.58 + 1.84 + 0.06 (2.0) = 3.54. If the house- hold has three persons, the probabilities of the alternatives for two and three or more vehicles can be computed, using Equation 4-1, as: U U 2 3 1 90 2 78 3 02 0 089 2 0 4 08 12 3 = â + + + = = â . . . . ( . ) . . 8 3 04 4 14 0 12 2 0 4 96+ + + = â. . . ( . ) . The probabilities of owning zero, one, two, etc., vehicles are computed using Equation 4-2: P exp(0) exp 3.54 exp 4.08 exp 4.90 = ( ) + ( ) + ( ) + âexp 0 6 1.06 percent P1 ( )[ ] = = ( ) ( ) +exp . exp exp3 54 0 3. exp . exp . . 54 4 08 4 96 36 43 ( ) + ( )[ + â( )] = percent P2 = ( ) ( ) + ( ) + ( )[ + exp . exp exp . exp . ex 4 08 0 3 54 4 08 p . . exp . exp â( )] = = â( ) ( ) 4 96 62 51 4 96 0 percent P3 + ( ) + ( )[ + â( )] = exp . exp . exp . . 3 54 4 08 4 96 0 01 percent
37 In model application, these probabilities would be com- puted and applied separately to segments of households of each type as defined by the variables (number of persons, income level, etc.), and the probabilities for each segment applied to the households in each segment. Because no two of the models presented in Tables C.2 through C.4 have identical specifications, the values for spe- cific coefficients may differ significantly between models. The presence or absence of other variables in a model can affect the coefficients of other variables. So it is much more valid to transfer individual models rather than composites of models with different variables. As discussed previously, there is little experience with which to guide planners in transferring vehicle availability models, or even to determine how transferable the param- eters of such models are. The best guidance that can be pro- vided if one wished to transfer one of the models shown in Tables C.2 through C.4 is to choose one of the models based on the similarity to the metro areas based on the charac- teristics provided above (location within the United States, population, and average vehicles per household). Because of the differences in model specification, a composite of two or more of these models cannot be created. If the chosen model proves difficult to calibrate, perhaps another model could be chosen for transfer. 4.4 Trip Generation Trip generation is commonly considered as the first step in the four-step modeling process. It is intended to address the question of how many trips of each type begin or end in each location. It is standard practice to aggregate trips to a specific unit of geography (e.g., a traffic analysis zone).5 The estimated numbers of trips will be in the unit of travel that is used by the model, which is usually one of the following: â¢ Vehicle trips; â¢ Person trips by motorized modes (auto and transit); or â¢ Person trips by all modes, including both motorized and nonmotorized (walking, bicycling) modes. Trip generation models require explanatory variables that are related to trip-making behavior and functions that estimate the number of trips based on these explanatory variables. While these functions can be nonlinear, they are usually assumed to be linear equations, and the coefficients associated with these variables are commonly called trip rates. Whether the function is linear or nonlinear, it should always estimate zero trips when the values of the explanatory variables are all zero. Mathematically, this is equivalent to saying that the trip generation equations should include no constant terms. 4.4.1 Model Function The purpose of trip generation is to estimate the num- ber of average weekday trip ends by purpose for each zone. In four-step models, the trip ends of home-based trips are defined as productions, representing the home ends of trips, and attractions, representing the nonhome end, regardless of whether home is the origin or destination. In other words, for home-based trips, the production end may be the destination and the attraction end, the origin if the trip-maker is return- ing home. For nonhome-based trips, for convenience the production end is defined as the trip origin and the attraction end as the trip destination. For home-based trips, the number of trip productions in a zone is, naturally, based on the number of households in the zone. Household characteristics can affect trip making; there- fore, in trip production models, households are usually clas- sified by some of these characteristics, which often include the number of persons, workers, children, or vehicles, or the household income level. The trip rates for each purpose vary depending on the household classifications, which may not be the same for all trip purposes. Trip attractions are based on other variables besides households, because several types of activities (commercial, employment, residential, etc.) are often located at the non- home trip end. The type of activity that affects the number of trip attractions depends on the trip purpose. For example, home-based work trip attractions are usually estimated best by using employment as the explanatory variable. Other purposes typically use different sets of variables (school enrollment or employment for home-based school trips, retail employment for home-based shopping trips, etc.). Home-based nonwork, home-based other, and nonhome- based trip attraction models usually use a linear combina- tion of several different variables (employment by type, households, etc.). The number of nonhome-based trips made in a region does depend on the number of households, but unlike home-based trips, they need not have one end in the zone where the household of the trip-maker is located. One way in which models deal with this issue is to use household-based nonhome-based trip production rates to estimate regional productions and to allocate this regional total to zones based on other variables. A common convention is to assume that the regional nonhome-based trips are allocated to each zone based on the number of nonhome-based trip attractions in the zone. 5While the geographic units of some travel models are not zones, the term âzonesâ is used in the remainder of the chapter for convenience.
38 Special Generators While estimates of passenger trip activity based on rates applied to household or employment in a zone can address the majority of conditions, there are special conditions when these rates are insufficient to accurately estimate trip activity. These conditions might be because the trip activity is due to considerations not directly related to the number of employees or households in a zoneâfor example, trips to airports, hospitals, colleges, or large recreational facilities. Addi- tional estimates of trip activity may also be necessary because the trip generation rates are for average conditions that are not applicable to specialized conditionsâfor example, shop- ping productions or attractions to âbig boxâ retail stores that have shopping trip rates per employee that are higher than typical retail employment. These activity locations are often referred to as âspecial generators.â The term âspecial generatorsâ is somewhat misleading in that the different travel behavior associated with them is not limited to trip generation. While it is true that the number of trips generated by these sites is not readily modeled using conventional trip attraction models, the sensitivity of trip dis- tribution (see Section 4.5) and mode choice (see Section 4.7) to variables such as time and cost is also different than that of other trips. Ideally, such travel should be treated as a separate trip purpose so that separate models for trip generation, trip distribution, and mode choice could be applied, but unless there are detailed surveys of the special generator with a suf- ficient sample size for model estimation, it is unlikely that this could be done. Trip rates are not developed for special generators. Rather, the numbers of trips attracted to these locations are exoge- nously estimated using separate data sources, such as surveys or counts conducted at the special generators. Hence there are no parameters for trip generation at special generators, and default parameters cannot be provided. It is important to consider how special generator travel is considered relative to the trip purposes used in the model. Generally, trips attracted to special generators are estimated separately from the attrac- tions for the trip purposes used in the model, but the special generator attractions must be considered in examining the balance between productions and attractions. Since separate trip distribution, time-of-day, and mode choice models are not available for special generator travel, the analyst must decide how these features will be modeled for special genera- tors (for example, using the models for home-based nonwork or nonhome-based travel). Balancing Productions and Attractions The regional totals of productions and attractions for each trip purpose are equal because each trip has one production end and one attraction end. However, the model results may not be equal because productions and attractions are esti- mated separately. While trip distribution models (see Sec- tion 4.5) can often be applied with different production and attraction totals, certain types of model formulations (such as the gravity model) produce better results if productions and attractions are equal, or close to equal. Because trip productions are estimated for the household, which is the same as the basis of the sampling frame of the surveys from which trip generation models are estimated, trip production models are generally estimated using records representing individual households, for which the total num- ber of trips should be reported in the household survey. Trip attractions, on the other hand, occur at locations for which a complete set of survey records comprising all trips to the attractor will not be available. It is therefore common con- vention to adjust trip attractions to match productions by purpose at the regional level. This âbalancingâ of productions and attractions must take into account trips with one end outside the region (see Section 4.6 on external travel) and trips attracted to special generators. It is good practice to review the ratio between unbalanced attractions and productions as a large difference might indi- cate problems with employment estimates, trip rates, etc. Most literature on best practices recommends that the differ- ence between unbalanced regional attractions and produc- tions be kept to +/-10 percent for each purpose, although a review of model validation reports shows that this standard is often exceeded. Upwards of +/-50 percent difference at the regional level might be considered acceptable under certain conditions and trip purposes. 4.4.2 Best Practices Trip Productions While other model forms are sometimes used, the most common form of trip production model is the cross-classifi- cation model. The households in each zone are classified by two or more variables, and the number of households in each category is multiplied by the appropriate âtrip rate,â repre- senting the average number of trips per household for the category. Mathematically, the number of trips generated in a zone is given by: P P rate hi p pk ik k = â ( )4 7- where: Ppi = Number of trip ends produced for purpose p in zone i; Pratepk = The production trip rate for purpose p per house- hold for category k; and hik = The number of households in category k in zone i.
39 The state of the practice for trip production models is to create tables of trip rates by two or more dimensions, for example by household income and by household size (num- ber of persons). Most commonly, trip production models are two-dimensional, although three-dimensional models are sometimes used, especially in larger areas where more data are available. The households in each zone are segmented along the two dimensions, and the trip rate is estimated for each combi- nation of the two variables. For example, a cross-classification of households by three income levels (say, low, medium, and high) and number of persons (1, 2, 3, and 4+) would have the number of households divided into 12 segments, one for each income levelânumber of persons combination, and would use 12 corresponding trip production rates. Trip Attractions Accurately estimating trip attractions can be significantly more difficult and problematic than estimating trip produc- tions. Whether trip attraction model parameters are estimated from local data or are transferred, they are usually derived from household survey data, which collects travel information at the production end of trips. Such surveys do not provide control totals at trip attraction locations. It is common practice to estimate the parameters, such as coefficients in linear regres- sion equations, at an aggregate level such as districts (groups of zones), implying that the results may not be as accurate at more disaggregate spatial levels (such as zones). Some regions have attempted to address this issue through the use of estab- lishment surveys, where the data are collected at the attraction end of trips, but the wide variety of establishment types and the expense of obtaining sufficient sample sizes at each type means that accuracy issues are not completely resolved. It is therefore recommended that analysts use the information provided here (indeed, locally derived trip attraction information as well) with extreme caution and to be prepared to adjust parameters to produce more reasonable results as needed. Trip attraction models are most often linear equations with variables representing the amount of activity in a zoneâ typically employment by type, student enrollment at school sites, and households or populationâand coefficients reflect- ing the effects of these variables on trip making to the zone for the appropriate purpose. The equations follow the form: A A rate vi p pk ik k = â ( )4 8- where: Api = Attraction of trip ends for purpose p in zone i; Aratepk = Rate of attraction trip ends for purpose p per unit of variable k; and vik = Value of variable k in zone i. To summarize, the model parameters for trip generation are the trip production and attraction rates, represented by Pratepk in Equation 4-7 and Aratepk in Equation 4-8. 4.4.3 Basis for Data Development When sufficient local data are available, best practice for the development of trip generation models is to estimate the model parameters from household activity/travel survey data using statistical techniques such as linear regression. Typi- cally, sample sizes for these surveys are sufficient for model estimation, although the required amount of data depends on factors such as: â¢ The number of parameters to be estimated, such as the number of cells in cross-classification models; â¢ The number of households occurring in each cross- classification cell in the population, and in the survey sample; and â¢ The resolution of the geographic units (e.g., zones) at which the models will be applied. If local data for model estimation are not available, param- eters may be transferred from another model. Transferable parameters for general use are presented in Section 4.4.4. Trip Productions For trip productions, cross-classification trip rates were estimated from the 2009 NHTS for the classic three trip pur- poses, for urban areas stratified by population. Additionally, trip rates for home-based school trips are presented, along with a home-based other trip purpose that represents all home-based nonwork and nonschool trips. These rates rep- resent average weekday person trips, including both motor- ized and nonmotorized trips, and were estimated using the weighted NHTS data. Initially, separate rates were estimated for the six urban area population ranges, but, in many cases, the rates did not vary by population category, and combined rates for multiple population ranges are presented. Note that the 2009 NHTS does not include travel for children younger than five years old. If an analyst wishes to model the travel of younger children and to use the informa- tion provided in this chapter, he/she should be prepared to slightly adjust the trip rates for all purposes except home- based work upward, with a more substantial increase in home-based school trips (if that purpose is modeled and includes pre-school/day care travel). Trip Attractions Documented trip attraction models from a number of MPOs were available in the MPO Documentation Database.
40 One conclusion from the review is that there is little com- monality among MPOs regarding the variables to include in trip attraction models. The variables ranged from employ- ment stratified by three basic groups to employment strati- fied by seven or eight groups. In a number of trip attraction models, school enrollment was included. The number of trip purposes and the variables used for each trip purpose also varied substantially. Different model calibration methods also added to the vari- ation among models. Some of the models were estimated using regression techniques that could produce somewhat surprising results. For example, regression model calibration techniques can result in negative coefficients for some of the variables. A home-based shop trip attraction model could have, say, a posi- tive coefficient for retail employment and a negative coefficient for basic employment. Such occurrences might be explained as âsecond-levelâ relationshipsâeach retail employee attracts a certain number of home-based shop trips during the day, but as the amount of basic employment increases around the retail location, the number of home-based shop trips decreases due to unattractiveness of, say, an industrial area. However, some illogical regression results were also observed in the review. An example is a home-based work model using multiple employment categories as independent variables with some of the coefficients being positive and some nega- tive. Since each employee should attract a reasonable average number of home-based work trips each day, a negative model coefficient for an employment category is not logical. 4.4.4 Model Parameters Trip Productions The household trip production rates classified by variables representing household characteristics were estimated from the 2009 NHTS data. These rates represent the number of person trips, including both motorized and nonmotorized trips, per household. To determine the best variables to use for the rates provided here, trip rates were summarized for the following variables: â¢ Number of persons, â¢ Number of workers, â¢ Income level, and â¢ Number of vehicles. The number of persons categories ranged from 1 to 5+. The number of workers categories ranged from 0 to 3+. The num- ber of vehicles categories ranged from 0 to 3+. The household income levels (in 2008 dollars) were defined as: â¢ $0 to $9,999; â¢ $10,000 to $24,999; â¢ $25,000 to $49,999; â¢ $50,000 to $100,000; and â¢ Over $100,000. To determine which variables best explained trip gen- eration behavior in the NHTS data, an analysis of variance (ANOVA) was performed to explore the explanatory power of the variables. This parametric statistical technique pro- vides a basis to identify the most statistically significant cross- classification of explanatory variables for each trip purpose and thereby select dimensions across which the trip produc- tion rates were categorized. The ANOVA results indicate that all of the independent variables have significant effects on home-based work trip production rates. However, among all interaction effects, the household vehicles versus household workers variable appears to be the strongest predictor of the home-based work trip production rate. For home-based nonwork and home-based other trips, household workers versus house- hold persons appears to be the strongest predictor of the trip production rate. For the nonhome-based trip purpose, the ANOVA results suggest that household workers by house- hold persons is again found to be the strongest predictor of the trip production rate. The MPO Documentation Database indicated that two other cross-classifications are commonly used: number of persons by income level and number of persons by number of vehicles. Parameters for these cross-classifications, also estimated from the NHTS data set, are presented for all trip purposes. For home-based school trips, trip rates were estimated for the cross-classification of number of persons by number of children. Since some modeling agencies do not forecast the number of children, trip rates were also estimated for num- ber of persons by income level and number of persons by number of vehicles. Tables C.5 through C.9 in Appendix C show the trip rates by purpose cross-classified by the preferred pairs of variables, based on 2009 NHTS data, for home-based work, home- based nonwork, nonhome-based, home-based school, and home-based other trips, respectively. The NHTS data showed nearly the same trip rates for all population ranges for most trip purposes, apparently due at least in part to the relatively low sample sizes and resulting large errors associated with some of the cells. For home-based nonwork and home- based other trips, the NHTS data indicated lower trip rates for urban areas under 500,000 in population and nonurban areas, and so separate rates are presented for such areas for these trip purposes. Use of a cross-classification trip production model requires that the households in each zone are classified along the same dimensions as the model. For example, if the first model in
41 Table C.5 is used, the households in each zone must be cross- classified by number of workers (0, 1, 2, and 3+) and number of autos (0, 1, 2, and 3+). If the demographic estimates avail- able to the modeler are not already classified in the required manner, there are procedures that may be used to estimate the percentages in each cell and to apply them to the total households. Common sources for these percentages include the CTPP, NHTS, and local survey data. Depending on sam- ple sizes, however, these sources may not provide statistically significant percentages at the zone level, and it may be nec- essary to estimate percentages for groups of zones based on area type and location within the region. Example Calculations Consider a zone with 1,000 households located in an urban area of under 500,000 in population where a trip production model with the classic three trip purposes is being developed. The MPO has estimated the number of households in the zone cross-classified by number of persons and number of vehicles, as depicted in Table 4.2. For home-based work trips, the number of households in each cell is multiplied by the trip rate from the second section of Table C.5, yielding the number of home-based work trips in each cell of the cross-classification in Table 4.3. So this zone produces 1,839 home-based work trips. Simi- larly, home-based nonwork and nonhome-based trip produc- tions can be computed using the fourth section of Table C.6 and the second section of Table C.7, performing the same type of calculations. Reasonableness checks of the trips per household by pur- pose estimated from trip production model results can be performed. Information on the national sample represented by the NHTS, as represented by Tables C.5 through C.7, indi- cate that the average household in urban areas of greater than 500,000 in population makes 10.0 person trips: 1.4 home- based work trips, 5.6 home-based nonwork trips, and 3.0 nonhome-based trips. The average household in urban areas of less than 500,000 in population makes 9.5 person trips: 1.4 home-based work trips, 5.1 home-based nonwork trips, and 3.0 nonhome-based trips. The range of person trips per household in the MPO Documentation Database is about 1.3 to 2.0 home-based work trips, 2.6 to 5.9 home-based non- work trips, and 1.6 to 4.5 nonhome-based trips. Total person trips per household range from 7.0 to 11.5. Trip Attractions Table 4.4 summarizes average daily trip attraction rates for the classic three trip purposes from the analyses of the models in the MPO Documentation Database. These rates were all estimated from local or statewide household travel surveys. While all of these models used person trips as the unit of travel, some used person trips in motorized modes while others used total person trips, including those by walk- ing and bicycling. While Table 4.4 shows average rates for commonly defined models, achieving commonality required substantial process- ing. Although trip attraction models are defined for the clas- sic three trip purposes, development of rates for home-based nonwork and nonhome-based trips often required aggrega- tion of more purpose-specific submodels. For example, if a region used both home-based shop and home-based other (representing nonwork and nonshopping travel) trip attrac- tion models, the trip rates per retail employee were added in the composite home-based other trip attraction model. If Persons Autos 1 2 3 4 5+ Total 0 10 10 10 0 0 30 1 50 100 70 20 10 250 2 0 150 200 100 50 500 3+ 0 0 40 80 100 220 Total 60 260 320 200 160 1,000 Table 4.2. Example number of households by numbers of persons and autos. Persons Autos 1 2 3 4 5+ Total 0 2 7 11 0 0 20 1 30 80 84 34 15 243 2 0 195 400 200 115 910 3+ 0 0 104 232 330 666 Total 32 282 599 466 460 1,839 Table 4.3. Example number of home-based work trips.
42 a region stratified trip attraction rates by area type, aver- ages of the trip rates were estimated. If data were available for the various strata that had to be combined, weighted averages were estimated; where data were not available for weighted averages, simple averages were used. Finally, composite trip rates were estimated for three main employ- ment groups: basic employment, retail employment, and service employment. Since the presence or absence of other variables in a model can affect the coefficient for a specific model variable, Table 4.4 shows sets of trip rates for trip attraction models with com- mon independent variables. Rates are provided for all per- son trips and motorized person trips only. Note that there are some combinations of variables that none of the models in the database used for motorized person trip attraction models. To use the information in Table 4.4 to obtain param- eters for trip attraction models, the analyst should choose a model that is consistent with the unit of travel (motorized or nonmotorized trips) and variables that are available for use in model application. The number of attractions can then be computed for each zone. For example, for a zone with 20 households, no school enrollment, 200 basic employees, 10 retail employees, and 100 service employees, the home- based nonwork trip attractions computed from Model 3 are: 0.7 î° 20 + 0.7 î° 200 + 8.4 î° 10 + 3.5 î° 100 = 588. Table 4.4 shows substantial variation in the trip attrac- tion rates for the various model forms. The variation may reflect the different sizes of urban areas, different travel characteristics, and different development densities or area types, as well as the impact of variables included or excluded from the different model forms. It should be noted that no trends in trip attraction models by urban area population were evident; although the number of models examined is small, this is consistent with previous documentation efforts such as NCHRP Report 365 (Martin and McGuckin, 1998). The trip attraction rates shown in Table 4.4 may provide reasonable starting points for models for areas lacking the locally collected data necessary to develop trip attraction models. The selection of the specific model forms to be used could be made based on the types of independent data avail- able for model application. The results of such initial model specifications should be reviewed to ensure that they reflect Number of MPO Models Summarized Householdsa School Enrollmentb Employment Basicc Retaild Servicee Total All Person Trips Home-Based Work Model 1 16 1.2 Home-Based Nonwork Model 1 2 1.2 1.4 0.2 8.1 1.5 Model 2 8 2.4 1.1 7.7 0.7 Model 3 2 0.7 0.7 8.4 3.5 Nonhome Based Model 1 5 0.6 0.5 4.7 1.4 Model 2 8 1.4 6.9 0.9 Motorized Person Trips Home-Based Work Model 1 8 1.2 Home-Based Nonwork Model 1 1 0.4 1.1 0.6 4.4 2.5 Model 3 4 1.0 0.3 5.9 2.3 Nonhome Based Model 1 6 0.6 0.7 2.6 1.0 a The number of households in a zone. b The number of elementary, high school, or college/university students in a zone. c Employment primarily in two-digit North American Industry Classification System (NAICS) codes 1â42 and 48â51 [Standard Industrial Classification (SIC) codes 1â51]. d Employment primarily in two-digit NAICS codes 44â45 (SIC codes 52â59). e Employment primarily in two-digit NAICS codes 52â92 (SIC codes 60â97). Source: MPO Documentation Database. Table 4.4. Trip attraction rates from selected MPOs (person trips per unit).
43 known travel conditions and behave reasonably for a region. Three examples are provided in the following paragraphs. These examples all use the models for âall person tripsâ in the upper portion of Table 4.4. Example 1. Suppose the trip attraction rates from home- based work model 1, home-based nonwork model 3, and nonhome-based model 1 are applied for a region. In a review of traffic assignment results, it is discovered that too many trips are crossing the cordon boundary around the CBD. In such a case, it might be reasonable to reduce the home-based nonwork and nonhome-based trip attraction rates for retail and service employment in the CBD and to balance those reductions in the CBD trip rates with increases of the values for the rates for non-CBD zones. However, before making such adjustments, other checks should be performed, includ- ing the accuracy of CBD socioeconomic data, mode shares to the CBD, and comparison of CBD through traffic to observed origin-destination data. Example 2. Suppose a region has forecasts for only households, retail employment, and nonretail employ- ment available. None of the three home-based nonwork model forms match the independent variables available for the region. In this case, it might be reasonable to test both home-based nonwork models 2 and 3, ignoring the coeffi- cients for the missing variables. Careful attention should be paid to traffic assignment results around industrial areas and educational facilities. The âbest performingâ model in terms of reproducing traffic volumes would be selected. If neither model performed well, it might be appropriate to mix the rates to address the issues. Example 3. Again, suppose a region has employment stratified only by retail and nonretail at the zone level. If regional totals for basic and service employment can be determined, nonretail attraction rates for the home-based nonwork and nonhome-based trip purposes can be esti- mated by applying home-based nonwork model 1 (or model 3) at the regional level and estimating a weighted average trip rate for nonretail employment. The same procedure could be applied using rates from nonhome-based model 1 to develop a weighted average nonretail employment trip rate. If the regional totals for basic and service employment are not available, the straight averages of the rates for basic and service employment could be used. For example, if using model 3 for home-based nonwork attractions for motor- ized trips, one could use the average of the basic and service employment coefficients (1.3) as the coefficient for nonretail employment. It is difficult to perform reasonableness checks of trip attraction model results for most trip purposes because the models are multivariate. The coefficients of a model that has the same variables could be compared to those in one of the models in Table 4.4, but having the same or different coef- ficients as one other model would not provide confirmation of the reasonableness or unreasonableness of the model. For home-based work trips, the vast majority of attraction models in the MPO Documentation Database have coef- ficients for total employment in the range of 1.0 to 1.5, and so coefficients in this range may be considered reasonable. 4.5 Trip Distribution Trip distribution is the second step in the four-step mod- eling process. It is intended to address the question of how many of the trips generated in the trip generation step travel between units of geography, e.g., traffic analysis zones. These trips are in the same units used by the trip generation step (e.g., vehicle trips, person trips in motorized modes, or per- son trips by all modes including both motorized and non- motorized modes). Trip distribution requires explanatory variables that are related to the impedance6 (generally a func- tion of travel time and/or cost) of travel between zones, as well as the amount of trip-making activity in both the origin zone and the destination zone. The inputs to trip distribution models include the trip generation outputsâthe productions and attractions by trip purpose for each zoneâand measures of travel imped- ance between each pair of zones, obtained from the trans- portation networks. Socioeconomic and area characteristics are sometimes also used as inputs. The outputs are trip tables, production zone to attraction zone, for each trip purpose. Because trips of different purposes have different levels of sensitivity to travel time and cost, trip distribution is applied separately for each trip purpose, with different model parameters. 4.5.1 Model Function The gravity model is the most common type of trip distri- bution model used in four-step models. In Equation 4-9, the denominator is a summation that is needed to normalize the gravity distribution to one destination relative to all possible destinations. This is called a âdoubly constrainedâ model because it requires that the output trip table be balanced to attractions, while the numerator already ensures that it is bal- anced to productions. 6The term âimpedanceâ is used in this report to represent the general- ized cost of travel between two zones. In most cases, the primary com- ponent of generalized cost is travel time, and so impedance is often expressed in time units such as minutes.
44 Gravity Model T P A f t K A f t K ij p i p j p ij ij j p ij ij j = ( ) ( ) â² â² â² â²â Zones â ( )4 9- where: Tpij = Trips produced in zone i and attracted to zone j; Pi p = Production of trip ends for purpose p in zone i; Aj p = Attraction of trip ends for purpose p in zone j; f(tij) = Friction factor, a function of the travel impedance between zone i and zone j, often a specific function of impedance variables (represented compositely as tij) obtained from the model networks; and Kij = Optional adjustment factor, or âK-factor,â used to account for the effects of variables other than travel impedance on trip distribution. Destination Choice Trip distribution can be treated as a multinomial logit choice model (see Section 4.2) of the attraction location. In such a formulation, the alternatives are the attraction zones, and the choice probabilities are applied to the trip produc- tions for each zone. The utility functions include variables related to travel impedance and the number of attractions (the âsize variableâ), but other variables might include demo- graphic or area-type characteristics. A logit destination choice model is singly constrained since the number of attractions is only an input variable, not a con- straint or target. Sometimes such a model is artificially con- strained at the attraction end using zone-specific constants or post processing of model results. Development of Travel Impedance Inputs Zone-to-zone (interzonal) travel impedance. One of the major inputs to trip distribution is the zone-to-zone travel impedance matrices. The first decision is on the components of the travel impedance variable. The simplest impedance vari- able is the highway (in-vehicle) travel time, which is often an adequate measure in areas without a significant level of mon- etary auto operating cost beyond typical per-mile costsâfor example, relatively high parking costs or toll roadsâor exten- sive transit service. In some areas, however, other components of travel impedance should be considered. These may include distance, parking costs, tolls, and measures of the transit level of service. These measures, and the relative weights of each component, are often computed as part of utility functions in mode choice (Section 4.7). The individual components of travel impedance are com- puted as zone-to-zone matrices through âskimmingâ the highway and transit networks using travel modeling software. The components may be combined through a simple weight- ing procedure, which might be appropriate if all components are highway related, or through the use of a logsum variable, which can combine highway- and transit-related variables. In this case, the logsum represents the expected maximum utility of a set of mode choice alternatives and is computed as the denominator of the logit mode choice probability func- tion. The logit mode choice model is discussed in Section 4.7. Terminal times and costs. The highway assignment process (discussed in Section 4.11) does not require that times be coded on the centroid connectors since those links are hypothetical constructs representing the travel time between the trip origin/destination and the model networks, includ- ing walking time. However when the skim times from a net- work assignment are used in trip distribution, the travel time representing travel within zones, including the terminal time, which may include the time required to park a vehicle and walk to the final destination, must be included. If the distri- bution model includes consideration of impedance based on travel times, this same consideration should also be made for the centroid-based terminal considerations. Intrazonal impedance. Network models do not assign trips that are made within a zone (i.e., intrazonal trips). For that reason, when a network is skimmed, intrazonal times are not computed and must be added separately to this skim matrix. There are a number of techniques for estimating intrazonal times. Some of these methods use the average of the skim times to the nearest neighboring zones and define the intra- zonal time as one-half of this average. Various mechanisms are used to determine which zones should be used in this cal- culation, including using a fixed number of closest zones or using all zones whose centroids are within a certain distance of the zoneâs centroid. Other methods compute intrazonal distance based on a function of the zoneâs area, for example, proportional to the square root of the area. Intrazonal time is computed by applying an average speed to this distance. Friction factors. There are two basic methods for devel- oping and calibrating friction factors for each trip purpose: â¢ A mathematical formula and â¢ Fitted curves/lookup tables. Three common forms of mathematical formulas are shown below, where Fpij represents the friction factor and tij the travel impedance between zones i and j: â¢ Power function, given by the formula Fpij = t a ij. A common value for the exponent a is 2.
45 â¢ Exponential, given by the formula Fpij = exp(-m î° tij). An advantage of this formula is that the parameter m repre- sents the mean travel time. â¢ Gamma function, given by the formula: F a t c tij p ij b ij= ( ) exp ( )4 10- The parameters a, b, and c are gamma function scaling factors. The value of b should always be negative. The value of c should also generally be negative (if a positive value of c is used, the function should be carefully inspected across the full expected range of input impedance values to ensure that the resulting friction factors are monotonically decreasing). The parameter a is a scaling factor that does not change the shape of the function. Section 4.5.4 presents some typical values for the parameters b and c. These factors may be adjusted during model calibra- tion to better fit the observed trip length frequency distribution data (usually from household travel surveys). This adjustment is commonly done on a trial-and-error basis. Some modeling software packages allow the input of a lookup table of friction factors for each trip purpose, with some providing the capability of fitting these factors to best fit observed trip length frequency distributions. 4.5.2 Best Practices While best practice for trip distribution models would be considered to be a logit destination choice model, the grav- ity model is far more commonly used, primarily because the gravity model is far easier to estimate, with only one or two parameters in the friction factor formulas to calibrate (or none, in the case of factors fitted directly to observed trip length frequency distributions), and because of the ease of application and calibration using travel modeling software. There is no consensus on whether it is better to always have a singly constrained or doubly constrained trip distribution model. For home-based work trips, some type of attraction end constraint or target seems desirable so that the number of work trip attractions is consistent with the number of peo- ple working in each zone. For discretionary travel, however, the number of trip attractions can vary significantly between two zones with similar amounts of activity, as measured by the trip attraction model variables. For example, two shop- ping centers with a similar number of retail employees could attract different numbers of trips, due to differences in acces- sibility, types of stores, etc. A doubly constrained model would have the same number of shopping attractions for both shopping centers, and a doubly constrained trip distri- bution model would attempt to match this number for both centers. So it might be reasonable to consider singly con- strained models for discretionary (nonwork, nonschool) trip purposes, although implied zonal attraction totals from such distribution models should be checked for reasonableness. Besides segmentation by trip purpose, it is considered best practice to consider further segmentation of trip distribution using household characteristics such as vehicle availability or income level, at least for home-based work trips. This additional segmentation provides a better opportunity for the model to match observed travel patterns, especially for work trips. For example, if the home-based work trip distri- bution model is segmented by income level, work trips made by households of a particular income level can be distributed to destinations with jobs corresponding to that income level. However, it may be difficult to segment attractions by income or vehicle availability level since the employment variables used in trip attraction models are not usually seg- mented by traveler household characteristics. Often, regional percentages of trips by income level, estimated from the trip production models, are used to segment attractions for every zone, especially for nonwork travel, but this method clearly is inaccurate where there are areas of lower and higher income residents within the region. Methods to estimate household incomes by employee at the work zone have begun to be used but are not yet in wide- spread practice. Kurth (2011) describes a procedure used in the Detroit metropolitan area. This procedure consists of estimating the (regional) proportions of workers by worker earnings level based on industry, calculating the shares of workers by worker earnings group for each industry by area type, and calculating the shares of workers by household income for each worker earnings group by area type. The model is applied using the workers by industry group for each zone. Some advantages to segmentation by vehicles rather than income level include: â¢ Often, a better statistical fit of the cross-classification trip production models; â¢ Avoidance of the difficulty in accurate reporting and fore- casting of income; â¢ Avoidance of the need to adjust income for inflation over time and the difficulty of doing so for forecasting; â¢ Avoidance of the need to arbitrarily define the cutoffs for income levels because income is essentially a continuous variable; and â¢ Likelihood that vehicle availability has a greater effect on mode choice, and possibly trip distribution as well. That being said, there are also advantages to using income level for segmentation, which is a more common approach in U.S. travel models. Perhaps the main advantage is that the trip attractions can be more easily segmented by income level. For example, home-based work trip attractions at the zone level are usually proportional to employment, and employ- ment is easier to segment by income level than by number
46 of autos. Some employment data sources provide informa- tion on income levels for jobs; no such information exists for vehicle availability levels. [However, it should be noted that income for a specific work attraction (job) is not the same as household income, which includes the incomes of other workers in the household.] No one method for developing friction factors is consid- ered âbest practice.â Some analysts find the gamma function easier to calibrate, because it has two parameters to calibrate compared to a single parameter for power and exponential functions. Since the exponential functionâs parameter is the mean travel time, this value can be easily obtained from observed travel data (where available), but matching the mean observed travel time does not necessarily mean that the entire trip length frequency distribution is accurate. It is important to understand that matching average observed trip lengths or even complete trip length frequency distributions is insufficient to deem a trip distribution model validated. The modeled orientation of trips must be correct, not just the trip lengths. The ability to calibrate the origin- destination patterns using friction factors is limited, and other methods, including socioeconomic segmentation and K-factors, often must be considered. 4.5.3 Basis for Data Development The best practice for the development of trip distribution models is to calibrate the friction factors and travel patterns using data from a local household activity/travel survey. If such a survey is available, it is straightforward to determine observed average trip lengths and trip length frequency dis- tributions for each trip purpose and market segment. Cali- brating friction factors to match these values is an iterative process that is usually quick and may be automated within the modeling software.7 Household survey data can also be used as the basis for estimating observed travel patterns for use in validation, although sample sizes are usually sufficient to do this only at a more aggregate level than travel analysis zones. The question is what to do if there is insufficient local survey data to develop the estimates of the observed values. Data sources such as the NHTS have insufficient sample sizes for individual urban areas to develop trip length frequency estimates for each trip purpose (although if an urban area is located in an NHTS add-on area, the sample size might be sufficient). Trip length distributions can vary significantly depending on the geography of a model region and its extent, which can often depend on factors such as political bound- aries, the size of the region, physical features such as bodies of water and mountain ranges, and the relative locations of nearby urban areas. Therefore, simply using friction factors from another model may result in inaccurate trip distribu- tion patterns. The best guidance in this situation is to start with param- eters from another modeling context and to calibrate the model as well as possible using any local data that are avail- able, including data on work travel from the ACS/CTPP, traffic counts, and any limited survey data that might be available. Section 4.5.4 (Model Parameters) provides information from two sources. First, sample gamma function param- eters for friction factors from seven MPOs, obtained from the MPO Documentation Database, are summarized. Math- ematically, it does not make sense to average these param- eters, nor can consensus factors be derived. The guidance is to choose a set of parameters as a starting point, perhaps by testing different sets of parameters to see which provide the best results, and adjusting them as needed. This process is described more completely Section 4.5.4. The second data source is the 2009 NHTS, from which average trip lengths by trip purpose for each urban area size category are presented. This information could be used as a starting point for developing friction factors as well as for rea- sonableness checks of modeled trip lengths in areas without local survey data. They should not be used as âhardâ valida- tion targets for specific urban area models. 4.5.4 Model Parameters Gravity Model Parameters Gamma function parameters were available for the classic three trip purposes for seven MPOs from the MPO Docu- mentation Database. Table 4.5 presents the b and c param- eters used by these MPOs. Since friction factors can be scaled without impacting the resulting distribution, the parameters shown in Table 4.5 were scaled to be consistent with one another. The resulting friction factor curves for the home- based work, home-based nonwork, and nonhome-based trip purposes are shown in Figures 4.2 through 4.4. The MPO size categories for Table 4.5 are: â¢ Large MPOâOver 1 million population; â¢ Medium MPOâ500,000 to 1 million population; â¢ Medium (a) MPOâ200,000 to 500,000 population; and â¢ Small MPOâ50,000 to 200,000 population. The guidance is to choose one of these seven sets of param- eters (the six b and c parameters from the same model) based 7Frequency distributions of trip length as reported from survey respon- dents are âlumpyâ due to rounding of times. One way of resolving this issue is to use only the respondentsâ reported origins and destinations and to use the travel times from the networks for the corresponding origin-destination zones to create the frequency distributions. This method also has the advantage of using a consistent basis for travel time estimation across all survey observations.
47 Home-Based Work Home-Based Nonwork Nonhome Based b c b c b c Large MPO 1 â0.503 â0.078 â3.993 â0.019 â3.345 â0.003 Large MPO 2 â1.65 â0.0398 â1.51 â0.18 â1.94 â0.116 Large MPO 3 â0.156 â0.045 â1.646 â0.07 â2.824 0.033 Medium MPO 1 â0.81203 â0.03715 â1.95417 â0.03135 â1.92283 â0.02228 Medium MPO 2 â0.388 â0.117 â2.1 â0.075 â1.8 â0.16 Medium (a) MPO 1 â0.02 â0.123 â1.285 â0.094 â1.332 â0.1 Small MPO 1 â0.265 â0.04 â1.017 â0.079 â0.791 â0.195 Source: MPO Documentation Database. Table 4.5. Trip distribution gamma function parameters for seven MPOs. 1 10 100 1,000 10,000 100,000 1,000,000 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 Friction Factors Time (Minutes) Large 1 Large 2 Large 3 Medium 1 Medium 2 Medium (a) Small 1 Source: MPO Documentation Database. Figure 4.2. Home-based work trip distribution gamma functions. 0.0001 0.0010 0.0100 0.1000 1.0000 10.0000 100.0000 1,000.0000 10,000.0000 100,000.0000 1,000,000.0000 1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 Friction Factors Time (Minutes) Large 1 Large 2 Large 3 Medium 1 Medium 2 Medium (a) Small 1 Source: MPO Documentation Database. Figure 4.3. Home-based nonwork trip distribution gamma functions.
48 on the characteristics of the analystâs model region. The curves shown in Figures 4.2 through 4.4 may be useful in identifying the sensitivity to travel time and the general shape of the fric- tion factors compared to what the analyst knows about travel in his/her region. Note that since a is a scaling parameter that does not change the shape of the gamma function curve, it can be set at any value that proves convenient for the modeler to interpret the friction factors. Whichever modelâs parameters are chosen, they should serve as a starting point for calibrating the model to local conditions. If the analyst is unsure which set of parameters to choose, multiple sets of parameters could be tested to see which provides the best fit to observed trip length frequen- cies. Regardless of which set is chosen, the analyst should adjust the parameters as needed to obtain the most reason- able model for the region. Average Trip Lengths (Times) Table C.10 presents respondent-reported average trip lengths and standard deviations in minutes from the 2009 NHTS data set. This information can be used to help find starting points for friction factor parameters (for example, as initial values for parameters in exponential friction factor functions) and to test trip length results from trip distribu- tion models for reasonableness. The information is presented for auto, transit, and nonmotorized modes as well as for all modes. Initially, the trip length data were summarized for the six population ranges available in the NHTS data set. However, the trip lengths do not vary much by urban population for nonwork travel, and many of the differences appear to be small fluctuations between population ranges. The recom- mendations, therefore, represent mean trip lengths averaged across urban area population ranges in most cases. It should be noted that the sample sizes for transit trips, especially for urban areas under 1 million in population, were insufficient to estimate separate meaningful average trip lengths by population range. This was true for nonmotorized trips as well in some cases. Even though average trip lengths are fairly consistent across urban area sizes, this should not be construed to imply that trip lengths are the same among all individual urban areas, even within each population range. Some patterns can be noted from the data shown in Table C.10: â¢ Average home-based work trip lengths are longer in larger urban areas, particularly for auto and nonmotorized trips; â¢ Transit trips are over twice as long as auto trips in terms of travel time; and â¢ Average trip lengths for nonmotorized trips for all purposes are about 15 minutes and are consistently in the mid-teens. This equates to about 0.75 miles for walking trips. 4.6 External Travel Travel demand models estimate travel for a specific geo- graphic region. While the trip generation process estimates the number of trips to and from zones within the model region based on socioeconomic data for those zones, not every trip will have both trip ends internal to the boundary 0.0001 0.0010 0.0100 0.1000 1.0000 10.0000 100.0000 1,000.0000 10,000.0000 100,000.0000 1,000,000.0000 10,000,000.0000 1 6 11 16 21 26 31 36 41 46 51 56 6661 71 76 81 86 Friction Factors Time (Minutes) Large 1 Large 2 Large 3 Medium 1 Medium 2 Medium (a) Small 1 Source: MPO Documentation Database. Figure 4.4. Nonhome-based trip distribution gamma functions.
49 of the model. In nearly all models, some trips will have one or both trip ends outside of the geography served by the model. Trips with at least one external trip end, depending on the size of the urban area and its location with respect to other areas, might represent a substantial portion of travel within the region. By convention, zones located inside the model region are called âinternal zones.â External zones representing relevant activity locations outside the model region are represented in the model by points at which highway network roadways (and sometimes transit lines) enter and leave the region, often referred to as âexternal stations.â Trips for which both ends are internal to the model region are referred to as âinternalâ internalâ (II). Trips that are produced within the model region and attracted to locations outside the model region are called âinternalâexternalâ (IE), while trips produced outside the region and attracted to internal zones are called âexternalâ internalâ (EI). Trips that begin and end outside the region but pass through the region are labeled âexternalâexternalâ (EE). (In some regions, the letter âXâ is used rather than the letter âE,â as in IX, XI, and XX trips.) Sometimes all trips with one end inside the model region and one end outside are referred to as IE/EI trips. Generally, the terms âexternal tripsâ and âexternal travelâ refer to all IE, EI, and EE trips. 4.6.1 Model Function/Best Practices Usually, external trips are treated as vehicle trips, even if the II trips are treated as person trips. This means that exter- nal transit trips are typically ignored as well as changes in vehicle occupancy for external auto trips. In many areas, there is little or no regional transit service that travels out- side the model region, or HOV or managed lanes crossing the regional boundary, that might require the ability to ana- lyze mode choice for external travel. Since urban area travel models lack sufficient information to model choices involv- ing interurban travel, it is common practice to treat interur- ban trips by nonauto modes as having the external trip end at the station or airport, essentially treating these trips as II (with airports usually treated as special generators or airport access/egress treated as a separate trip purpose). Most of the areas where some treatment of external transit trips is desirable are larger areas, often those close to other urban areas (for example New York and Philadelphia). For the vast majority of urban areas, though, treatment of exter- nal vehicle trips is sufficient. Because larger areas tend to have more survey data available, and there are insufficient examples of external transit travel models to evaluate their transferability, the remainder of Section 4.6 concentrates on the modeling of external vehicle trips. It is important to recognize the relationship between the trip generation and distribution steps for II trips and the external travel modeling process. Two points must be con- sidered in developing modeling procedures for external trips: â¢ The trip generation models described in Section 4.4 are esti- mated from household survey data. These surveys include both II and IE trips, and, unless the IE trips were excluded from the model estimation, the resulting trip production models include both II and IE trips. The trip rates pre- sented in Tables C.5 through C.9 based on the NHTS data include all trips generated by the respondent households (II and IE). In most models, the II trips dominate regional travel, and the effect of IE trips is minimal. However, the amount of IE travel generated in zones near the model region boundary can be significant. â¢ On the other hand, trip attraction models estimated from household survey data include only those trips produced in the model region. So, estimated attraction models include only II trips. Because it is common practice to balance trip attractions to match regional productions and EI trips are modeled using other data sources, the use of only II trips in the models generally does not have the effect of âmissingâ the EI trips, although the quality of estimates of the split between II and EI attractions depends on the availability and quality of data on external travel, as well as the local household survey data. Data Sources Household activity/travel surveys include IE trips, but not EI trips as defined on a production/attraction basis. Further- more, the information provided on the attraction end of IE trips is based on the ultimate destination and does not specify the external zone that would be the effective destination of a modeled trip. This means that the main information to be obtained on external travel from the household survey would be total numbers of IE trips for different segments of zones and perhaps some rough orientation information regarding the external destinations. Additionally, the number of IE trips reported in household surveys is often low. Thus the house- hold survey cannot serve as the primary source for external model development. A more complete data source would be an external sta- tion survey. In such a survey, drivers of vehicles observed on a roadway crossing the model region boundary are sur- veyed through vehicle intercept or mailout/mailback surveys, where the license plates are recorded to determine to whom to send the surveys. Ideally, every external station (zone) would be surveyed, although this may be impractical in areas with a large number of external zones, and it may be very inefficient to survey a large number of low-volume roadways. Data from an external station survey could be used to develop models that estimate the number of IE/EI trips generated by internal zones, by trip purpose if the data have
50 sufficient observations by purpose. Distribution models for IE/EI trips could also be estimated; such models would essen- tially match the vehicle trip ends between the external and internal zones. External Productions and Attractions The definitions of productions and attractions remain the same for external trips as for II trips. That is, the home end of a home-based trip is the production end and the non- home end is the attraction end; for nonhome-based trips, the origin is the production end and the destination is the attraction end. For simplicity, some models have treated all IE/EI trips as produced at the external zone (i.e., as if all such trips were EI). In these contexts, this simplification probably is ade- quate since there are relatively few significant trip attrac- tors outside the urban area for residents of the region, and so the majority of IE/EI trips are, in fact, EI. However, in some regions, especially as areas close to the model regionâs boundary have become more developed, the share of IE trips has become more significant. So if data are sufficient, it may make sense to model IE and EI trips separately. External trip generation totals for the external zones include EI, IE, and EE trips. The total number of vehicle trips for an external zone for the base year is equal to the observed traffic volume on the corresponding roadway at the regional boundary. For forecast years, most areas must rely on growth factors applied to the base year traffic volumes. Generally, the external zone volume serves as a control total for the sum of EI, IE, and EE trips. External trip generation totals for the internal zones include EI and IE trips. The total number of these trips over all internal zones is controlled by the sum of external trips for the external zones, based on the traffic volumes as described above, and excluding the EE trips. The percentage split between EE and IE/EI trips at each external zone is typically the starting point in estimating external travel components by external zone. Ideally, the percentage split should come from a roadside cordon line survey; however, guidance is provided in the following paragraphs on tendencies that can be used to determine the percentage of EE trips. ExternalâExternal Trips The amount of EE travel may depend on a number of fac- tors, including: â¢ Size of the regionâGenerally, larger regions have fewer through trips. â¢ Presence of major through routesâNaturally, the pres- ence of these routes, usually Interstate highways, results in higher EE travel. â¢ Location of the urban area relative to othersâIf other urban areas are located near the boundary of the urban area, this can have significant effects on orientation of travel within the region. â¢ Location of physical features and barriersâIf there are any of these in or near the model region, they may affect the amount of through travel. A fairly complete set of external station surveys for a region would be the best source for estimating EE travel. Such a survey could be used to develop a zone-to-zone trip table of EE trips for the base year. Forecast year tables could be developed by applying growth factors at the zone level, based on projected growth inside and outside the region for areas served by each roadway. A Fratar process is often used for this purpose. This process uses iterative proportional fitting to update a matrix when the marginal (row and column) totals are revised. In this case, the row and column totals are updated to represent the change in EE trips for each external zone between the base and forecast years. In the absence of such survey data, the true EE trip table will be unknown, as will the error between the modeled and actual EE trips. The validity of transferring EE trip percentages from other regions is unknown; in addition, because the fac- tors listed previously can vary significantly between regions, finding a region similar enough to the application context that has the necessary survey data can be difficult and, even if such a region is found, it is unknown how much the EE travel per- centages between the regions would actually vary. Transferring EE trip tables is therefore not recommended. A suggested method for synthesizing EE trip tables is as follows: 1. Identify which external zone pairs are most likely to be carrying EE trips. These external zone pairs should include any pairs of zones where the corresponding highways are Interstates, freeways, or principal arterials. Figure 4.5 illustrates some examples of external zone pairs that are likely or unlikely to have EE travel. External zone pairs that do not include logical paths within the model region should be excluded. For example, zone 1001 to zone 1002 in Figure 4.5 would be unlikely to include many EE trips as both zones lead to the same general location, meaning that a trip between these two zones would essentially be a âU-turnâ movement. Zone pairs with short logical paths through the model region should probably be included even if one or more of the corresponding roadways is of a lower facility type (for example, zone 1002 to zone 1003 in Figure 4.5). While there are undoubtedly a few EE trips that would be made in the model region between external zone pairs that do not meet these criteria, these are prob- ably very small in number and can be ignored without significant impacts on the model results.
51 2. Estimate the number of EE trips for each zone pair identi- fied in Step 1 that represent reasonable percentages of the total volumes of both highways. It makes sense to focus on the roadway with the lower volume in terms of making sure that the percentages are reasonable. There is little guidance available to estimate percentages. Martin and McGuckin (1998) cites a study by Modlin (1982) that provided a formula, intended to be used in urban areas of less than 100,000 population, that estimates the percentage of total external travel that is EE, based on facility type daily traffic volumes, truck percentages, and model region population. This formula results in EE travel percentages of about 30 percent for principal arterials and 70 percent for Inter- states in urban areas of 50,000 population and of about 10 percent and 50 percent, respectively, for urban areas of 100,000 population (note that these figures represent total EE travel on a roadway to all other external zones). 3. During highway assignment, checks on volume-count ratios along âinternalâ segments of these roadways should help indicate whether or not the EE trips were overestimated or underestimated. For example, a persistent over-assignment along an Interstate passing through a region could indicate that the number and percentage of EE trips might have been overestimated. While this process is very rough given the lack of data used, the amounts of EE travel are usually fairly small; therefore, the error associated with these estimates, while unknown, is likely small. InternalâExternal and ExternalâInternal Trips The process of modeling IE/EI trips includes the following steps: 1. Identifying the trip purposes to be used for IE/EI trips; 2. Deciding whether to treat all IE/EI trips as EI; 3. Deciding on external zone roadway types to be used; 4. Estimating the number of IE/EI vehicle trips for each external zone by purpose and splitting them into IE and EI trips; 5. Estimating the number of IE/EI vehicle trips for each internal zone by purpose and splitting them into IE and EI trips; and 6. Distributing IE and EI trips between external and internal zones by purpose. The result of this process is a set of IE and EI vehicle trip tables by trip purpose. These trip tables can be combined into a single trip table, or combined with vehicle trip tables for II trips, for highway assignment. The six steps are described in more detail in the following paragraphs. Step 1: Identifying the trip purposes to be used for IE/ EI trips. Often, the available data are insufficient to model multiple IE/EI trip purposes, and the relatively small num- ber of these trips means that the added cost of separating IE/EI trip purposes does not usually provide a great benefit. Most models, therefore, do not distinguish among trip pur- poses for IE/EI trips, although some models separate trips into home-based work and all other. Another consideration is that without an external station survey, there may not be enough information to determine the percentage of IE/EI trips by purpose. Areas that would benefit most from allocating IE/EI trips into multiple purposes are those with an adjacent urban area on the other side of the study area cordon line. In fact, it may become necessary for proper validation of such a model to allow internally generated IE/EI trips such as work to be attracted to external zones, if in fact a large percentage of resi- dents work in the adjacent urban area. Such an adjustment is sometimes made using special generators or by modifying the trip generation program to estimate home-based work attractions to external zones. External Zone 1001 External Zone 1002 Model Region External Zone 1003 Node 99999 Figure 4.5. Example of external zone pairs with and without EE trips.
52 Step 2: Deciding whether to treat all IE/EI trips as EI. As mentioned above, some models treat all IE/EI trips as pro- duced at the external zone (i.e., as if all such trips were EI). The analyst must decide whether this distinction is warranted by the volume and orientation of external trips in the model region and the availability of data to distinguish between IE and EI trips. Generally, it is probably not worth modeling IE and EI trips separately in regions with low volumes of external travel and regions with little nonresidential activity located just outside the model area boundary. If data from an external station survey are available, they could be used to determine whether there is a high enough percentage of IE trips to make modeling them separately worthwhile. Step 3: Deciding on external zone roadway types to be used. Travel characteristics vary significantly depending on the type of highway associated with an external zone. In general, the higher the class of highway at the cordon, the longer its trips are likely to be. For example, some roads, such as Interstate highways, carry large numbers of long-distance trips. On average, a smaller percentage of the total length of trips on these roadways would be expected to occur in the model region, implying that travelers might be willing to travel farther within the region once they cross the regional boundary. Other roads carry predominantly local traffic. Since local trips are generally short, there is a much greater likelihood that the local ends of these trips are near the boundary. The facility type of the external zone highway, therefore, becomes a strong surrogate for other determinants of the types and kind of external travel. The following stratification scheme for external zones is often used to account for these differences: â¢ Expressway; â¢ Arterial near expressway; â¢ Arterial not near expressway; and â¢ Collector/local. These roadway types are, in effect, the trip purposes for the externalâinternal trips. Other âspecialâ roadway categories that may exist in a region, such as bridge crossings for major bodies of water at the regional boundary, toll roads and turnpikes that carry a large amount of long-distance travel, or international boundary crossings, may warrant separate categories. Once the roadway types are chosen, each external zone is classified accordingly. Step 4: Estimating the number of IE/EI vehicle trips for each external zone by purpose and splitting them into IE and EI trips. The control total for IE/EI trips for each exter- nal zone is the total volume for the zone minus the EE trips for the zone. If the trips are not separated by purpose or into IE and EI trips, then only total EI trips are needed, and they will be equal to the control total. Otherwise, percentages must be estimated to divide the trips. An external station survey would be the only source for actual percentages. Unfortu- nately, there is little information available that could be used to develop transferable parameters; even if there were, the substantial differences between urban areas and the influence of areas outside the model region would make transferability questionable in this case. Step 5: Estimating the number of IE/EI vehicle trips for each internal zone by purpose and splitting them into IE and EI trips. The total IE/EI trips, by purpose and split into IE and EI trips, over all external zones serves as the control total of IE/EI trips for all internal zones. One example of a model used to estimate the IE/EI trips for each zone is discussed below. This example assumes that all IE/EI trips are EI trips, but the same type of model could be used separately for each trip purpose and for IE trips. The functional form of the external trip generation model for internal zones is presented in Equation 4-11. These trips are treated as being produced at the external station and attracted to the internal zone. The attractions generated by each internal zone are computed as a function of the total trip attractions and the distance from the nearest external zone. The internal trip attraction model generates, for each inter- nal zone, the EI trips as a percentage of the total internal trip attractions. The trip generation model has the form: E AT Dj j jB= ( )4 11- where: Ej = EI trips generated in internal zone j; Tj = Total internal trip attractions generated in internal zone j; Dj = Distance from zone j to the nearest external sta- tion; and A, B = Estimated parameters. The EI trip attractions generated by this formula are sub- tracted from the total internal person trips generated for the zone to produce revised total II trip attractions for the zone. Note that these are person trips that must be converted to vehicle trips, using vehicle occupancy factors (see Section 4.8). The model parameters A and B are estimated for each road- way type through linear regression based on an external station survey data set. This is done by transforming Equation 4-11 using logarithms: log log log ( )E A T B Dj j j( ) = +( )+ ( )( ) 4 12- The distance variables Dj are obtained by skimming the highway network and can be expressed in any distance units,
53 although miles are customary. The total trip attractions Tj are determined from the internal trip generation process, as described in Section 4.4. The external trips Ej are obtained directly from the external survey data set. These parameters are calibrated to produce an exact match between the modeled EI vehicle trips and the observed external zone volumes. Step 6: Distributing IE and EI trips between external and internal zones by purpose. As is the case for the internal trips, the most common approach to distributing IE/EI trips is the gravity model (See Equation 4-9). If external station sur- vey data are available, the friction factors can be estimated in a manner that matches the observed trip length (highway travel time) frequency distribution. K-factors are often used in model calibration to match travel patterns on an aggregate (district) basis. If survey data are unavailable, friction factors from the internal travel model could be used as a starting point for model calibration. 4.6.2 Basis for Data Development As discussed previously, an external station survey data set is a valuable resource in estimating and calibrating external travel models. If such a survey is unavailable, Section 4.6.3 provides external trip generation parameters from an example urban area. 4.6.3 Model Parameters Table 4.6 provides sample A and B parameters for the IE/EI trip generation equation (4-11). These were estimated using external station survey data for a large U.S. urban area. Example Consider an internal zone j with 100 total attractions, located the following distance from an external station of each facility type: â¢ Freeway/expresswayâ10 miles; â¢ Arterial near expresswayâ10 miles; â¢ Arterial not near expresswayâ5 miles; and â¢ Collector/localâ2 miles. The number of EI trips attracted to zone j for each external station facility type is given by (using the parameters shown in Table 4.6): â¢ Freeway/expressway: Ej = (0.071) (100) (10-0.599) = 1.8 trips; â¢ Arterial near expressway: Ej = (0.118) (100) (10-1.285) = 0.6 trips; â¢ Arterial not near expressway: Ej = (0.435) (100) (5-1.517) = 3.8 trips; and â¢ Collector/local: Ej = (0.153) (100) (2-1.482) = 5.5 trips. In this example, about 12 of the 100 trip attractions in zone j are EI trips. 4.7 Mode Choice Mode choice is the third step in the four-step modeling process. In models where the unit of travel is vehicle trips, only automobile travel is modeled, and therefore there is no need for a mode choice step. (Hence, these models are some- times referred to as âthree-step models.â) The automobile occupancy step, discussed in Section 4.8, is not needed in these models either. Mode choice is required in models where the unit of travel is person trips by all modes, or by all motorized modes. The mode choice model splits the trip tables developed in trip distribution into trips for each mode analyzed in the model. These tables are segmented by trip purpose and in some cases further segmented by income or number of vehicles, as discussed in Section 4.5.2. If the unit is person trips by motorized modes, these modal alternatives include auto and transit modes. If the unit is person trips by all modes including nonmotorized modes, then the modal alternatives may also include walking and bicycling, although sometimes nonmotorized trips are factored out prior to mode choice. 4.7.1 Model Function Modal Alternatives The first step in mode choice is determining which modal alternatives are to be modeled. Generally, alternatives can be classified as auto, transit, and nonmotorized modes. The simplest models may model just these three main modes (or two, if nonmotorized travel is not included in the model). Auto modes are generally classified by automobile occu- pancy level (e.g., drive alone, two-person carpool, and three- or-more-person carpool). Sometimes autos using toll roads Station Type A B Freeway/Expressway 0.071 0.599 Arterial Near Expressway 0.118 â â 1.285 Arterial Not Near Expressway 0.435 â1.517 Collector/Local 0.153 â1.482 Source: Cambridge Systematics, Inc. (2002). Table 4.6. Sample trip generation model parameters.
54 are modeled as separate alternatives, often also classified by auto occupancy level. Transit modes apply to complete (linked) trips from origin to destination, including any walk or auto access or egress as well as transfers. These may be classified by access (and sometimes egress) mode and by type of service. Because such variables as walk time and parking cost are important elements in mode choice, walk access and auto access transit modes should be modeled separately, unless there is little demand for transit where people drive or are driven to the transit stop. Service types that may be modeled separately are often defined by local (e.g., local bus) versus premium (e.g., commuter rail) service. Among the modes that have been included in mode choice models in the United States are local bus, express bus, light rail, heavy rail (e.g., subway), and commuter rail. Some models include a generic âpremium transitâ mode. There are advantages and disadvantages to having a large number of modal alternatives defined by service type. An advantage is that differences in level of service can be consid- ered more readily, and many travelers view various transit types very differently (for example, some travelers who use commuter rail might not consider using local bus). A dis- advantage is that having more modes makes the model more complex, and therefore harder to estimate and more time consuming to apply, and the complexity may result in com- plicated nesting structures that are hard to estimate and diffi- cult to find transferable parameters for. Another issue is how to classify âmixed modeâ trips, for example, a trip where a traveler uses both local bus and heavy rail. There is no ideal method to classify such trips; methods such as classifying trips as the âmore premiumâ of the modes used would be inappropriate for trips that are primarily on a less premium mode, and most modeling software does not provide a way of identifying the percentage of each submode between an origin and destination. Nonmotorized modes are sometimes separated into two modes, walk and bicycle, but are often treated as a single modal alternative. (Note that a walk or bicycle access segment of a transit trip is not considered a separate trip; it is considered part of the transit trip.) Mode choice is applied by first estimating the probability of choosing each modal alternative for each traveler or segment of travelers. The probability is based on a set of explanatory variables that include characteristics of the modal level of ser- vice, traveler characteristics, and features of the areas where the travel takes place. In four-step models, the probabilities are applied as shares of the market segments to which they apply; that is, if a mode has a 75 percent probability of being chosen by a market segment (e.g., work trips for an origin- destination zone pair), 75 percent of the travelers in that segment are allocated to that mode. Most mode choice models use the logit formulation. In a logit mode choice model, the alternatives represent the modes. The utility is a function of the explanatory variables. These variables may include the following: â¢ Modal level of serviceâAuto in-vehicle time, transit in-vehicle time, wait time, walk access/egress time, auto access time, transit fare, parking cost, number of transfers; â¢ Traveler characteristicsâVehicle availability (sometimes relative to other potential drivers), household income, gender, age, worker/student status; and â¢ Area characteristicsâDevelopment density, pedestrian environment. At a minimum, mode choice models need to include level-of-service variables so that the effects of changes in level of service (e.g., run time improvements, fare increases, parking costs) can be analyzed. Transportation investment and policy alternatives usually change the level of service for one or more modes relative to the others, and so the effects on modal usage need to be estimated. The inclusion of traveler characteristics allows the model to be sensitive to changing demographics. Including area characteristics allows the model to consider the effects of land use changes, which may be part of policy alternatives the model is being used to help analyze. The values for the modal level-of-service variables must be obtained for every origin-destination zone pair. These values are obtained through the process of skimming the networks, as discussed in Section 4.5. A separate skim matrix is needed for each modal alternative (and each time period, if time- of-day modeling, discussed in Section 4.9, is employed). This requirement implies that a network is needed for each mode. These individual modal networks are developed from the basic two networksâhighway and transitâand by adjusting parameters to match the assumed use of the mode. For example, skims for a local bus mode could be obtained by allowing travel only on local bus routes in the transit network. For transit auto access modes, provision must be made for allowing auto portions of these trips to be made along the highway network. For nonmotorized modes, the usual practice is to revise the highway network by eliminating links on which only motorized vehicles are allowed (freeways, ramps, etc.) and skimming the network using minimum distance paths. While the foregoing description of obtaining the mode- specific paths may appear to be relatively simple, great care must be used in the process to ensure that the paths and skims obtained are consistent with the mode choice model. This may be difficult when obtaining paths for âhigher-levelâ modes. For example, while drive-alone paths could be obtained by turning off HOV links in the path-building process, it might be necessary to âencourageâ the use of HOV links (or discour- age the use of drive-alone links) in order to obtain reason-
55 able HOV paths and skims for the mode choice model. At the same time, this encouragement should be performed in such a way that preserves the relationships between param- eters used in the path-building process and mode choice coefficients. This is especially true for transit path-building. If the mode choice model coefficients show that out-of-vehicle time is twice as onerous as in-vehicle travel time (i.e., the ratio of the coefficients is two to one), it is improper to use a different relationship between out-of-vehicle time and in-vehicle time in the path-building process. 4.7.2 Best Practices As is the case with trip distribution models, mode choice model accuracy can be enhanced by segmenting the model by income or vehicle availability level. When there are more than two modal alternatives, as is common in mode choice models, the multinomial logit model can introduce inaccuracies in the way it estimates how people choose among alternatives. One way of dealing with this issue is the use of a nested logit model (see Section 4.2). A major advantage of nested structures for mode choice is that similar modes, such as transit with auto access and transit with walk access, can be grouped as a subset, all branching from a common âcomposite mode.â As discussed in Section 4.2, the ânesting coefficientâ must be between zero and one and should be statistically significantly different from zero and one. In the literature review of trans- ferability studies (see Appendix B), no research was found into the transferability of nesting coefficients from one area to another. In models around the United States, nesting coefficients are often asserted with values ranging from about 0.2 to 0.8, nearly the entire valid range. The IIA assumption (discussed in Section 4.2) can be problematic in mode choice models with more than two alternatives. For example, if car, bus, and rail are the alterna- tives and they all had equal utilities, the probability of choosing a transit mode would be greater than that of choosing the car mode. The modeler would need to decide if this were a correct formulation (i.e., although rail and bus may not be perfect substitutes, such a formulation may still be problematic). A nested logit formulation of this choice set would help address this issue by subordinating the somewhat related bus versus rail choice beneath a car versus transit choice. 4.7.3 Basis for Data Development Logit mode choice model parameters are estimated using statistical techniques and specialized software designed to estimate this type of model. As in the estimation of a lin- ear regression model, the data required are individual trip observations that include the trip origin and destination, the necessary traveler characteristics, and of course the chosen mode for the trip. Information on the level of service by each available mode can be added to the estimation data set from the network skims; information on area characteristics based on the origin and destination can also be added. The only data source likely to provide a set of travel observa- tions that include all modal alternatives is a household survey data set. Unfortunately, except in areas with high transit use (or very large survey sample sizes), the number of observations in a household survey for transit modes is likely to be too small to estimate statistically significant model parameters. There- fore, the household survey data set is often supplemented with data from a transit rider survey. Even with typical household survey sample sizes and large transit rider survey data sets, it is often difficult to estimate mode choice model parameters that are both statistically sig- nificant and of reasonable sign and magnitude. As a result, the model development process often includes âconstrainingâ some model parameters (utility coefficients) to specific values, often relative to one another. For example, parameters for transit out-of-vehicle time (wait time, walk time, etc.) might be constrained to be a multiple of the coefficient for in-vehicle time, say two or three, to reflect the fact that travelers find walking or waiting more onerous than riding. Because of the difficulty in model estimation and in obtain- ing sufficient estimation data sets, mode choice is the model component most often characterized by parameters that are not estimated from local data, even in urban areas where parameters for other model components are estimated in that way. This practice of transferring parameters from other models has resulted, ironically, in a relative lack of recent models available for consideration as the estimation context. Many recently estimated models include at least some con- strained coefficients. The MPO Documentation Database includes mode choice model parameters for a limited number of models. These are presented in Section 4.7.4. 4.7.4 Model Parameters Even for applications with similar circumstances, unless models have identical specifications, the values for specific coefficients may differ significantly between models. The alternative definitions, nesting structures, and presence or absence of other variables in a model can affect the coefficients of any variable. So it is much more valid to transfer individual models rather than composites of models with different vari- ables or structures. With that in mind, the best guidance for an MPO without sufficient local data for model estimation (the application context) is to transfer a complete model from another area (the estimation context), preferably from an area of similar demo- graphic, geographic, and transportation system characteristics.
56 Model parameters can then be calibrated to ensure reasonable results in the application context, preferably retaining the relationships (i.e., ratios) between coefficients that have been estimated elsewhere. Care should be taken to note whether any of the model parameters in the estimation context were trans- ferred themselves from elsewhere or otherwise constrained. It is, of course, impractical to present in this report every mode choice model that might be considered in the estimation context. Analysts are encouraged to research specific models from likely estimation contexts and obtain information from sources such as direct contact of MPOs or on-line model doc- umentation. If this is not feasible, information is presented in Tables 4.7 through 4.15 in simplified form for some of the models in the MPO Documentation Database for the classic three trip purposes. The information from the MPO Documentation Database includes parameters for the level-of-service variables likely to be used in mode choice models in areas to which mode choice models are likely to be transferred. The MPO Documentation Database includes mode choice model parameters for about 30 MPO models. All of these models are located in urban areas with populations over 500,000 and most are in areas with populations over 1 million. For some of the models in the MPO Documentation Database, information on the mode choice models is incomplete, and some models have unusual or complex variable or modal alternative definitions that would make transferring parameters difficult. These models were excluded from the tables below, and so the number of models for which information on transferable parameters is available is less than 30. Table 4.7 presents the characteristics of nine mode choice models for home-based work trips from the MPO Documen- tation Database. These models can be summarized as follows: â¢ Eight models from areas with populations over 1 million, and one model from the 500,000 to 1 million population range; â¢ Six nested logit and three multinomial logit models; â¢ Two models that include nonmotorized trip modes, and seven that do not; and â¢ Two models that have transit modes separated into local and premium submodes; one that separates transit into local, premium (e.g., express bus), and rail submodes; and six that use generic modes representing all transit. All nine models have separate modes for walk and auto access to each transit submode. The nesting structures for the nested models in this group include separate nests for auto, transit, and nonmotorized modes. Table 4.8 presents the coefficients of the variables in the nine models described in Table 4.7. Note that six models use a generic out-of-vehicle time variable while the others have separate components for some types of out-of-vehicle time. All of these coefficients are âgeneric,â meaning they do not differ by modal alternative although some of the variables do not pertain to all modes (for example, wait time is not included in the utilities for auto modes). Table 4.9 presents some of the relationships between pairs of coefficients for these models. There are some notable similarities among the parameters shown in Table 4.8 and the relationships shown in Table 4.9. The in-vehicle time coefficients range from -0.019 to -0.044, indicating similar sensitivity to travel time. It should be noted that the FTA guidance for New Starts forecasts indicates that compelling evidence is needed if the in-vehicle time coefficient does not fall between -0.020 and -0.030 (Federal Transit Administration, 2006), and most are close to this range. All of the models have out-of-vehicle time coefficients that are greater in absolute value than the in-vehicle time coefficients, with the ratios ranging from 1.5 to 4.7. FTA guidance for New Starts forecasts also indicates that compelling evidence is needed if the ratio does not fall between 2.0 and 3.0, and most are within this range. Model Population Range Nested Logit? Include Nonmotorized? Auto Submodes Transit Submodes A < 1 million Yes No DA/SR Local/Premium B > 1 million No No DA/SR None C > 1 million No No DA/SR None D > 1 million No No None None E > 1 million Yes No DA/SR Local/Premium F > 1 million Yes No DA/SR Local/Premium/Rail G > 1 million Yes No DA/SR None H > 1 million Yes Yes DA/SR None I > 1 million Yes Yes DA/SR None DA = drive alone, SR = shared ride. Table 4.7. Characteristics of home-based work mode choice models from the MPO Documentation Database.
57 Model In-Vehicle Time Out-of- Vehicle Time Walk Time First Wait Time Transfer Wait Time Cost A 0.021 â0.054 â0.098a â0.098 â0.0031 B â â 0.030 â0.075 â0.0043 C â0.036 â0.053 â0.0077 D â0.019 â0.058 â0.081 â0.040 â0.0072 E â0.025 â0.050 â0.0025 F â0.044 â0.088 â0.0067 G â0.028 â0.065 â0.0055 H â0.033 â0.093 â0.038 â0.038 â0.0021 I â0.025 â0.050 â 0.0050b The units of time variables are in minutes; cost variables are cents. a Model A uses a first wait time stratified by the first 7 minutes and beyond. The coefficient shown is for the first 7 minutes; the coefficient for beyond 7 minutes is â0.023. b Model I has a separate coefficient for auto parking cost, which is â0.0025; the coefficient shown is for all other auto operating and transit costs. Table 4.8. Coefficients from home-based work mode choice models in the MPO Documentation Database. Model Out-of-Vehicle Time/ In-Vehicle Time Walk/ In-Vehicle Time First Wait/ In-Vehicle Time Value of In-Vehicle Time A 2.6 4.7 $4.06 per hour B 2.5 $4.19 per hour C 1.5 $2.81 per hour D 3.1 4.3 $1.58 per hour E 2.0 $6.00 per hour F 2.0 $3.94 per hour G 2.3 $3.05 per hour H 2.8 1.2 $9.43 per hour I 2.0 $3.00 per hour Table 4.9. Relationships between coefficients from home-based work mode choice models in the MPO Documentation Database. The value of time is computed as the ratio of the in-vehicle time and cost coefficients, converted to dollars per hour. It represents the tradeoff in utility between in-vehicle time and cost; for example, in Model E an average traveler would be indifferent between a travel time increase of 6 minutes and a transit fare increase of 60 cents. There is some variability in the implied values of time, with model D on the low end.8 The guidance for choosing a model from Tables 4.7 through 4.9 is to look for a model with similar modal alter- natives to those that the analyst wishes to model in the application context. For example, if nonmotorized modes are to be included, Models H and I can be considered. Other considerations include whether a nested logit model is desired or required (A, E, F, G, H, or I), perhaps the popu- lation of the area (although most of the models in the tables are for large urban areas), the variables the analyst wishes to include, the prevalence of existing transportation modes, and the analystâs assessment of the reasonableness of the parameters and relationships given his or her knowledge of the region. Tables 4.10, 4.11, and 4.12 show the model characteristics, parameters, and relationships, respectively, for eight models from the MPO Documentation Database for home-based nonwork trips. Tables 4.13, 4.14, and 4.15 show the model characteristics, parameters, and relationships, respectively, 8Note that these values of time are implied to be constant for all persons making home-based work trips. This is, of course, a substantial simplifi- cation, as people value time differently. In some models where segmen- tation of travel by income level occurs, as discussed in Section 4.5.2, the cost coefficients, as shown in the last column of Table 4.8, may vary by income level. However, even this is a simplification, as varying income levels are not the only reasons why individuals value time differently. Further segmentation is difficult, however, since data for segmentation and estimation of different values of time are not readily available, and the time and resources required for model application increase with additional segmentation.
58 Model Population Range Nested Logit? Include Nonmotorized? Auto Submodes Transit Submodes A < 1 million No No None None D > 1 million No No None None E > 1 million Yes No DA/SR Local/Premium G > 1 million No No DA/SR None I > 1 million Yes Yes DA/SR None J > 1 million No No None None K > 1 million Yes No DA/SR Local/Premium L < 1 million No Yes DA/SR None DA = drive alone, SR = shared ride. Table 4.10. Characteristics of home-based nonwork mode choice models from the MPO Documentation Database. Model In- Vehicle Time Out-of Vehicle Time Walk Time First Wait Time Transfer Wait Time Cost Auto Operating Cost Parking Cost Transit Cost (Fare) A 0.007 â0.017a â0.005 D â â 0.011 â0.066 â0.061 â0.059 â0.033 E â0.020 â0.060 â0.003 G â0.010 â0.046 â0.029 I â0.008 â0.025 â0.010 â0.025 â0.010 J â0.025 â0.075 â0.050a â0.050 â0.170 â0.085 â0.250 Kb â0.022 â0.066 â0.009 L â0.007 â0.017a â0.009 The units of time variables are minutes, cost variables are cents. a Models A, J, and L use a first wait time stratified by the first 7 minutes and beyond. The coefficient shown is for the first 7 minutes; the coefficient for beyond 7 minutes is â 0.007 for Model A, â0.025 for Model J, and â0.007 for Model L. b Model K has an additional variable for âtransfer penalty,â which has a coefficient of â0.154. This coefficient is seven times the in-vehicle time coefficient, which implies that a transit transfer has the same effect on utility as an increase in travel time of 7 minutes. Table 4.11. Coefficients from home-based nonwork mode choice models in the MPO Documentation Database. for 11 models from the MPO Documentation Database for nonhome-based trips. The information in these tables is pre- sented and used the same way as the information in Tables 4.7, 4.8, and 4.9 for home-based work trips. Note that most of the models are simpler than for work trips, with fewer sub- mode alternatives and fewer nested logit models. Note that the parameters are a bit more variable for nonwork trips than for work trips, and the values of time are lower for nonwork travel, as expected. The coefficients shown in Tables 4.8, 4.11, and 4.14 are used in the utility function for each mode (see Equation 4-1). For example, the utility for transit with auto access for Model B in Table 4.8 is given by: Vtw tw= ( )Î² 0 â â 0.030 in-vehicle time 0.075 out-of-vehicle time 0.0043 cost( ) ( )â The utilities are then used to compute the choice prob- abilities using Equation 4-2. The logit model utility and prob- ability computations are performed the same way as in the vehicle availability logit model example presented in Section 4.3.4. Note that values for the alternative-specific constants (bn0 in Equation 4-1) are not provided in Tables 4.8, 4.11, and 4.14. These constants are not considered transferable, and their values are determined during mode choice model calibration or transfer scaling. 4.8 Automobile Occupancy The highway assignment step, discussed in Section 4.11, requires tables of vehicle trips while the output of early model steps is in person trips. (As mentioned earlier, some models use auto vehicle trips as the unit of travel. Since such models
59 Model Out-of-Vehicle Time/ In-Vehicle Time Walk/ In-Vehicle Time First Wait/ In-Vehicle Time Value of In-Vehicle Time A 2.4 $0.48 per hour D 6.0 5.6 $0.21 per hour E 3.0 $3.69 per hour G 4.6 $0.21 per hour I 3.1 $0.48 per hour J 3.0 2.0 $0.09 per hour K 3.0 $1.40 per hour L 2.4 $0.80 per hour Table 4.12. Relationships between coefficients from home-based nonwork mode choice models in the MPO Documentation Database. Model Population Range Nested Logit? Include Nonmotorized? Auto Submodes Transit Submodes A < 1 million No No DA/SR None D > 1 million No No DA/SR None E > 1 million Yes No DA/SR Local/Premium F > 1 million Yes No DA/SR Local/Premium/Rail G > 1 million No No DA/SR None I > 1 million Yes No None None J > 1 million No No None None L < 1 million No No None None M > 1 million No Yes DA/SR None N > 1 million Yes No DA/SR None O < 1 million No Yes DA/SR None DA = drive alone, SR = shared ride. Table 4.13. Characteristics of nonhome-based mode choice models from the MPO Documentation Database. Model In- Vehicle Time Out-of- Vehicle Time Walk Time First Wait Time Transfer Wait Time Cost Auto Operating Cost Parking Cost Transit Cost (Fare) A 0.026 ââ 0.065 â0.065a â0.065 â0.008 D â0.011 â0.066 â 0.061 â0.059 â0.033 E â0.020 â0.060 â0.002 F â0.022 â0.044 â0.003 G â0.006 â0.068 â0.008 I â0.020 â0.050 â0.006 â0.016 â0.006 J â0.025 â0.075 â0.050a â0.050 â0.179 â0.090 â 0.250 L â0.026 â0.065 â0.065a â0.065 â0.013 Mb â0.013 â0.032 â0.032a â0.050 â0.002 Nb â0.030 â0.053 â0.083 â0.083 â0.182 O â0.035 â0.082 â0.011 The units of time variables are minutes, cost variables are cents. a Models A, J, L, and M use a first wait time stratified by the first 7 minutes and beyond. The coefficient shown is for the first 7 minutes; the coefficient for beyond 7 minutes is â0.026 for Model A, â0.025 for Model J, â0.026 for Model L, and â0.025 for Model M. b Models M and N have an additional variable for âtransfer penalty,â which has a coefficient of â0.306 in Model M and â0.030 in Model N. Table 4.14. Coefficients from nonhome-based mode choice models in the MPO Documentation Database.
60 have no mode choice step, and the outputs of trip distribu- tion will already be in vehicle trips, the auto occupancy step is not needed in these models.) A process to convert person trips made by auto to vehicle trips is therefore required. This conversion typically is based on a set of factors, called auto occupancy factors, which are applied to the various automo- bile passenger trip tables produced by the mode choice step described in Section 4.7. Because the auto occupancy factors vary considerably by trip purpose, it is recommended that the categorization of passenger trips by purpose used through the preceding steps be retained. Sometimes mode choice models include multiple auto modes that are defined based on automobile occupancy levels (e.g., drive alone, two-person carpool, and three-or- more-person carpool). In such models, much of the con- version process from auto person trips to auto vehicle trips takes place in the mode choice model: There is one vehicle trip per drive-alone auto person trip and one vehicle trip per two-person carpool person trip (i.e., the conversion factors for these modes are 1.0 and 2.0, respectively). For three-or-more-person carpool trips, a conversion factor equivalent to the average vehicle occupancy for vehicles with three or more occupants is used. These factors, which may vary by trip purposes, are generally derived from local household survey data or transferred from comparable MPO models. 4.8.1 Model Function Auto occupancy factors are scalar factors which are applied to the passenger automobile tables. In some cases the auto occupancy factor is adjusted based on Travel Demand Management policies, but the choice to ride in a shared-ride automobile mode is more properly a mode choice decision as presented in Section 4.7. It has already been stated that the automobile occupancy is expected to vary based on trip purpose; for example, the auto occu- pancy of a work trip is typically much lower than the automobile occupancy for a recreational trip. Other con- siderations that may affect automobile occupancy are met- ropolitan size and density, transit availability, automobile ownership, and income. There is also support to suggest that automobile occupancy may vary by time of day. For example, work trips with lower auto occupancy may predominate during the peak hours. This possibility suggests that disaggregating passenger trips by time of day, which is discussed in Section 4.9, might be more appropriately done before applying auto occupancy factors. When the calculations are done in this order, the time-of-day effect on trip purpose and the associated auto occupancies by purpose will result in lower auto occupancies during peak hours. The scalar formula for converting auto passenger trips into auto vehicle trips is: Auto T AOCij p ijauto p p = ( )4-13 where: Autopij = Auto vehicle trips between zone i and zone j for purpose p; Tpijauto = Auto person trips between zone i and zone j for purpose p; and Model Out-of-Vehicle Time/ In-Vehicle Time Walk/ In-Vehicle Time First Wait/ In-Vehicle Time Value of In-Vehicle Time A 2.5 $2.01 per hour D 5.8 5.4 $0.21 per hour E 3.0 $5.45 per hour F 2.0 $4.04 per hour G 11.3 $0.46 per hour I 2.5 $2.00 per hour J 3.0 2.0 $0.08 per hour L 2.5 $1.20 per hour M 2.5 $5.08 per hour N 1.7 2.8 $0.10 per hour O 2.3 $1.86 per hour Table 4.15. Relationships between coefficients from nonhome-based mode choice models in MPO Documentation Database.
61 AOCp = Auto occupancy factor (persons, including driver, per auto) for purpose p. Typical values for the auto occupancy factors are presented in Section 4.8.4. 4.8.2 Best Practices If the model will be used to analyze changes in auto occu- pancy levels due to changes in transportation level of ser- vice, policy changes, or specific implementations designed to affect carpooling (such as HOV lanes), then it is necessary to include in the mode choice model separate modal alterna- tives related to auto occupancy levels (i.e., drive alone, shared ride with two occupants, etc.) with level-of-service variables that are specific to the various alternatives. If the model is not to be used for these types of analyses, and person trips are the unit of travel, then using auto occupancy factors by trip purpose to convert auto vehicle trips to auto person trips using Equation 4-13 may be considered best practice. 4.8.3 Basis for Data Development When sufficient local data are available, best practice for obtaining automobile occupancy rates is to estimate them by trip purpose from household activity/travel survey data. This type of data source would also be used in estimating the parameters of mode choice models related to the choice between auto modes defined by occupancy level. To provide information for areas without local data, the 2009 NHTS data set was used to develop vehicle occupancy factors by trip purpose and urban area population shown in Table 4.16. 4.8.4 Model Parameters Table 4.16 shows the average daily vehicle occupancy levels by trip purpose from the 2009 NHTS. These factors are presented for average weekday, morning peak period (7:00 to 9:00 a.m.), and afternoon peak period (3:00 to 6:00 p.m.) trips. Because there is no clear correlation between urban area population and vehicle occupancy, rates are not presented by urban area population range. This find- ing is consistent with the information presented in NCHRP Reports 365 and 187 (Martin and McGuckin, 1998; Sosslau et al., 1978). Table 4.16 presents occupancy rates for three groups: all auto trips, carpools with two or more persons, and carpools with three or more persons. If a mode choice model has three auto modesâdrive alone, two-person carpool, and three- or-more-person carpoolâthen the rates for carpools with three or more persons can be applied to the three-or-more- person carpool person trips from the mode choice model to obtain vehicle trips. If a mode choice model has two auto modesâdrive alone and two-person carpoolâthen the rates for carpools with two or more persons can be applied to the two-or-more-person carpool person trips from the mode choice model to obtain vehicle trips. Example Consider an urban area where the outputs of the mode choice model with the classic three trip purposes include morning peak period person trip tables for the drive-alone, two-person Trip Purpose Vehicle Occupancyâ Time Period Home- Based Work Home- Based Nonwork Home- Based School Home-Based Other (Excluding School) Nonhome Based All Trips All Auto Modes daily 1.10 1.72 1.14 1.75 1.66 1.55 Carpool 2 Plus Onlyâ â daily 2.42 2.71 2.35 2.71 2.75 2.72 Carpool 3 Plus Onlyâdaily 3.60 3.81 3.46 3.81 3.79 3.80 All Auto Modesâa.m. peak 1.09 1.66 a a 1.43 1.34 Carpool 2 Plus Onlyâa.m. peak 2.36 2.65 a a 2.65 2.61 Carpool 3 Plus Onlyâa.m. peak 3.42 3.57 a a 3.68 3.64 All Auto Modesâp.m. peak 1.11 1.66 a a 1.65 1.50 Carpool 2 Plus Onlyâp.m. peak 2.45 2.62 a a 2.72 2.65 Carpool 3 Plus Onlyâp.m. peak 3.63 3.66 a a 3.75 3.70 a Use daily parameters; NHTS data insufficient to estimate. Source: 2009 NHTS. Table 4.16. Average daily vehicle occupancy by trip purpose by time period.
62 carpool, and three-or-more-person carpool modes. Say that one origin-destination zone pair has the following values in these trip tables: â¢ Home-based work: Drive aloneâ50, two-person carpoolâ 10, three-or-more-person carpoolâ2 â¢ Home-based nonwork: Drive aloneâ40, two-person carpoolâ50, three-or-more-person carpoolâ20 â¢ Nonhome based: Drive aloneâ30, two-person carpoolâ 30, three-or-more-person carpoolâ10 The person trips for the morning peak period can be con- verted to vehicle trips using the values in Table 4.16: â¢ Home-based work: Vehicle trips = 50/(1) + 10/(2) + 2/ (3.42) = 55.58. â¢ Home-based nonwork: Vehicle trips = 40/(1) +50/(2) + 20/(3.57) = 70.60. â¢ Nonhome based: Vehicle trips = 30/(1) +30/(2) + 10/(3.68) = 47.72. This zone pair would have a total of 55.58 + 70.60 + 47.72 = 173.90 vehicle trips. 4.9 Time of Day It is desirable for many reasons to estimate travel by time of day, including the need for temporally varying model outputs (for example, speeds by time of day for air quality conformity analysis) and to enhance model accuracy (levels of congestion and transit service may vary significantly between peak and off- peak periods). To do this, daily travel measures are converted to measures by time of day at some point in the modeling process using a discrete number of time periods. Typically, a four-step model with time-of-day modeling uses three to five periods (for example, morning peak, mid-day, afternoon peak, night). In urban areas that experience significant congestion, it has become standard modeling practice to perform highway assignment separately for different time periods while smaller urban areas often continue to use daily assignment procedures. The MPO Documentation Database indicates the following percentages of MPOs using time period rather than daily high- way assignment: â¢ MPO population greater than 1 million: 88 percent; â¢ MPO population between 500,000 and 1 million: 64 percent; â¢ MPO population between 200,000 and 500,000: 45 percent; and â¢ MPO population between 50,000 and 200,000: 30 percent. 4.9.1 Model Function It is typical for models to start by estimating daily travel in the trip generation step. In a four-step model, the trip generation model is typically applied to estimate average weekday trips. It is important to consider how to determine the period in which a trip occurs, especially if it begins in one period and ends in another. Trips can be assigned to a time period based on: â¢ The departure time; â¢ The arrival time; and â¢ The temporal midpoint of the trip. In an aggregately applied model such as a four-step model, the midpoint would be the most logical way to define a tripâs time period, since the majority of the trip would occur dur- ing that period. Some models use the concepts of âtrips in motion,â essentially splitting trips into components to deter- mine percentages of travel by time period. The specific defi- nition usually makes little difference in aggregately applied models in the percentages of trips occurring in each period, but the definition must be known in order to estimate and validate the model. The most common method of time-of-day modeling in four-step models is simple factoring. At some point in the modeling process, fixed factors specific to trip purpose and direction are applied to daily trips to obtain trips for each time period. (Sometimes, this factoring is done in two steps, with daily trips split into peak and off-peak trips, and later the peak trips split into morning peak and afternoon peak, and perhaps off-peak trips split into additional periods.) While this method is relatively easy to implement and to apply, it is not sensitive to varying transportation levels of service, limit- ing its usefulness in analyzing policy changes or congestion management activities. The ways in which fixed time-of-day factors may be applied within the four-step process are as follows (Cambridge Sys- tematics, Inc., 1997a): â¢ In pre-distribution applications, the daily trips are factored between the trip generation and trip distribution steps of the modeling process. The data required include factors representing the percentage of trips by purpose during each hour and for each direction, production-to-attraction or attraction-to-production as well as directional split factors. It should be noted, however, that the directional split factors cannot be applied until after both ends of trips have been determined (i.e., after trip distribution). An advantage of this method is that differences in travel characteristics by time of day can be considered in both trip distribution and mode choice. In models with feedback loops, this method can provide a âcleanâ way to feed back travel times from
63 one iteration to the next; trip distribution, mode choice, and trip assignment can be run separately for each time period, since the factors are applied prior to these steps. â¢ In post-distribution applications, the factors are applied between the trip distribution and mode choice steps. The data required for this approach to splitting includes factors representing the percentage of trips by purpose during each period and for each direction, production-to-attraction or attraction-to-production. This process also provides an opportunity to consider that some trips are in the attraction- to-production direction and to use skims that reflect cor- rect directionality. However, the modeler should decide whether the additional complexity introduced by doing so is worthwhile. â¢ In post-mode choice applications, the factors are applied to daily trips between mode choice and the assignment steps. The data required include factors representing the percent- age of the trips by purpose and mode during each time period and for each direction, production-to-attraction or attraction-to-production. An issue with this approach is that transit path-building procedures may not be consistent between mode choice and transit assignment, since mode choice would be done on a daily basis while transit assign- ment would be done by time period. â¢ In post-assignment applications, the factors are applied to loaded trips after the assignment step is complete. The data required include factors that represent the percentage of daily traffic or transit ridership for each time period on a link and can also include directional split factors depend- ing on how the link-level factor is represented. The main limitation of this type of procedure is that equilibrium high- way assignment on a daily basis is much less meaningful than assignment for shorter, more homogeneous periods. Also, changes in land use that could affect temporal distribution of traffic are not considered when using fixed link-based factors. 4.9.2 Best Practices While activity-based models are beginning to consider the time of day at which trips will occur based on the sequence of travel activities from a household, in four-step models the usual practice is to allocate the daily trips that are calculated from trip distribution and mode choice to time period during the day based on a fixed set of factors. These factors typically are developed from the temporal patterns of trips reported in household surveys or, for auto or transit passenger trip tables, from reported demand, such as vehicle counts for autos or ridership for transit, by time period. The typical application is: T T FijmTOD p ijm p mTOD p = ( )4-14 where: TpijmTOD = Trips between zone i and zone j by mode m for purpose p during the period TOD; Tpijm = Daily trips between zone i and zone j by mode m for purpose p; and FpmTOD = Percentage of daily trips by mode m for purpose p that occur during period TOD. While there is no consensus on the best point in the model- ing process where daily trips should be converted to peak and off-peak period trips, based on the points in the previous discussion, many analysts prefer to perform the conversion prior to mode choice (in models that include a mode choice step). This could mean applying factors after trip generation (to productions and attractions) or after trip distribution (to person trip tables in production-attraction format). If peak hour trips are desired, a two-step process may be used, where factors to convert peak period to peak hour trips are applied to the peak period trips. Nevertheless, the information in the MPO Documentation Database indicates that the majority of MPOs currently apply time-of-day factors after mode choice, due to the methodâs simplicity. However, using different sets of parameters for auto and transit travel may lead to inconsistencies between the transit path-building for mode choice and transit assign- ment. For example, say there is a corridor whose only avail- able transit service is express bus that operates only during peak periods. The mode choice model, applied to daily trips, would estimate some transit trips for the corridor based on the presence of the express bus service. If, say, a fixed set of factors converting daily trips to trips by time period is used, the application of the factors will result in some off-peak trips in the corridor, which the transit assignment process will be unable to assign since there is no off-peak transit service. This problem would occur even if there were separate time-of-day factors for auto and transit trips. The definition of the time periods used should depend on the analysis needs of the region, characteristics of congestion, and differences in transportation service (for example, frequency of transit service). In larger, more congested urban areas, travel conditions typically vary significantly between peak and off- peak periods, and so treating them separately would produce more accurate results. If the situations in the morning and afternoon peak periods, or between mid-day and night off- peak periods, are substantially different, then it would be preferable to separate those periods in the model. It is important to recognize, however, the more periods, the greater the cost in terms of model estimation, validation, pro- gramming, and run time; therefore, there are good reasons to limit the number of periods used. The most common number of time periods in models that perform assignments by time of day is four, with morning peak, mid-day, afternoon peak, and
64 night periods. Models that separate the night period into eve- ning and overnight (with the dividing point reflecting the time when transit service ceases or is greatly reduced), and models that combine the mid-day and night periods into a single off- peak period, are also used. The lengths of the peak periods depend on the extent of congestion in the region. Household survey data can be examined to determine the extent of the peak periods. In areas where such survey data are unavailable, traffic count data can be used. 4.9.3 Basis for Data Development The basic data required for estimating time-of-day models of any type are household survey data, specifically the reported beginning and ending times of activities, tours, or trips. The survey data are processed for the specific type of model being estimated (fixed factor, logit, etc.) and are used separately by trip/tour purpose. These survey data (in expanded form) are also valuable for time-of-day model validation, although, as is the case anytime when the estimation data set is used for validation, the data must be used with caution. For areas without local household survey data, factors from other sources, such as the NHTS, may be transferred. However, as discussed below, time-of-day distributions vary significantly among urban areas, and so significant model validation is required when using transferred time- of-day data. Time-of-day distributions for truck and freight travel usually differ from those for passenger travel and can vary among urban areas. The best sources of data for these distributions are local vehicle classification counts by time of day. 4.9.4 Model Parameters This section presents the time-of-day distributions by hour for each trip purpose, by direction for home-based trips derived from 2009 NHTS data for weekdays. Table C.11 in Appendix C shows these time-of-day distributionsâfor all modes9 and individually for auto, transit, and nonmotorized modesâfor use in areas where time-of-day factors are applied after mode choice. There does not seem to be a relationship between time of day and urban area population, and so the results are not stratified by population range. The numbers shown in Table C.11 can be used to develop factors by trip purpose for any time periods defined as begin- ning and ending on the hour. However, while the factors are fairly consistent across urban area size categories, there can be considerable variation between different urban areas. Peaking conditions can vary greatly based on many factors. The type of economic activity that predominates in an area can affect peakingâfor example, an area with large manufacturing plants might have peaks defined mainly by shift change times while an area with a large tourism industry may see later peaks. Another factor has to do with regional geography and dis- persion of residential and commercial activities. Areas where commuters may travel long distances may see earlier starts and later ends to peak periods. Levels of congestion can also affect peaking, as peak spreading may cause travel to increase in âshoulder periods.â The last two rows of each section of Table C.11 show the combined factors for a typical morning peak period (7:00 to 9:00 a.m.) and a typical afternoon peak period (3:00 to 6:00 p.m.). If factors for a period defined differently are desired, then the appropriate rows from Table C.11 can be summed. For example, if factors for all modes for an after- noon peak period defined from 4:00 p.m. to 6:00 p.m. for the classic three trip purposes are desired, the factors for the rows labeled with hours ending at 5:00 and 6:00 p.m. in the all modes section of the table are added together. This would result in the following factors: â¢ Home-based work: From homeâ1.5 percent, To homeâ 19.5 percent. â¢ Home-based nonwork: From homeâ6.9 percent, To homeâ9.5 percent. â¢ Nonhome based: 15.5 percent. The factors are applied to daily trips by purpose, as illus- trated by the following example. Say that afternoon peak period auto vehicle trips are desired for a period defined as 3:00 to 6:00 p.m. The factors from the auto modes section of Table C.11 are: â¢ Home-based work: From homeâ2.6 percent, To homeâ 25.7 percent. â¢ Home-based nonwork: From homeâ9.5 percent, To homeâ15.3 percent. â¢ Nonhome based: 25.0 percent. These factors are applied to the daily auto vehicle trip table. Say that the daily home-based work production-attraction 9Distributions by mode are presented for models where time-of-day factors are applied after mode choice. However, it should be noted that the NHTS sample sizes for transit and nonmotorized trips are much lower than those for auto trips, and so the transit and nonmotorized factors have more error associated with them, and the trips in the sam- ple are concentrated in larger urban areas.
65 trip table has 100 trips from zone 1 to zone 2 and 50 trips from zone 2 to zone 1. Applying these factors results in the following origin-destination trips (recall that the home end is the production end for home-based trips): â¢ 2.6 home to work trips from zone 1 to zone 2. â¢ 25.7 work to home trips from zone 2 to zone 1. â¢ 1.3 home to work trips from zone 2 to zone 1. â¢ 12.9 work to home trips from zone 1 to zone 2. This means that there are 15.5 home-based work trips traveling from zone 1 to zone 2 and 27.0 home-based work trips traveling from zone 2 to zone 1 in the afternoon peak period. As expected for the afternoon peak, most of these trips are returning home from work. This process would be repeated for the other two trip purposes. Since nonhome-based trips are already on an origin-destination basis, only a single factor is applied to this trip table. As noted previously, the information provided in Table C.11 represents average national factors from the NHTS, but peak- ing can vary greatly from one area to another, regardless of urban area size. To illustrate this point, Table 4.17 shows the percentage of daily travel by purpose occurring during two periodsâ7:00 to 9:00 a.m. and 3:00 to 6:00 p.m.âfor nine urban areas with populations of approximately 1 million according to the 2000 U.S. Census. While the averages pre- sented in this table, based on data from the 2001 NHTS, have associated statistical error ranges not presented here, it is clear that the percentages for some areas differ significantly from those for other areas. For example, the reported percentage of daily home-based work travel between 3:00 and 6:00 p.m. was nearly twice as high in Providence as in Memphis. This variation indicates that when default parameters such as those in Table C.11 are used in lieu of local data, calibration may be required to obtain model results that are consistent with local conditions. 4.10 Freight/Truck Modeling Truck models and freight models are different, although the terms are often used interchangeably. Freight models are multimodal and consider freight activities based, generally, on commodity flows. Truck models consider trucks regard- less of whether they serve freight. Although most urban area freight is carried in trucks, it is also true that truck travel serves purposes other than just carrying freight. Trucks carrying commodities are referred to as âfreight trucksâ; nonfreight trucks are also referred to as service trucks. This section dis- cusses freight and truck modeling functions, practices, and parameters and points the reader to appropriate resources for additional information. 4.10.1 Model Function Freight and truck models enhance the overall travel demand forecasting framework and support additional decision making and alternatives evaluation. Modeling of freight/truck traffic can be important for a variety of reasons. One reason is that it typically makes a disproportionately high contribution to mobile source emission inventories in urban areas, especially for nitrogen oxide and fine particulate matter. Another rea- son is that in many areas and Interstate highway corridors, truck traffic is a significant component of travel demand, and the magnitude of truck traffic influences the available road capacity for passenger car movements. A third reason is that many regions have placed increased emphasis on goods Urban Area Home-Based Work Home-Based Nonwork Nonhome Based All Trips 7 9 a.m. 3ââ 6 p.m. 7â9 a.m. 3â6 p.m. 7â9 a.m. 3â6 p.m. 7â9 a.m. 3â6 p.m. Austin 32.3% 20.8% 12.5% 23.8% 6.9% 24.6% 13.6% 23.7% Buffalo 23.7% 26.7% 9.3% 23.6% 5.9% 23.6% 9.7% 23.8% Greensboro 30.3% 24.0% 12.2% 25.6% 8.1% 26.7% 12.7% 25.8% Jacksonville 29.6% 24.7% 10.4% 24.4% 9.1% 27.1% 11.6% 25.3% Hartford 26.0% 29.5% 9.2% 25.3% 7.2% 20.5% 10.4% 24.3% Memphis 35.0% 18.2% 13.6% 25.6% 6.9% 27.2% 13.5% 25.4% Nashville 32.7% 23.8% 10.1% 24.9% 7.5% 24.7% 10.4% 24.7% Providence 28.9% 33.7% 11.8% 24.9% 7.9% 16.3% 11.8% 22.4% Raleigh 32.4% 26.3% 12.0% 26.5% 8.0% 19.1% 12.2% 24.0% Average 30.1% 25.3% 11.2% 25.0% 7.5% 23.3% 11.8% 24.4% Source: 2001 NHTS. Table 4.17. Time-of-day percentages for urban areas of approximately 1 million in population.
66 move ment and the role of the transportation system in facili- tating economic activity. Having freight or truck models can help enable the evaluation of alternative strategies influenc- ing freight or truck levels. NCFRP Report 8: Freight-Demand Modeling to Support Public-Sector Decision Making (Cambridge Systematics, Inc. and Geostats, LLP, 2010) includes a discussion on classifying freight models and provides an overall forecasting framework, which includes nonfreight/service trucks. Adapted from this presentation, the basic freight/truck model types are as follows: â¢ Trend analysisâTrend analysis directly forecasts freight activity using, at most, historical or economic trends. It does not provide a trip table that could be used in travel demand models but can be used to calculate the background truck traffic on highway links which automobiles must consider. When used in this way, truck traffic cannot be rerouted in response to congestion. â¢ Commodity forecasting â Synthetic modeling of commodity flowsâThis model type develops modal commodity flow origin-destination tables using commodity generation, distribution, and mode choice models and then uses payload and tempo- ral factors (1) to convert those commodity tables to a suitable format for assignment to modal networks and (2) to evaluate the flows on those networks. â Direct acquisitions of commodity flowsâThis model type directly acquires a commodity flow table instead of following the synthetic process. If the acquired table includes modal flows that are directly used, use of these mode-specific tables may replace mode choice, other- wise a mode choice model is required. After the modal commodity table is obtained, payload and temporal factors are used to convert those commodity trip tables to a suitable format for assignment to modal networks and then to evaluate the flows on those networks as is done in the synthetic model. â¢ Nonfreight trucksâsynthetic modelingâGeneration of information for nonfreight trucks is necessary to determine correct multiclass highway performance for freight trucks. If not, freight performance will not consider the inter- action with what may be a majority of trucks on the road. The creation of nonfreight trip tables will often follow the traditional trip generation and trip distribution steps. It will not include a mode choice step because by definition only one mode, that of trucks, is being considered, and these truck trips would be generated and distributed in vehicle equivalents. â¢ All trucksâsynthetic modelingâSynthetic modeling as described for nonfreight trucks can also be used to produce estimates of all trucks. If it is, the performance of freight trucks cannot be separated from the performance of all trucks. However, it is also possible to employ a hybrid approach where freight models are developed for some segments of truck travel (e.g., for trucks with an external trip end). With the commodity forecasting methods in particular, freight demand forecasting can be thought of as a series of steps similar to those described in previous sections for passenger modeling, in which a trip table of transportation demand is created and then assigned to a modal network. Thus, freight generation is similar to the steps described in Section 4.4 for passenger trip generation; freight distribution is similar to the steps described in Section 4.5; freight mode choice is similar to the steps described in Section 4.7 for passenger mode choice; and the estimation of freight vehicles from tons and the tempo- ral distribution is similar to the time-of-day process described in Section 4.9. 4.10.2 Best Practices At the time of a national survey of practice conducted in 2005 (Committee for Determination of the State of the Practice in Metropolitan Area Travel Forecasting, 2007), truck trips were modeled in some fashion by about half of small and medium MPOs and almost 80 percent of large MPOs, although few MPOs reported the ability to model all freight movement. However, as freight and nonfreight truck movement volumes have increased and communities have become more concerned with infrastructure needs and investments, more interest in including freight or truck treatment in models has developed. Two standard sources that comprehensively discuss methods for developing freight and truck models are the original Quick Response Freight Manual (QRFM 1) (Cam- bridge Systematics, Inc. et al., 1996) and its update, Quick Response Freight Manual II (QRFM 2) (Cambridge System- atics, 2007b), both prepared for FHWA. The interested reader can refer to these manuals to obtain more information about freight and truck modeling. The manuals discuss growth factor methods, incorporating freight into four-step travel forecasting, commodity models, hybrid approaches, and economic activity models. Several case studies are included as well. NCHRP Synthesis of Highway Practice 384: Forecasting Metropolitan Commercial and Freight Travel (Kuzmyak, 2008) identifies methods of freight and commercial vehicle fore- casting currently used in professional practice, with a primary focus on MPO forecasting, although some consideration is given to statewide freight models. The report finds that metropolitan freight and commercial vehicle forecasting is
67 performed primarily through the use of traditional four-step models but acknowledges inherent limitations for this pur- pose and notes the desirability to collect data from shippers or carriers that are reluctant to divulge confidential business information. Four case studies are presented along with nine profiles of MPO freight modeling practice, covering Atlanta, Baltimore, Chicago, Detroit, Los Angeles, New York, Phila- delphia, Phoenix, and Portland (Oregon). Since the publication of the QRFM 2, the FHWA has also released the Freight Analysis Framework, Version 3 (FAF3), which includes several data products. The 2007 U.S. Com- modity Flow Survey forms the core data for the FAF3, but several additional data sources were employed in developing the products. Among the data products are origin-destination- commodity-mode flow matrices and GIS link files that contain FAF3 estimates of commodity movements by truck and the volume of long-distance trucks over specific highways (Oak Ridge National Laboratory, 2010). The GIS link files were developed through the use of models to disaggregate interregional flows from the Commodity Origin-Destination Database into flows among localities and assign the detailed flows to individual highways. These models are based on geographic distributions of economic activity rather than a detailed understanding of local conditions. The developers of the FAF3 data caution that while FAF provides reasonable estimates for national and multistate corridor analyses, FAF estimates are not a substitute for local data to support local planning and project development (Oak Ridge National Laboratory, 2011). 4.10.3 Basis for Data Development A variety of data sources can inform freight/truck model development, including: â¢ Socioeconomic, demographic, and employment data from public or commercial data sources; â¢ Locally sourced and FHWA HPMS vehicle classification counts, separating trucks by type; â¢ Commercial vehicle travel surveys, bearing in mind that such surveys are generally difficult to conduct and that response rates can prove particularly challenging; â¢ FAF3 data products, understanding that care must be taken to understand the associated limitations and error potential; and â¢ Commodity flow surveys, public or commercial. This list of potential data sources is not exhaustive, and not all sources are required for every application. (Note that the first two items refer to information that is also used for passenger travel demand modeling and is likely available to MPO modelers in some form.) The interested reader may refer to the QRFM 2 or NCHRP Synthesis 384, which provide more detailed discussion about freight and truck model data sources and uses. 4.10.4 Model Parameters Freight models typically include many of the same steps as do passenger models. The difference is in the travel purposes considered and the decision variables used. Also, in freight models, cargo must be converted into modal vehicles, and these vehicles, primarily trucks, are modeled directly. The following discussion describes steps in the freight/truck modeling process: (1) freight trip generation, (2) freight trip distribution, (3) freight mode choice, (4) application of payload and temporal factors, and (5) creation of vehicle trip tables. These steps cover the freight/truck demand modeling process prior to vehicle assignment. Steps 1 through 4 pertain to commodity-based freight modeling only, while Step 5 pertains to both freight and truck modeling. In fact, in some cases, Step 5, creation of vehicle trip tables, comprises the entire truck modeling process prior to highway assignment. All steps are summarized herein to give the reader a broad overview to potential methods. Step 1âFreight Trip Generation: Productions and Attractions by Commodity in Tons This step estimates cargo freight productions and attractions. To be consistent with the modeling of passenger travel, these productions and attractions are estimated for an average weekday (if a source is used that presents information for another temporal level, such as annual, a conversion is needed). The volumes of commodity flows that begin in a zone (called âproductionsâ) and end in a zone (called âattractionsâ) must be determined for each zone. If freight mode choice is included, the freight flows must be expressed in units that are common to all modes. In the United States, tons are commonly used although other multimodal units, such as value, can be used. As described for passenger trips in Section 4.4, the productions and attractions of freight are calculated by applying trip rates to explanatory variables. Commodity cargo trips are one-way trips, not round-trips, and so the production rates and explanatory variables are different than those used for attractions. The production and attraction rates vary by commodity type, which is anal- ogous to trip purpose in passenger models. The explanatory variables are typically measures of the activity in economic sectors, such as employment, which produce or consume (attract) freight cargo.
68 Public agencies generally develop equations for their own study area from a commodity flow survey of their area. For an FHWA project (not yet published as of this writing), some general linear equations have been developed to disaggregate FAF data from regions to counties. A sample of coefficients for these equations is shown in Table 4.18. In this table, the variables represent employment by type, except for farm acres (in thousands). For example, the equation for the âother agricultural productsâ commodity type is: Tons produced food manufacturing employm= 0.188 ent farm acres in thousands+ 0.051 ( ) Average equations should be used with caution, since the economies of each state and region are so different that equa- tions developed for average economic conditions cannot be expected to apply in all cases. Step 2âFreight Trip Distribution: Trip Table Origins and Destinations This step estimates freight trips between origins and destinations. As is the case for passenger trip distribu- tion, described earlier in Section 4.5, the most common means to distribute freight trips between zones is through the use of a gravity model. For freight models, the imped- ance variable in the gravity model for the large geogra- phies considered by freight is most often distance. In the most common freight distribution models, an exponen- tial function is used (see the discussion of friction factors in Section 4.5.1) to compute the friction factors, where the parameter is the inverse of the mean value of the impedance. By examining commodity flow survey data, it is possible to determine those parameters, such as the average trip length by commodity, that are used to vary the accessibility in response to changes in the impedance variable. Using locally derived Commodities (SCTGa) NAICS Variables Coefficient T-Stat R2 Cereal Grains (2) 311 Food Manufacturing 0.407 5.11 0.48 Farm Acres (in thousands) 0.441 4.20 Other Agriculture Products (3) 311 Food Manufacturing 0.188 10.43 0.65 Farm Acres (in thousands) 0.051 2.14 Meat/Seafood (5) 311 Food Manufacturing 0.053 25.94 0.86 Milled Grain Products (6) 311 Food Manufacturing 0.053 13.64 0.62 Logs (25) 113 Forestry and Logging 0.323 4.02 0.70 115 Support Activities for Agriculture and Forestry 0.843 3.91 321 Wood Product Manufacturing 0.465 6.48 Wood Products (26) 321 Wood Product Manufacturing 0.625 18.37 0.75 Newsprint/Paper (27) 113 Forestry and Logging 0.887 13.59 0.73 323 Printing and Related Activities 0.086 7.38 Paper Articles (28) 322 Paper Manufacturing 0.101 10.76 0.81 323 Printing and Related Activities 0.038 4.82 Base Metals (32) 331 Primary Metal Manufacturing 0.424 8.69 0.75 333 Machinery Manufacturing 0.085 3.24 Articles of Base Metals (33) 332 Fabricated Metal Product Manufacturing 0.115 14.51 0.65 Machinery (34) 332 Fabricated Metal Product Manufacturing 0.085 2.92 0.63 333 Machinery Manufacturing 0.081 2.01 Electronic and Electrical (35) 333 Machinery Manufacturing 0.02 3.00 334 Computer and Electronic Product Manufacturing 0.012 4.35 0.70 335 Electrical Equipment, Appliance, and Component Manufacturing 0.029 2.44 aStandard Classification of Transported Goods Source: Federal Highway Administration (2009a). Table 4.18. Tonnage production equations for selected commodities (2002 Kilotons).
69 data is encouraged, as economic conditions and geographic locations of model regions vary to such an extent that the average trip lengths for one model may not be applicable for another region. Table 4.19 presents average trip lengths from a statewide model for Texas. Step 3âFreight Mode Choice: Trip Table Origins and Destinations by Mode This step estimates cargo freight between origins and destinations by mode. As was discussed in Section 4.7 for passenger trips, the choice of mode used by freight is a com- plicated process. For freight, the choice will be based on many considerations, including characteristics of the mode, charac- teristics of the goods, and characteristics of the production and attraction zones. Typically, insufficient detail exists to properly model this choice, because either the format and parameters of the choice equations or the data on the characteristics are not known for the base or forecast year. Frequently, the future choice of mode is assumed to be the same as the existing choice of mode. Table 4.20 shows tonnages and mode shares for freight in California from the FAF2. This information can be obtained from the FAF for any state. Table 4.19. Average trip lengths by commodity group. Commodity Group Average Trip Length (Miles) Code Name 1 Agriculture 845.30 2 Mining 593.58 3 Coal 946.86 4 Nonmetallic Minerals 141.13 5 Food 826.70 6 Consumer Manufacturing 1,071.04 7 Nondurable Manufacturing 1,020.29 8 Lumber 548.44 9 Durable Manufacturing 980.87 10 Paper 845.99 11 Chemicals 666.41 12 Petroleum 510.47 13 Clay, Concrete, Glass 359.77 14 Primary Metal 945.74 15 Secondary and Miscellaneous Mixed 586.47 Source: Alliance Transportation Group, Inc. and Cambridge Systematics, Inc. (2010). Table 4.20. FAF freight shipments from California shipments by weight, 2002 and 2035 (millions of tons). 2002 From State 2035 From State Mode Number Percentage Number Percentage Truck 92.8 73 366.0 77 Rail 11.7 9 35.4 7 Water 1.2 1 2.2 < 1 Air and Truck 0.4 < 1 2.6 < 1 Truck and Rail 4.0 3 14.3 3 Other Intermodal 5.0 4 29.5 6 Pipeline and Unknown 12.4 10 26.7 6 Total 127.4 100 476.9 100 Source: http://www.ops.fhwa.dot.gov/freight/freight_analysis/faf/state_info/faf2/ca.htm.
70 Step 4âFreight Payload and Temporal Factors: Trip Table Origins and Destinations by Mode by Vehicle This step converts the estimates of cargo freight flow by mode in tons per year into vehicle flows. For the purposes of this report, the vehicle flows of concern are freight trucks. The conversion of truck tons into truck vehicles is similar to the auto occupancy step described for passenger travel in Section 4.8. The tons in the commodity origin-destination tables are divided by the payload factor for the commodity type. The payload factors, in tons per truck, must match the behavioral commodity classification system used by the model. These payload factors should always vary by com- modity. They may also vary by distance traveled. These fac- tors may also consider the empty mileage, the class of the vehicles, etc. A conversion is also necessary to correct the time period from annual to daily. If the average weekday in the fore- casting model should be for midweek truck flows, it may be appropriate to divide annual flows by 295 days, which reflects observations of midweek truck traffic at continuous count- ing stations compared to annual truck counts at those same locations. To adjust the daily flows to hourly flows NCFRP Report 8 recommends that the hourly flows for trucks should be considered to be 6 percent of daily flow for each of the hours from 11:00 a.m. to 7:00 p.m. Table 4.21 shows payload factors used by Tennessee in freight forecasting. Step 5âCreate Vehicle Origin-Destination Tables The transportation of freight is not the only reason for truck travel. Nonfreight trucks, which provide services, move construction materials and equipment, and are used in main- tenance activities as well as the local movement of goods, are not included in the commodity flow table methodology. Freight trucks may constitute the majority of trucks on the road on rural principal highways, but in urban areas, non- freight trucks can represent from 50 to 70 percent of the trucks on major highways, according to calculations from FAF highway assignments. In addition, the scale of the distances traveled by freight and nonfreight trucks is much different. Freight truck trips tend to average distances of hundreds of miles, much longer than the tens of miles typically traveled on individual trips by service trucks. The differences in impact level and travel behavior of freight versus nonfreight trucks have a major bearing on the types of truck trips that are included in travel demand models. Freight may move over national distances, and the model area used in forecasting freight flows may not be the same as the model area needed to address nonfreight trucks, which have primarily a local area of operation. Thus, MPO models may primarily include nonfreight trucks and only include freight trucks as external trips. State or multistate models, which have zone systems and networks that cover larger areas, are more likely to need to include freight truck trips with two internal trip ends. Models typically calculate trip tables for nonfreight trucks separately from freight trucks. Sometimes these are distinguished as heavy trucks and medium trucks. The forecasts of nonfreight trucks will most often be through a synthetic process of trip generation and trip distribution, similar to the steps for freight described in Steps 1 and 2 above. Although the trip generation rates and the trip distribution factors should be developed through the use of commercial vehicle surveys, the next three subsections discuss sample parameters for total truck trip generation, nonfreight truck trip generation, and truck trip distribu- Commodity Pounds per Truck Tons per Truck Agriculture 48,500 24 Chemicals 48,500 24 Construction and mining 50,500 25 Food and kindred products 48,500 24 Household goods and other manufactures 38,500 19 Machinery 36,500 18 Mixed miscellaneous shipments, warehouse and rail intermodal drayage, secondary traffic 36,500 18 Paper products 46,500 23 Primary metal 51,500 26 Timber and lumber 53,000 27 Source: PBS&J (2005). Table 4.21. Freight model truck payload after adjustment.
71 tion. However, the interested reader is encouraged to con- sult NCHRP Synthesis 384 for a broader array of sample parameters. As noted in the introduction to this section, the freight commodity flow framework is but one method used by modelers to address truck trip making in models. Where the concerns are concentrated on representing truck flows within an area largely to support more accurate passenger car assignment or where truck survey data are not avail- able, areas often use simplified approaches. Several areas use vehicle classification counts, specifically truck counts by truck type, to calibrate input origin-destination trip tables of regional truck models using an Origin-Destination Matrix Estimation (ODME) process. The ODME process iteratively updates the input origin-destination trip table of the model so that model truck volume results match with observed truck counts. A base year ODME matrix can be factored to place future-year truck demand on the network as well. The user of such methods should take care to rec- ognize the limitations inherent in both ODME and growth factor techniques. Total truck trip rates. Table 4.22 presents truck daily vehicle trip generation rates from two sources: a survey done by Northwest Research Group (NWRG) for southern California and the Puget Sound Regional Council (PSRC) truck model. These rates are linear equations where the dependent variables are the number of truck vehicle trip ends and the independent variables are the number of households and employment by type. They can be applied at the zone level to estimate the total number of truck trip ends per zone. Note that the two sources have different definitions of trucks for which rates are provided. NWRG defines rates for trucks of 14,000â28,000 pounds while PSRC defines rates for single-unit trucks of two to four axles, six or more tires, and 16,000â52,000 pounds. Both of these definitions exclude smaller trucks and commercial vehicles that may not be included directly in passenger travel models. Nonfreight truck trip rates. An example of daily trip rates for nonfreight trucks only (as opposed to all trucks, as shown in Table 4.22) is shown in Table 4.23. This table shows rates from NCHRP Synthesis of Highway Practice 298: Truck Trip Generation Data (Fischer and Han, 2001). A nonfreight truck trip table may be developed by adapt- ing an existing total truck table. If this is the case, care must be taken to avoid double counting the trucks that carry freight. It will be necessary to adjust the total truck trip rates and distributions to account for freight trucks, which are handled separately. Truck trip distribution. As is the case with freight modeling as discussed previously, the most common pro- cedure for distributing truck trips uses the gravity model. The calibration of friction factors should be consistent with observed truck travel. As examples, NCHRP Synthesis 384 presents friction factor curves for the Atlanta and Baltimore truck models, adjusted to provide the best fit with the known Truck Type 14,000 28,000 Pounds 2â4 Axles, 6+ Tire, Single Unit, 16,000â52,000 Pounds NWRG Survey PSRC Truck Model Land Use Production Attraction Production Attraction Households 0.011 0.011 0.0163 0.0283 Employment Agriculture/Mining/Construction 0.040 0.044 Agriculture 0.0404 0.2081 Mining 0.0404 10.8831 Construction 0.0453 0.0644 Retail 0.032 0.035 0.0744 0.0090 Education/Government 0.037 0.038 0.0135 0.0118 Finance, Insurance, Real Estate 0.008 0.008 0.0197 0.0276 Manufacturing Products 0.050 0.050 0.0390 0.0396 Equipment 0.0390 0.0396 Transportation/Utility 0.168 0.170 0.0944 0.0733 Wholesale 0.192 0.190 0.1159 0.0258 Source: Cambridge Systematics, Inc. (2008a). Table 4.22. Sample total truck trip rates by truck type and land use.
72 average trip lengths of trucks. Table 4.24 provides a summary of average trip lengths or travel times (if known), and date of origin, used by a sample of MPOs. 4.11 Highway Assignment All of the preceding sections have dealt with the devel- opment of trip tables. Assignment is the fourth step in a four-step travel demand model. This section deals with highway assignment while Section 4.12 deals with transit assignment. Highway assignment is the process by which vehicle trips for each origin-destination interchange included in the vehicle trip tables are allocated to the roadway network. The allocation process is based on the identification of paths through the network for each origin-destination interchange. The assignment process may be mode-specific with, for example, paths for single occupant vehicles being determined using different criteria than paths for multi- occupant vehicles or trucks. 4.11.1 Model Function There are a number of methods by which a trip table can be assigned to a network. All of these methods are basically variations of the formula: V t Pa ij ij ija= â ( )4-15 where: tij = The number of vehicle trips from origin i to desti- nation j; Pija = The probability of using link a on the path from origin i to destination j; and Va = The volume of vehicles on link a. While the algorithms and computer code required to efficiently solve the assignment problem, as well as the require- ments for storing the probability matrix, do not often lead to the assignment problem being defined in this way, describing the process in this manner does allow for the identification of features that distinguish the various assignment methods. When the probability matrix is predetermined in some manner that cannot be changed, the method is called a fixed path assignment. When the probability matrix takes on the value of one when the link is used and zero when the link is not used it is said to be an all or nothing (AON) assignment. When the cells of the probability matrix are calculated from a stochastic formula that calculates the percentage of trips to be assigned to a set of links contained in reasonable paths, the method is called a stochastic assignment. Land Us e Maricopa As so ciation of G overn me nts Southern California Associa tion of G overn me nt s Households 0.069 0.008 7 Employment Agriculture/M ining/Co nstr ucti on 0.106 0.083 6 Retail 0.132 0.096 2 Education/Go ve rnm en t 0.006 0.002 2 Fina ncial, Insura nce, Real Estate 0.021 Manufacturing Products 0.100 0.057 5 Tr ansportation/Utility 0.106 0.457 0 Wh olesale 0.106 0.065 0 Othe r 0.106 0.014 1 Note: Truck definition for Maricopa Association of Governments data is 8,000 to 28,000 pounds, while for Southern California Association of Governments it is 14,000 to 28,000 pounds. Source: Rates are from NCHRP Synthesis 298 (Fischer and Han, 2001) as cited in Cambridge Systematics, Inc. (2008a). Table 4.23. Sample nonfreight truck trip rates by land use. Truck Type Atlanta (1996) Baltimore (1996) Detroit (1999) Los Angeles (2000) Heavy 22.8 min. 34.0 min. 20.1 min. 24.1 miles Medium 19.9 min. 17.5 min. 20.5 min. 13.1 miles Light 16.2 min. 18.3 min. 5.9 miles Source: NCHRP Synthesis 384 (Kuzmyak, 2008). Table 4.24. Sample average truck trip lengths or travel times.
73 When the probability matrix takes on discrete values associated with the percentages of the trip table which are assigned in successive AON assignments, where between iterations the congested time is updated based on a com- parison of the assigned volume on a link to its capacity, new AON paths are then calculated, and those percent- ages are applied to each of the successive AON probabili- ties (i.e., one or zero), the method is called incremental capacity-restrained assignment. When the cells of the probability matrix are calculated from the percentage of the trip table assigned to successive applica- tions of AON as in the incremental capacity-restrained assign- ment, but those percentages are selected through an iterative process that will result in satisfying Wardropâs first principle, which states that âthe journey times in all routes actually used are equal and less than those which would be experienced by a single vehicle on any unused routeâ (Wardrop, 1952), the method is said to be a user equilibrium assignment. A vari- ant of this method, called stochastic user equilibrium, uses stochastic assignment rather than AON assignment in succes- sive steps to arrive at equal journeys on used paths, in which case the perceived times are said to be reasonably equal. A common method to determine the allocation of a trip table to successive iterations is the Frank-Wolfe algorithm (Frank and Wolfe, 1956). An additional consideration in assignment is the number of trip tables that will be assigned and the manner in which the trip tables are assigned. If the trip table is assigned to the network links prior to a user equilibrium assignment, for example by assigning that trip table to fixed or AON paths that do not consider congestion, that trip table is said to be preloaded. Those trip tables (i.e., classified by vehicle and/or purpose) that are assigned jointly in a user equi- librium assignment are said to be a multimodal multiclass assignment. The first three assignment processes previously describedâ fixed path, AON, and stochasticâare insensitive to congestion impacts that occur when demand for a network link approaches the capacity of the link. The last two assignment methodsâ capacity restrained and user equilibriumâexplicitly attempt to account for congestion impacts in the traffic assignment process. The last two procedures are typically preferred for future forecasts because they inject a level of realism into the assignment process through reductions of travel speeds as traffic volumes on links increase. In addition, the last two procedures are required if air quality impacts of various alter- natives or land use scenarios need to be estimated from traffic assignment results. While the first three assignment procedures are insensitive to congestion impacts, these can provide important analy- sis capabilities. For example, AON assignments are useful for determining travel desires in the absence of congestion impacts and are commonly used to preload truck trips and other external through-trip movements in regional models. Such information can also be useful in targeting transpor- tation improvements. In uncongested networks, stochastic assignment may be the only method available to represent user choices of similar alternative paths. In all capacity-restrained and user equilibrium assignments, link travel times are adjusted between iterations using a vehicle- delay function (sometimes referred to as a âvolume-delay,â âlink performance,â or âvolume-timeâ function). These func- tions are based on the principle that as volumes increase relative to capacity, speeds decrease and link travel times increase. One of the most common of these vehicle-delay functions was developed by the BPR, the predecessor agency of the FHWA. The BPR equation is: t t v c i i i i = + ï£«ï£ï£¬ ï£¶ï£¸ï£· ï£« ï£ï£¬ ï£¶ ï£¸ï£·0 1 Î± Î² ( )4-16 where: ti = Congested flow travel time on link i; t0i = Free-flow travel time on link i; vi = Volume of traffic on link i per unit of time (some- what more accurately defined as flow attempting to use link i); ci = Capacity of link i per unit of time (see below); a = Alpha coefficient, which was assigned a value of 0.15 in the original BPR curve; and b = Beta coefficient, the exponent of the power function, which was assigned a value of 4 in the original BPR curve. While ti represents the link i travel time and is expressed in units of time (usually minutes), it may also reflect other costs associated with travel, especially tolls and auto operating costs such as fuel costs. The value ti (and t0i) may therefore be represented by something like Equation 4-17: t tt di i i i= + +K1 K2 toll 4-17 ( ) where: tti = Actual travel time on link i; di = Length of link i in units of distance (e.g., miles); tolli = Per vehicle toll on link i in monetary units; K1 = Parameter reflecting marginal per-mile auto oper- ating cost and conversion from monetary to time units; and K2 = Parameter reflecting conversion from monetary units to time units. Parameter K2, therefore, represents the inverse of the value of time. Note that the value of time is also an implied
74 parameter in mode choice (see Section 4.7.4). However, the values of time implied by mode choice model parameters are often lower than those used in highway assignment, especially those used in toll road planning studies. This reflects, in part, the different market segments analyzed in each model com- ponent (travelers by all modes for mode choice, highway users in potential toll corridors in assignment), but also the artificial separation of mode and route choices in a four-step model. A 2003 memorandum (U.S. Department of Trans- portation, 2003) indicated a âplausible rangeâ for the value of time in year 2000 dollars for local travel to be $7.90 to $13.40 per hour, with a recommended value of $11.20 for autos (the value for trucks was $18.10). These values are substantially higher than the values of time implied by the mode choice parameters presented in Section 4.7.4. It is customary to express capacity in vehicles per hour. In models where daily (weekday) highway assignment is used (and therefore the volume variable is expressed in vehicles per day), the hourly capacity estimates must be converted to daily rep- resentations. This conversion is most commonly done using factors that can be applied to convert the hourly capacity to effective daily capacity (or, conversely, to convert daily trips to hourly trips, which is equivalent mathematically). These factors consider that travel is not uniformly distributed throughout the day and that overnight travel demand is low. The conver- sion factors are therefore often in the range of 8 to 12, as opposed to 24, which would be the theoretical maximum for an hourly-to-daily factor. [These factors are sometimes referred to as âCONFAC,â the variable name in the Urban Transporta- tion Planning System (UTPS) legacy software on which many aspects of modern modeling software are still based.] These types of conversion factors continue to be needed in models where time periods for assignment greater than 1 hour in length are used. In such cases, the factors convert the hourly capacity to the capacity for the appropriate time period. For example, if a morning peak period is defined as 6:00 to 9:00 a.m., the conversion factor will convert hourly capacity to capacity for the 3-hour period. It is important to consider that travel is not uniformly distributed throughout the 3-hour period, although it is likely to be more evenly dis- tributed over a shorter time period, especially a peak period that is likely to be relatively congested throughout. The theo- retical maximum for the factor is the number of hours in the period (three, in this example), and in a period where there is roughly uniform congestion throughout the peak period, the factor could be close to three. Typical factors for a 3-hour peak would range from two to three. The factors for longer off-peak periods would likely be well lower than the theoreti- cal maximum. Depending on the application, the value of ci (Equation 4-16) may not represent the true capacity of the link in a traffic oper- ations sense (see Section 3.3). In the original BPR function, ci represented the limit of the service volume for LOS C, which is often approximately 70 percent of the âultimateâ capacity (at LOS E), although the conversion between these two values is not simple. Current best practice is to use the LOS E capacity for the following reasons (Horowitz, 1991): 1. Ultimate capacity has a consistent meaning across all facility types while design capacity does not. For example, it is a relatively simple matter to relate the capacity of an intersection to the capacity of the street approaching that intersection. 2. Ultimate capacity is always easier to compute than design capacity. Finding the design capacity of a signalized inter- section is especially difficult. 3. Ultimate capacity can be more easily related to traffic counts than design capacity, which would also require estimates of density, percent time delay, and reserve capacity or stopped delay. 4. Ultimate capacity is the maximum volume that should be assigned to a link by the forecasting model. Design capacity does not give such firm guidance during calibration and forecasting. For these reasons, ultimate capacity (LOS E) is assumed to be used for capacity in the remainder of this chapter. As noted in Section 3.3.1 of this report, detailed capacity calculations as presented in the Highway Capacity Manual may not be pos- sible in travel model networks as some of the variables used in the manual are not available in these networks. 4.11.2 Best Practices While there is much ongoing research into the use of dyna mic assignment and traffic simulation procedures, the state of the practice for regional travel models remains static equilibrium assignment. There has been some recent research into more efficient algorithms to achieve equilibrium than Frank-Wolfe, and some modeling software has implemented these algorithms. Since most urban areas are dependent on the major proprietary software packages for their model applica- tions, static equilibrium procedures will continue to be used for regional modeling for the time being. There have been some highway assignment implementations that incorporate node delay as a better way of identifying intersections that may cause congestion on multiple links, sometimes referred to as junction modeling. Some modeling software has incorporated methods to consider node delay. For project planning and design applications to determine link volumes, the use of post-processing techniques such as those discussed in NCHRP Report 255: Highway Traffic Data for Urbanized Area Project Planning and Design (Pedersen and Samdahl, 1982) are recommended rather than reliance on raw
75 model output. Post-processing techniques are recommended because the assigned volumes on individual links can have substantial error, as noted when comparing highway assign- ment outputs to traffic counts (although count data are often sampled and also have associated error). 4.11.3 Basis for Data Development Horowitz (1991) fit the BPR formula (among others) to the speed/volume relationships contained in the Highway Capacity Software, Version 1.5, based on the 1985 Highway Capacity Manual (Transportation Research Board, 1985). The results of this work are presented in Section 4.11.4. These values were also presented in NCHRP Report 365. There is a wealth of literature on volume-delay function form and parameters, including the 2010 Highway Capacity Manual, that the analyst may wish to consult. The MPO Documentation Database provided BPR function parameters from 18 MPOs for freeways and arterials. These also are presented in Section 4.11.4. 4.11.4 Model Parameters The BPR formula parameters estimated by Horowitz are presented in Table 4.25. The speeds shown in this table rep- resent facility design speeds, not model free-flow speeds. According to the information in the MPO Documentation Database, the BPR formula is the most commonly used volume- delay function. MPOs use a variety of values for the a and b parameters, and most use different parameters for freeways and arterials. Table 4.26 presents BPR function parameters used by 18 MPOs for which data were available from the database. Figures 4.6 and 4.7 graph the ratios of the congested speeds to free-flow speeds on facilities at different volume/capacity Freeways Multilane Highways Coefficient 70 mph 60 mph 50 mph 70 mph 60 mph 50 mph 0.88 0.83 0.56 1.00 0.83 0.71 9.8 Î± Î² 5.5 3.6 5.4 2.7 2.1 Source: Horowitz (1991). While the terms âfreewaysâ and âmultilane highwaysâ are not defined, it can be assumed that the term âfreewaysâ refers to modern âInterstate standardâ limited access highways and âmultilane highwaysâ includes lower design roadways, including those without access control. Table 4.25. BPR coefficients estimated using the 1985 Highway Capacity Manual. Table 4.26. BPR function parameters (morning peak period). Average Minimum Maximum Standard Deviation n Freeways MPO population greater than 1,000,000 13 0.48 6.95 0.10 4.00 1.20 9.00 0.36 1.39 MPO population between 500,000 and 1,000,000 5 0.43 8.82 0.15 5.50 0.88 10.00 0.39 1.92 MPO population between 200,000 and 500,000 1 0.15 8.00 0.15 8.00 0.15 8.00 MPO population between 50,000 and 200,000 1 0.15 8.80 0.15 8.80 0.15 8.80 Arterials MPO population greater than 1,000,000 11 0.53 4.40 0.15 2.00 1.00 6.00 0.29 1.66 MPO population between 500,000 and 1,000,000 4 0.42 5.20 0.15 3.20 0.75 10.00 0.29 3.22 MPO population between 200,000 and 500,000 1 0.50 4.00 0.50 4.00 0.50 4.00 â â MPO population between 50,000 and 200,000 2 0.45 5.60 0.15 3.20 0.75 8.00 0.42 3.39 n = number of models in MPO Documentation Database Source: MPO Documentation Database. Î± Î² Î± Î² Î± Î² Î± Î²
76 Figure 4.6. Freeway congested/free-flow speed ratios based on BPR functions. 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Congested/Free Flow Speed Ratio V/C Large MPO Medium MPO Medium MPO Medium MPO Medium MPO Small MPO Average Curve Source: MPO Documentation Database. Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Figure 4.7. Arterial congested/free-flow speed ratios based on BPR functions. 0.00 0.20 0.40 0.60 0.80 1.00 1.20 0.1 0 .2 0.3 0.4 0 .5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 Congested / Free Flow Speed Ratio V/C Large MPO Medium MPO Small MPO Average Curve Source: MPO Documentation Database. Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Large MPO Medium MPO
77 ratios using the BPR functions from the 18 MPOs. In addition, each graph includes an âaverageâ BPR function based on the curves shown in Figures 4.6 and 4.7. The average BPR func- tions differ from the parameter averages shown in Table 4.26 in that the functions were derived via linear regressions to match the averages of the congested/free-flow speed ratios for the different volume/capacity ratios.10 The resulting average BPR functions are: â¢ Freeways: â Alpha = 0.312. â Beta = 5.883. â¢ Arterials: â Alpha = 0.514. â Beta = 3.001. 4.12 Transit Assignment While highway assignment deals with the routing of auto- mobiles over a highway network, transit assignment deals with the routing of linked passenger trips (including walk and auto access and egress) over the available public transportation network. Differences from highway assignment include the following: â¢ The transit network includes not only links but also routes comprising the links, which represent the different transit services running between stops or stations; â¢ The flow unit in the trip table which is being assigned is passengers, not vehicles; â¢ The impedance functions include a larger number of level-of-service variables, including in-vehicle time, wait time, walk access and egress time, auto access and egress time, fare, and transfer activity; and â¢ Some paths offer more than one parallel service, sometimes with complex associated choices (e.g., express bus versus local bus service). 4.12.1 Model Function Transit assignment is closely tied to transit path build- ing. Typically, person trips estimated using a mode choice model are assigned to the transit paths built as input to the mode choice model. The typical transit assignment process is different from traffic assignment processes, where auto paths based on estimated congested travel times are input to a mode choice model and the output vehicle trips are assigned to the roadway network using an equilibrium or other capacity-restrained assignment method. The mode choice-traffic assignment process may require a feedback or iterative process to ensure that estimated roadway speeds used for mode choice (as well as for trip distribution) match the roadway speeds resulting from the traffic assignment process. Speeds on the transit network may also be affected by the roadway speeds, depending on the software and network coding methodologies.11 The transit speeds used to develop the transit paths used to construct the travel time and cost skims for input to mode choice and the resulting transit assignment should match. In the past, transit path-building and assignment were generally performed in production-attraction format with the production zone being defined as the home zone for home-based trips and the attraction zone being defined by the nonhome location. This procedure can be used to deter- mine boardings by line, revenues, and maximum load points. It has often been performed by time of day with transit paths and assignments being performed for morning peak and mid-day periods. Such an approach accounts for time-of-day differences in transit services with the afternoon peak period being assumed to be symmetrical to the morning peak period (which is an oversimplification). In regions offering nighttime transit service, the night service may either be modeled as a separate time period or aggregated with the mid-day service for assignment purposes. Finally, some areas provide the same basic levels of transit service throughout the day and, as a result, perform nontime-specific, or daily, transit path-building and assignments. More recently, some regions have started building transit paths in origin-destination format. This approach has been used to account for directional differences in service by time of day. Service differences may be due to different frequencies of service, different service periods, or different transit speeds due to different levels of traffic congestion. The information is particularly important for tour-based and activity-based modeling procedures, although it can also be used with trip- based modeling procedures. 4.12.2 Best Practices Table 4.27 summarizes the time-of-day directional assign- ment procedures for 23 MPOs. Of the 20 MPOs reporting the use of time-of-day transit paths, 17 indicated the trip purposes assigned to each time-of-day network. Four of the 17 MPOs assigned home-based work trips to the peak period 10Note that volume/capacity ratios over 1.0 are shown in Figures 4.6 and 4.7. In effect, what is really being shown are the modeled demand/ capacity ratios. In the real-world situations, traffic volumes cannot exceed roadway link capacities. 11In many models, run times are hard coded on transit lines resulting in no direct sensitivity to highway speed changes. However, good practice still dictates reviewing transit speeds for general consistency with the underlying highway speeds.
78 network and the remaining 13 estimated transit trips for each trip purpose by time of day and assigned the trips using time- of-day transit paths. Transit path-builders can be characterized into two basic groups: shortest path and multipath. Shortest path methods find the shortest path through the network, based on a speci- fied linear combination of impedance components including items such as walk or drive access time, wait time, in-vehicle time, transfer time, additional transfer penalties, walk egress time, and fare. The coefficients of the linear combination are usually based on the relative coefficients of these variables in the mode choice model.12 Multipath procedures find multiple âefficientâ paths through the transit network based on similar criteria. The multipath methods may include multiple paths for each interchange even if the alternate paths do not mini- mize total travel impedance. The inclusion or exclusion of alternate paths is based on a specified set of decision rules. The use of shortest path or multipath methods should be coordinated with the type of mode choice model used. Some mode choice models incorporate path choice in the mode choice structure. For example, in regions with both bus and rail service, the mode choice model might include walk to bus only, walk to rail only, and walk to bus/rail as separate modes. If the mode choice model is structured to include path choice, the use of a shortest path procedure is reasonable although careful use of a multipath method is also appropriate. Alternatively, some regions simply model transit use for all combined transit modes in the mode choice model. In these regions, use of a multipath method can be used to determine path choice. Of the 22 MPOs reporting their transit path- building procedures, 17 used shortest path for their peak period and off-peak period walk-to-transit paths and five used multipath procedures. For drive access to transit paths, 20 of the 22 MPOs used shortest path for their peak period and off- peak period drive-to-transit paths and two used multi path procedures. FTA has developed a number of guidelines for transit path-building and mode choice for Section 5309 New Starts applications. The FTA guidelines have influenced path-building procedures and parameters and should be reviewed prior to model development, especially if a New Starts application is being considered for a region. Two issues for transit path-building and the transit assign- ment process are: â¢ Source of bus speedsâAre bus speeds related to auto speeds in a reasonable manner, and do they reflect observed speeds? â¢ Consistency with mode choice parametersâAre transit path-building and assignment parameters consistent with the relationships used in the mode choice model? Table 4.28 summarizes the sources of bus speeds and the consistency of the path-building parameters with mode choice parameters for the 21 MPOs reporting the information. Information is reported for only the morning peak and mid- day networks since all of the MPOs had those two networks. 4.12.3 Basis for Data Development The basis for data development for the model parameters described below is the information obtained from 23 MPO models in the MPO Documentation Database, as discussed in the previous section. 4.12.4 Model Parameters The main model parameters for transit path-building are the relationships between the components of transit travel impedance. Common parameters, which are usually expressed in terms of their relationship to in-vehicle time, include: â¢ Monetary cost/fare (value of time) including transfer costs; â¢ Initial wait time; Number of MPOs MPO Regional Population Production-to-Attraction Origin-to-Destination A.M. Peaka Mid- Day P.M. Peak Night Daily A.M. Peak Mid- Day P.M. Peak Night Daily More than 1,000,000 12 11 3 3 0 3 3 3 1 0 200,000 to 1,000,000 3 3 1 0 3 1 1 1 0 0 50,000 to 200,000 1 1 0 0 0 0 0 0 0 0 a Includes MPOs assigning both morning and afternoon trips to the morning peak network in production-to-attraction format. Source: MPO Documentation Database. Table 4.27. MPOs using transit assignment procedures. 12As discussed in Section 4.7, there is usually a different mode choice model for each trip purpose, with different coefficients. While devel- opment of a separate set of transit paths for each trip purpose would be possible, transit trips are usually not assigned by purpose, and so a single set of paths is used. This is usually based on the home-based work mode choice model.
79 â¢ Transfer wait time; â¢ Transfer penalty time; â¢ Dwell time; â¢ Walk time; and â¢ Auto time. Typically, the auto time and dwell time parameters are set to 1.0, as both are actually in-vehicle time. While some MPOs consider fares in their transit path-building and assign- ment procedures, there is little variation in fares in some loca- tions, and so fare is often excluded from the path-building impedance. Two of the main parameter relationships that affect transit path-building and transit assignment are the ratio of walk time to in-vehicle travel time and ratio of wait time to in-vehicle travel time. Table 4.29 summarizes the ratios of walk time to in-vehicle travel time, and Table 4.30 summarizes the ratios of wait time to in-vehicle travel time, from models included in the MPO Documentation Database. As can be seen in the tables, there is little variation in the mean values of ratios, with all of the means falling in the range 2.0 to 3.0. Detailed inspection of the reported ratios shows that most of the ratios are 2.0, 2.5, or 3.0. This result is not surprising since FTA New Starts guidelines ask applicants to âprovide compelling evidenceâ if the ratio of out-of-vehicle time to in-vehicle time in a mode choice model is outside of the range of 2.0 to 3.0 and the guidelines also encourage consistency between transit path- building and mode choice model parameter relationships. Regional Population Bus Speeds Related to Auto Speeds (Yes/Total Reporting) Path-Building Parameters Consistent with Mode Choice (Yes/Total Reporting) Morning Peak Mid-Day Morning Peak Mid-Day More than 1,000,000 14/17 13/17 13/17 12/17 200,000 to 1,000,000 2/4 2/4 2/5 2/4 50,000 to 200,000 0/0 0/0 0/0 0/0 Source: MPO Documentation Database. Numbers refer to number of agencies in the database for each item. Table 4.28. Transit assignment consistency reported by MPOs. Regional Population Peak Period Off-Peak Period Walk Access Drive Access Walk Access Drive Access Mean Min Max Mean Min Max Mean Min Max Mean Min Max More than 1,000,000 2.2 1.5 3.0 2.2 1.5 3.0 2.4 1.5 3.0 2.3 1.5 3.0 200,000 to 1,000,000 2.4 1.5 3.0 2.0 1.0 3.0 2.4 1.5 3.0 2.0 1.0 3.0 50,000 to 200,000 â â â â â â â â â â Source: MPO Documentation Database. Table 4.29. Ratios of walk time to in-vehicle time reported by MPOs. Regional Population Peak Period Off-Peak Period Walk Access Drive Access Walk Access Drive Access Mean Min Max Mean Min Max Mean Min Max Mean Min Max More than 1,000,000 2.1 1.5 2.6 2.1 1.5 2.6 2.1 1.5 3.0 2.2 1.5 3.0 200,000 to 1,000,000 2.9 1.5 4.5 3.0 1.5 4.5 2.9 1.5 4.5 3.0 1.5 4.5 50,000 to 200,000 ââ â â â â â â â â â Source: MPO Documentation Database. Table 4.30. Ratios of wait time to in-vehicle time reported by MPOs.