Value of Travel Time Reliability in Transportation Decision Making: Proof of Concept—Portland, Oregon, Metro (2014)

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14 C h a p t e r 3 3.1 Definition of travel time reliability According to a recent survey (Cambridge Systematics 2013b), there are two fundamental definitions of travel time reliability: 1. Travel time reliability is defined in terms of travel time variability (i.e., how travel times vary over time, such as hour to hour or day to day). 2. Reliability is defined as the probability that a certain trip (from a given origin to a given destination) can be made successfully within a specified interval of time. This mea- sure is the probability of a “nonfailure over time” and is synonymous with “on-time performance.” Within this definition, a clear definition of “failure” in terms of travel time is required. One significant difference between these two definitions is that the latter measures the variation in individual traveler behavior. The notion of an “on-time arrival” varies from one traveler to another (i.e., depending on whether the individual is risk averse). The magnitude of any desired safety margin for each individual traveler also varies. In comparison, the first definition measures the average variation of all travelers in the system without elaboration of each individual traveler’s behavior. One fundamental assumption of the first definition is that travel times among links, and hence among routes, have a continuous probabilistic distribution function. From the standpoint of improving the quality of service, the first defi- nition requires a reduction in travel time uncertainty per se. The second definition, however, also includes adjusting trav- elers’ expectation of travel time variability (i.e., the individual- specific definition of “failure” or “on time”). To specify the research direction more clearly, the definition of reliability in the present project refers to the uncertainty of travel time (i.e., variability) from day to day, but for the same individual trip with the same departure time. The variance of travel times then contains two parts: vari- ance resulting from recurrent congestion and variance result- ing from nonrecurrent congestion. Recurrent congestion is predictable, and experienced individuals may be prepared to accept the variance of travel time for similar trips. Nonrecur- rent congestion typically is unexpected, difficult to predict, and more reluctantly accepted by travelers. In this project’s definition of travel time variability, the term “reliability” con- tains the variance of travel time resulting from both recurrent and nonrecurrent congestion. However, if one looks at the travel time variance under recurrent congestion, particular in the day-to-day context, the variability is small and nearly constant; travel time in the peak period is significantly longer than in the off-peak period, but with little uncertainty. Thus, we may represent equilibrium between the variance of travel time from recurrent congestion and travelers’ preparedness to deal with the variance of travel time. In comparison, travel time variance caused by nonrecurrent congestion is signifi- cant and may cause much larger variability in day-to-day travel times. 3.2 Brief review of reliability Studies 3.2.1 Measuring Travel Time Reliability Table 3.1 summarizes the commonly seen measurements of travel time reliability found in prior research and practice. 3.2.2 Measuring Travel Time Reliability at the Route Level and O-D Level Mean variance travel time statistics are based on travel time distribution. The travel time distribution is easily assessed on links, but it is difficult to assess on routes and among origin– destination (O-D) pairs. The challenge of measuring route- based variance lies in the correlation of travel times between links. In most practice, it is assumed that link travel times are Local Method for Determining Reliability Measures and Value of Travel Time Reliability

15 independent, and then both mean and variance of travel time are additive, as shown in Equations 3.1 and 3.2: ∑µ = µ ∈ (3.1)r a a r ∑σ = σ ∈ (3.2)2 2r a a r where r is route, and a is link. The independency assumption perhaps is problematic as link travel times are not independent if queue spillovers occur. If the travel times between links are perfectly corre- lated, then variance of travel time on routes is much higher than the simple algebra sum of variance of travel times on links. Taylor (2009) proposed a route-based reliability measure- ment based on speed as shown in Equation 3.3. , 1.44 1 (3.3) 2 R r t V V V Nrt rtd rtd rt ∑ ( )( ) = − − where R(r, t): reliability metric; r: route index; t: time index; d: day index; Vrtd: average speed of all vehicles on route r departing at time t on day d; – Vrt: average speed of all vehicles on route r departing at time t; and Nrt: sample size of vehicles on route r departing at time t. Taylor’s equation can be conveniently used in a simulation environment. Speeds of all vehicles on each route with each departure time clock are known in the simulator, and thus the route reliability metric in Equation 3.3 can be trivially com- puted for both freeways and arterials. 3.2.3 Valuating Travel Time Reliability Due to the two definitions of travel time reliability, there are two methods to value travel time reliability: the mean vari- ance method and the schedule delay method. 3.2.3.1 Mean Variance Method The mean variance method valuates travel time variability as shown in Equation 3.4: GC VOTT VTTR (3.4)i i= µ + σ where GC: generalized cost; VOTT: value of travel time; and VTTR: value of travel time variability. Table 3.1. Reliability Measurements Reliability Measurement Definition Annotation Statistics related Mean of travel time (µ) Mean of travel time Standard deviation (s) Standard deviation of travel time Coefficient of variation (s/µ) Standard deviation divided by mean Buffer index (BI) 95th percentile time ˆ ˆ − µ σ µˆ: estimated mean sˆ: estimated standard deviation Planning time index 95th percentile time free flow travel time Skew statistic 90th percentile time 50th percentile time 50th percentile time 10th percentile time − − Congestion index ˆ average free flow travel time µ Percentage on time trips travel time 1.1 ˆ total trips < µ Delay related Frequency of running behind schedule Self-explanatory For transit Lateness measure Average delay (unexpected waiting time per trip) For transit Risk measure Probability of delay of certain length

16 The user costs now possess two terms. One term is the usual cost of travel time measured by VOTT multiplied by the mean value of travel time µ, and the other term is the cost of travel time variability, measured by VTTR multiplied by the standard deviation of travel time s. VOTT is well calibrated and typically is known for most travel demand models in metropolitan areas, but VTTR is less known. In a more convenient way, practitioners use the con- cept of the reliability ratio (RR), which is the ratio of VTTR divided by VOTT, defined by Equation 3.5: =RR VTTR VOTT (3.5) If RR can be established and VOTT is known, then VTTR can be computed. Several facts known for RR (Cambridge Systematics 2012) include the following: • Past studies of reliability valuation for passenger travel have found a wide range of values, but more recent studies appear to be coalescing around an RR of 1.0 (Lam and Small 2001). • Many non-U.S. countries have undertaken their own review of reliability valuation and have recommended specific val- ues for VTTR and/or RR for use in economic analyses. They include 44 The Netherlands: 0.8 and −1.4 for personal auto and public transit, respectively 44 New Zealand: 0.8 for personal autos 44 Australia: 1.3 for personal autos 44 Sweden: 0.9 for all trip types 44 Canada: 1.0 for all trip types • Use of a single (composite) RR in technical analyses may be misleading. The RR value may vary according to number of factors. Researchers have noted that just as for VOTT, VTTR can vary by a number of factors. SHRP 2 Projects C04 and L04 derived an expansive set of RR for combinations of trip type, income, and trip length. In general, the influences of these factors are 44 Trip type: the RR for the trip to work is higher than the trip from work or nonwork trips 44 Income: for the work trip, lower income groups have a higher RR 44 Trip length: for the work trip, RR decreases with trip distance 44 Freight: some evidence exists that both the VTTR and RR are higher than for passenger travel, but these values are highly dependent on the type of commodity. 3.2.3.2 Schedule Delay Method In the schedule delay method, the utility of a trip is measured by Equation 3.6: ( ) ( ) ( ) ( )= α + β + γ + θi i iSDE SDL (3.6)E U E T E E pL where E(U): expected value of disutility; E(T): expected value of trip travel time; E(SDE): expected value of schedule delay earlier; E(SDL): expected value of schedule delay late; and pL: probability of being late. The stated-preference survey revealed that g > b > a. If it is assumed that (1) the travel time distribution is independent of departure time, (2) the standardized distri- bution of trip duration F is constant, (3) q = 0, and (4) an agency can choose departure time to maximize the expected disutility, then optimal maximum expected utility is given by Equation 3.7: ( ) ( )= αµ + β + γ Φ ββ + γ     σi , (3.7)maxE U H where Φ ββ + γ    ,H is the mean lateness factor depending on both the standardized travel time distribution and preference parameters of being late and earlier (Fosgerau and Karlstrom 2010). Note that Φ ββ + γ    ,H takes into account the skew of the travel time distribution. This result exhibits the connec- tion between two methods of mean–variance and schedule delay, and the RR in theory is given by Equation 3.8: = β + γ α Φ ββ + γ    RR , (3.8)H 3.2.4 Predicting Travel Time Reliability Mean travel time can be forecast by traffic assignment with the future-year data, but this is usually not the case for travel time variability. Existing practice and analytical methods described in the literature offer two methods to predict travel time vari- ability: the statistical method and the simulation method. 3.2.4.1 Statistical Method The statistical method assumes (and this assumption is partially supported by the data) that the standard deviation of travel time variability, or other similar reliability measurements [e.g., travel time index (Cambridge Systematics 2012)] could be interpreted as a function of mean of travel time (µ) or mean of travel time per mile (Northwestern University Transportation Center 2009). Several examples of regression models found in practice and the literature are summarized as follows: • Dutch Study (Peer et al. 2009) FFT1 2 3v c i ( )( )σ = β µ − +β β

17 where FFT is free-flow time and v/c is the ratio of volume divided by capacity. • Eliasson (2009) σ = −i iconst TT TT FFT 11.2 where const: a constant parameter; TT: travel time; and FFT: free-flow travel time. • Leeds Model (Vovsha 2009) ( ) ( )σ = µ −i i i0.148 FFS 1.61.781 0.781 0.285D D D where D is distance, and FFS is free-flow speed. 3.2.4.2 Simulation Method The simulation approach is usually implemented with the Monte Carlo method in conjunction with traffic flow models (Clark and Watling 2005). Monte Carlo methods generate samples with known probability density functions, run simu- lations, and produce aggregate statistical results. If incidents, which are regarded as a major source of travel time variabil- ity, can be predicted using a hazard model, then the resultant travel time variability could be produced using a Monte Carlo method (Dong and Mahmassani 2011). The simulation methods based on Monte Carlo are pri- marily seen in theoretical studies. These methods are seldom seen in practical applications, partly because (1) it is difficult to trace all possible sources that influence travel time reliabil- ity and difficult to validate the probability density function of those sources for future years, and (2) the approach is computationally expensive. 3.3 First Workshop: early Stage project planning and Coordination Two workshops were held in Portland, Oregon. These work- shops served to engage local policy makers and obtain feed- back with regard to the outcomes of this research project. The objective of the first workshop was to introduce key stakeholders of the Southwest Corridor project to the research agenda. Items discussed included the goals, scope, and role of the research as it related to the corridor project, the methods previously used to measure reliability, and the research oper- ation plan. The first workshop took place on July 9, 2013. In addi- tion to the project team, which included Portland Metro, University of Arizona, RST International Inc., and the Trans- portation Research Board (TRB) supervisory team, the tech- nical advisory committee for the Southwest Corridor study also attended the workshop. The technical advisory com- mittee membership included the Oregon Department of Transportation (DOT), City of Portland, City of Tigard, City of Sherwood, Washington County, TriMet, and other stakeholders. Workshop participants were first introduced to the project objectives, scope, and tasks in order for them to understand their role in this project and to set their expectations properly. After lively discussions on the notion of reliability and the reliability measures, participants engaged in a hands-on stated- preference exercise as part of the workshop. This exercise, which is discussed in Section 3.3.1, aimed to engage work- shop participants in an active cognitive process to elucidate their collective assessment of the value of travel time reliabil- ity (VTTR). The exercise was a simple binary choice of two alternate routes with varying travel time and reliability char- acteristics. This method was inspired by a recent Dutch study (Significance et al. 2013). The 20 workshop attendees included the following: • Project supervisory team—TRB • Project team—Portland Metro • Policy team 44 TriMet 44 Washington County 44 City of Tigard 44 Oregon DOT 44 City of Sherwood 44 City of Portland • Project team—University of Arizona • Project team (in kind)—University of Queensland (tentative) • Oregon DOT Transportation Planning and Analysis Unit observer. 3.3.1 VTTR Estimation Method and Decision Context The high-level concept proposed by the research team to estimate the utility function is given by the following equa- tion. The binary logit model was intended to represent the choice decision of interest. The utility function set up for this study is = α + α + αTT TR0 1 2U where TT = average route travel time; TR = standard deviation of the route travel time observa- tions; and ax = alternative specific constant or attribute coefficients.

18 RR can then be calculated as 1 2 α α because RR is calculated as the ratio of VOTT to VTTR, and both VOTT and VTTR are calculated with respect to a cost variable, which is intention- ally left out in this utility function. Mathematically, the coef- ficient of the cost term is canceled out when calculating RR. For a general-purpose survey the actual number of variables in the utility function would need to be more comprehensive, but because the purpose of this method is to obtain the inter- attribute relationship RR, then this utility function, with a limited number of generic variables, would be sufficient bar- ring that the overall goodness of fit may not be as high as if other relevant variables were to be included. The workshop exercise applied a simple binary route choice problem as the decision context setup. Route 1 was indicated in red, and Route 2 was in blue (Figure 3.1). Such a color scheme was kept consistent throughout the engagement process to ensure consistency in cognition. 3.3.2 Stated-Preference Problem Preparation The exercise technology was based on a classroom interactive learning module powered by Turning Technologies (Turning Technologies 2014). The technology has often been used for real-time in situ assessment of audience opinions by asking selected questions at the end of each module. Several types of questions can be displayed, but the most commonly used type of question is the multiple choice question. The ques- tions were set up using a procedure from a software package provided by Turning Technology that embeds a specialized function into Microsoft PowerPoint. Figure 3.2 is an example question prepared in a Turning Technology embedded PowerPoint slide. One can see that two route options are presented. Each route is given start time information and five past travel time observations. Each of the past experience observations is represented by both travel time and arrival time (by taking arrival time plus the start time). The five observations allowed respondents to assess both travel time average and variance simultaneously. The setup of the questions was inspired by a recently published travel time reliability report (Significance et al. 2013). A total of 20 questions were generated for this workshop. Twenty questions were chosen with the aim of collecting suf- ficient data without tiring participants with an excessive num- ber of questions. In each question, the attribute values of both routes were generated by a random process following a log- normal distribution with a user-specified mean and standard deviation input. Minor manual adjustments were performed to fine-tune the variability and average. In the example shown in Figure 3.2, Route 1 was given a higher mean and lower stan- dard deviation than the same values given for Route 2. The workshop participants were provided with a clicker and needed only to press the appropriate number button on the clicker when asked to make a choice for the type of question illus- trated in Figure 3.2. A wireless receiver was inserted into the USB port of the main computer to take signal inputs from all clickers, and polling was closed when all participants had entered their answer, usually in about 10 to 15 seconds. 3.3.2.1 Model Estimation Results Once the polling was closed, the PowerPoint immediately dis- played the aggregated choices by all participants, as shown in Figure 3.3. In this example, 21% of the participants chose Route 1 and 79% choose Route 2. One of the team members asked participants to discuss the reasons and considerations that led them to make a certain choice. Such a process provided the following advantages: • Participants were quickly engaged in lively discussions. • The instant feedback mechanism allowed them to review their personal choice in comparison to choices made by peers. • The variability of choices could be observed by the choice breakdown. Figure 3.1. Illustration of route choice exercise. Figure 3.2. Example route choice question.

19 After the workshop, the research team exported and pro- cessed the collected data into the format needed for the model estimation software. The study initially used the easy logit model developed by Frank Koppelman, an emeritus North- western University professor in transportation econometrics. Later, the model estimation tasks were performed using R. The model estimation results in Table 3.2 indicated a desir- able goodness of fit, with an adjusted Rho square valued at 0.34. The t-statistics for both generic variables, travel time (average) and travel time reliability (measured as standard deviation), were significant at -6.85 and -4.39, respectively. The sign of the coefficients is negative, which is intuitive. The resulting RR is 0.76, which is consistent with that reported in the literature; recall that the recent Dutch model reported a general value of 0.6 (Significance et al. 2013), as well as the following: • The Netherlands finding (passenger car) 44 Home-to-work trip (�3.75 versus �9.25) = 0.4 44 Business trip (�30.0 versus �26.5) = 1.1 44 Average (�5.75 versus �9.0) = 0.6; and • The Netherlands finding (transit) 44 Home-to-work trip (�3.25 versus �7.75) = 0.4 44 Business trip (�21.75 versus 19.0�) = 1.1 44 Average (�3.75 versus �6.75) = 0.6 Despite a large body of research on the value of reliability, obtaining a value that is plausible and acceptable and permit- ted by project scope was a challenging task. Considering the tight schedule to accomplish all the required project tasks, the research team employed a cost-effective method and a locally reasonable approach to obtain the local value. This local value was primarily used for the proof-of-concept, policy-maker engagement purpose of this project, rather than for a general- ized, actual policy-making application. It was jointly agreed by the research team and the policy group that a small-scale, stated-preference–based route choice survey would be used for the specific purpose of this research. The value obtained from the proposed method will not be sufficient for a general purpose. Discussions on how to extend the proposed method to a generalized context will be discussed. 3.4 General Concepts for travel time reliability Measure and Value of reliability 3.4.1 Determining a Travel Time Reliability Measure The L35A research team and the Metro policy group agreed to select standard deviation as the measure of reliability in this research due to the following considerations: 1. Participants at the first workshop expressed a general con- sensus that some form of expression of dispersion is an acceptable reliability measure. Although multiple mea- sures exist in reality under different decision contexts, only one measure could be used for this study, and dispersion was considered adequate. 2. Using standard deviation allowed the model estimation results to be consistent with results in the literature, par- ticularly the latest comprehensive Dutch study concerning travel time reliability (Significance et al. 2013). Figure 3.3. Aggregated route choice decision for Question 18 (Question 18 is shown in Figure 3.2). Table 3.2. Multinomial Logit Model Estimation Results Parameter or Statistic Estimated Value t-Statistic Generic Parameters Travel time (average) -0.1629 -6.8491 Travel time reliability (standard deviation) -0.1243 -4.3939 Alternative Specific Parameters Constant -0.7344 -3.7392 Model Statistics Log likelihood at zero -263.3959 Log likelihood at constants -215.8566 Log likelihood at convergence -138.6865 Rho squared w.r.t. zero 0. 4735 Rho squared w.r.t. constants 0.3575 Adjusted rho squared w.r.t. zero 0.4621 Adjusted rho squared w.r.t. constants 0.3466 Number of cases 380 Number of iterations 18 Note: w.r.t. = with respect to.

20 3. Dispersion is consistent and measurable using the proposed SHRP 2 L03 approach (Cambridge Systematics 2013a) with DynusT and FAST-TrIPs. 3.4.2 Determination of Travel Time Reliability Without overextending the scientific merit of using a simple interactive tool like the clicker, the workshop exercise did provide an effective situational engagement experience for participants, and it also produced desirable model estimation outcomes. After extensive discussion among L35A research team members and with TRB, the L35A research team decided to refine the questions and re-conduct a similar exercise with internal staff selected by Metro. The purposes of this second exercise were to 1. Refine the attribute values for questions. 2. Incorporate transit reliability into question sets. 3. Introduce trip purpose into the question set up so that responses were more contextual and became more consis- tent with the literature, which would indicate that the value of reliability could be highly related to trip purpose. This procedure allowed the research team to reasonably esti- mate the RR for both automobile and transit modes for the pur- pose of this project despite various limitations. RR also enabled estimation of the VTTR through the following rationale: ( ) =Reliability Ratio RR VTTR VOTT therefore = ×VTTR RR VOTT RR is estimated as described above. The VOTT is known in the current Metro travel demand model (TDM) and has been established by Metro through past effort so VOTT should not be changed by this survey. Instead, the survey focused on esti- mating the relativity of VOTT and VTTR; once this relation- ship is established, VTTR can be reasonably inferred. This method of estimating VTTR was considered accept- able by the policy group to avoid having to launch a new travel survey. This method is arguably theoretically sound, because prior studies have found both travel time and travel time reli- ability to be statistically significant when included in the same utility function, meaning that these two attributes are not highly correlated statistically. Adding the travel time reliability variable to the Metro utility function will not statistically change the coefficient for the travel time term. If these factors were to change, they would probably be scaled with a scaling factor, and the relative relationship would remain similar. Because RR was obtained in this study through an adequate stated-preference data collection procedure, the obtained RR was deemed reasonable, and thus deriving the value of travel time reliability by using the product of RR and the value of travel time was also considered reasonable. It is not the VTTR but instead the value of RR that is used in subsequent scenario analysis. More details on how the esti- mation results were used are presented in Chapter 5. 3.4.3 Validity of Reliability Ratio due to Limited Sample Size The L35A research team also explored the possibility of extend- ing the stated-preference survey for obtaining the RR by using a large external panel (20,000 members) maintained by Metro. This active panel has provided valuable inputs to various poli- cies contemplated by Metro in the past. To perform a similar survey with this panel was technologically feasible, but it was not within the scope of this project. Such a large survey would have required additional time and resources plus an institu- tional review board approval process and hence was deemed high risk from a project management standpoint. Nonetheless, this concept is worth exploring further. Without collecting regionwide data, the external validity of the estimated RR may be of concern if this value were to be applied to a real-world project selection process. The research team emphasized the research nature of L35A to the Metro decision-maker panel, and realistic expectations were established. A second round of online exercises was devised and deliv- ered to the Metro staff in early October 2013. Details on this modification of the questionnaire design and the results of this exercise are included in the next section. 3.5 Survey for estimating reliability ratio 3.5.1 Questionnaire Design and Instruments This questionnaire for the online survey maintained the same format as for the first workshop by providing two route options, each with five experienced travel time values. The options were improved by identifying the differences by trip purpose and time of day and providing the transit situation. With fewer than 80 participants expected and with two variables to be estimated, five questions for each type of trip purpose situa- tion were determined to provide a sufficient sample in model estimation. To incorporate RR into the Metro model further, the trip purpose and time-of-day situations were designed to be con- sistent with the existing four trip purposes in the Metro model. Three situations combining purpose and time of day

21 (work, peak hour; nonwork, peak hour; and off-peak hour) were chosen to simplify the model estimation and avoid a long questionnaire. Therefore, 15 questions needed to be pro- vided to each participant. The questionnaire was designed with both an automobile trip survey and a transit trip survey. Each respondent could answer either one according to his or her major travel mode or both surveys if automobile and transit were both com- monly used. The travel time values in each option were ran- domly generated given the travel time and standard deviation. The travel time for the automobile survey ranged from 15 to 50 min, and the standard deviation ranged from 2 to 20 min. If we consider the transit schedule and on-time performance, the travel time for the transit survey ranged from 25 to 50 min, and the standard deviation ranged from 0 to 7 min. To provide more diversity in the survey, two questionnaires were finally designed with different travel time options for each question. In the transit survey, one questionnaire emphasized that “travel time variability is due to variance in WAITING TIME AT THE TRANSIT STOP,” and another questionnaire empha- sized that “travel time variability is due to variance in TIME SPENT IN THE TRANSIT VEHICLE.” Example snapshots of the questionnaires are shown in Figures 3.4 and 3.5. Figure 3.4. Survey question snapshot for auto travel reliability. Figure 3.5. Survey question snapshot for transit travel reliability.

22 3.5.2 Model Estimation Results The online survey was active from September 20 to 27, 2013. In total, 36 members of the Metro staff responded to the questionnaire; 34 responses to the automobile survey and 24 responses to the transit survey were completed. The aver- age travel times were 28 min for the automobile survey and 36 min for the transit survey; the average standard deviations were 5.6 and 2.8 min, respectively, for automobile and transit. A dis tribution of travel time and standard deviation is shown in Figure 3.6. The model, which had the same formulation as for the workshop, was estimated in statistical software R. Because the same respondent was asked multiple questions, it was natural to consider using the mixed logit model to account for taste variation. After testing both the mixed logit and multinomial logit models, we found that the mixed logit model did not appear to be superior to the multinomial logit model, and multinomial logit–estimated RRs were more comparable to RR values reported in the literature. Multinomial logit model results were used in the subsequent steps of the project. The estimates in the mixed logit model appeared not to be significant for travel time and standard deviation for all Tran- sit and Auto_peakhour_nonwork trips. Only coefficients for two variables, Auto_peakhour_ work and Auto_offpeak trips, appeared to be significant. Comparing the log likelihood, the random parameter for travel time and reliability with mean and standard devia- tion did not improve the model goodness of fit with more parameters. RRs for the two models are shown in Table 3.3. There is no telling which one is “better,” but the multinomial logit results appeared to be more comparable to previous studies and were chosen for the case study in this project. The coefficients of the travel time and travel time reliabil- ity terms were estimated from the data, and RR was calcu- lated as the coefficient of travel time reliability divided by the coefficients of travel time, as shown in Table 3.4; model esti- mation results are shown in Table 3.5. There is a decreasing trend by situation from work peak to off peak, implying the strong importance of reliability during peak hours, especially for work-related trips. Transit riders in this survey appeared to have a higher evaluation of reliability than automobile users. This difference can be interpreted as transit riders’ expectation of more reliable service by transit and their low tolerance for delay if they choose transit instead of driving. This interpretation is likely for Portland, which is known to have reliable transit service. For other regions, if the highway system is (or becomes) more reliable than the transit system, a similar survey could find that highway users have a higher VTTR than transit riders. A low tolerance could also be attributed to a higher sched- ule delay penalty, as transit users could be counting on tran- sit’s on-time arrival for work and meetings and may have budgeted a smaller travel time buffer. The waiting area and weather conditions (such as rainy days in Portland) at the bus stop may also contribute to increased VTTR. 3.5.3 Comparison with the Literature The L35A research team found that, in spite of its simplified process, the RR obtained for automobile travel was consistent with values summarized in the literature, particularly in the Dutch study (Significance et al. 2013). The RR values for three trip purposes and for overall automobile trips were Figure 3.6. Distribution of average and standard deviation of travel time in the online survey questions. Table 3.3. Reliability Ratio Estimates with Multinomial Logit and Mixed Logit Models Trip Purpose and Time of Day Multinomial Logit Mixed Logit Transit work peak hour 1.439 4.094 Transit work off peak 1.431 1.624 Transit other 0.831 0.751 Auto work peak hour 0.681 1.257 Auto work off peak 0.343 0.169 Auto other 0.417 0.257 Table 3.4. Reliability Ratios for Automobile and Transit by Trip Purpose and Time of Day Trip Purpose and Time of Day Automobile Transit Work, peak hour 0.83 1.55 Nonwork, peak hour 0.35 1.51 Off peak 0.27 0.76 Overall 0.45 1.06

23 within the major range of 0.3 to 0.9 reported by that study, as shown in Table 3.6. The RR value for transit in the Dutch study (Significance et al. 2013) was higher than the expectation from the litera- ture. The highest value in the literature (shown in Table 3.7), 1.4, is from the expert workshop of 2004 in the Netherlands. In the present study, the two values for work peak and non- work peak were both above 1.5 (as shown in Table 3.4); that is, the values were much higher than the RR for off-peak hours. Therefore, transit riders care about travel time reliability much more during peak hour travel than off-peak travel. 3.6 reliability Measure Calculation 3.6.1 Modeling Reliability Measures for Automobiles As an input, reliability affects travelers’ decisions about trip making and choices of destination, mode, and route. It can be thought of as an extra impedance to travel over and above the average travel time generally used in demand models. Cur- rent models’ definition of average travel time is based solely on recurrent (demand and capacity) conditions. Considering reliability means nonrecurrent sources of congestion must be factored into the process. The concept of “extra impedance to travel over and above the average travel time” is probably the best way to incorpo- rate reliability into the modeling structure as an input. In its application of this approach, SHRP 2 Project L03 (Cambridge Systematics 2013a) characterized the impedance on a link as a generalized cost function that included both the average travel time and its standard deviation (which was used as the indicator of reliability). As discussed below, L03 functions were used in the present study to establish the total link impedance for trip distribution and assignment purposes. In order to apply this model framework, a method must exist for predicting the standard deviation of travel time. SHRP 2 Project L03 developed such methods from empirical data by using the travel time index (TTI) as the dependent Table 3.5. Summary of Model Estimation Results System Work, Peak Hour Nonwork, Peak Hour Off Peak Overall Estimate t-Statistic Estimate t-Statistic Estimate t-Statistic Estimate t-Statistic Automobile Constant -0.480 -1.718 -0.134 -0.753 -0.366 -0.892 -0.049 -0.458 Travel time -0.337 -5.710 -0.395 -4.412 -0.413 -5.244 -0.391 -9.750 Travel time reliability -0.280 -5.130 -0.140 -2.667 -0.111 -1.120 -0.177 -6.555 Adjusted r2 0.3756 0.1408 0.3338 0.2705 Transit Constant -0.155 -0.035 -0.255 -0.890 0.433 0.974 -0.013 -0.077 Travel time -0.620 -4.214 -0.434 -3.292 -0.860 -5.281 -0.719 -10.454 Travel time reliability -0.963 -2.894 -0.657 -2.797 -0.649 -3.110 -0.760 -7.125 Adjusted r2 0.3959 0.1015 0.4472 0.4151 Table 3.6. Snapshot of Reliability Ratio for Automobile Travel Study Country RR MVA (1996) United Kingdom 0.36–0.78 Copley et al. (2002) United Kingdom Pilot survey: 1.3 Hensher (2007) Australia 0.30–0.95 Eliasson (2004) Sweden NCHRP 431: 0.80–1.10 SHRP 2 C04: 0.40–0.90 Mahmassani (2011) United States 0.8 Significance et al. (2013) The Netherlands Commuting: 0.4 Business: 1.1 Other: 0.6 Source: Significance et al. (2013). Table 3.7. Snapshot of Reliability Ratio for Transit Travel Study Country RR MVA (2000) Norway Short trips: 0.69 Long trips: 0.42 Ramjerdi et al. (2010) The Netherlands 1.4 Significance et al. (2013) The Netherlands Commuting: 0.4 Business: 1.1 Other: 0.6 Source: Significance et al. (2013).

24 variable. TTI is defined as the ratio of the actual travel time to the travel time under free-flow conditions, as shown by Equa- tion 3.9: =TTI actual travel time free flow travel time (3.9) If actual travel time is a random variable, then TTI is a random variable. If the relationship between TTI and actual travel time is a linear relationship with a factor 1/(free-flow travel time), then the relationship between TTI and the stan- dard deviation of travel time is also a linear relationship. Equation 3.9 is a generalized equation for TTI. The follow- ing discussion defines several versions of TTI for use in reli- ability estimation. In addition to the TTI calculation, free-flow speed is required for estimating delay. In DynusT networks, each link is specified with a free-flow speed, so such a value can readily be used for TTI calculation. Because of limitations of the procedures being adapted, the smallest time period for which travel time performance mea- sures could be calculated was 1 hour. The same computation would apply for a different time period, such as 30 min, but with a different aggregation and average period. From SHRP 2 Project L03, the following measures for TTI have been pro- posed (Equations 3.10 through 3.18): • Performance measures for urban freeways p95th %ile TTI 1 3.6700 ln MeanTTI (3.10)( )= + p90th %ile TTI 1 2.7809 ln MeanTTI (3.11)( )= + p80th %ile TTI 1 2.1406 ln MeanTTI (3.12)( )= + MedianTTI MeanTTI0.8601 (3.13)= pStdDevTTI 0.71 MeanTTI 1 (3.14)0.56( )= − • Performance measures for signalized arterials p95th %ile TTI 1 2.6930 ln MeanTTI (3.15)( )= + p80th %ile TTI 1 1.8095 ln MeanTTI (3.16)( )= + MedianTTI MeanTTI 0.9149 (3.17)p= pStdDevTTI 0.3692 MeanTTI 1 (3.18)0.3947( )= − Mean TTI is the grand (overall) mean. Because mean TTI was developed from continuous detector data, it includes all the possible influences on congestion (e.g., incidents and inclement weather). Currently, DynusT provides an estimate only of the recurrent (bottleneck only) congestion that is related to volume and capacity. Therefore, a mean TTI based on current DynusT output cannot be used. The following method should be used to estimate the true mean TTI. The method uses the DynusT output to estimate recurrent delay and a sketch-planning method to estimate incident delay, and then combines these two measures. The steps are as follows: 1. Compute the recurrent delay for each link in hours per mile from the simulation model (Equation 3.19): RecurringDelay AverageTravelRate 1 FreeFlowSpeed (3.19)( ) = − where AverageTravelRate is the inverse of the DynusT speed. 2. Compute the delay due to incidents (IncidentDelay) in hours per mile for a one-hour period by using the lookup table from the ITS Deployment Analysis System (IDAS) User’s Manual (Cambridge Systematics 2009). This lookup table requires the v/c ratio and the number of lanes and provides the “base incident delay.” The IDAS table is repro- duced in Table 3.8 below. Table 3.8. IDAS Delay Lookup Table: IDAS Delay Rates for One-Hour Peaka Volume/Capacity Ratio Number of Lanes 2 3 4+ 0.05 3.44E-08 1.44E-09 4.39E-12 0.1 5.24E-07 4.63E-08 5.82E-10 0.15 2.58E-06 3.53E-07 1.01E-08 0.2 7.99E-06 1.49E-06 7.71E-08 0.25 1.92E-05 4.57E-06 3.72E-07 0.3 3.93E-05 1.14E-05 1.34E-06 0.35 7.20E-05 2.46E-05 3.99E-06 0.4 0.000122 4.81E-05 1.02E-05 0.45 0.000193 8.68E-05 2.34E-05 0.5 0.000293 0.000147 4.93E-05 0.55 0.000426 0.000237 9.65E-05 0.6 0.0006 0.000367 0.000178 0.65 0.000825 0.000548 0.000313 0.7 0.001117 0.000798 0.000528 0.75 0.001511 0.001142 0.00086 0.8 0.002093 0.001637 0.00136 0.85 0.003092 0.002438 0.002115 0.9 0.005095 0.004008 0.003348 0.95 0.009547 0.007712 0.005922 ≥ 1.0 0.01986 0.01744 0.01368 a Vehicle hour of incident delay per vehicle mile.

25 If incident management programs have been added as a strategy or if a strategy lowers the incident rate (i.e., fre- quency of occurrence), then the “after” delay is calculated as shown by Equation 3.20: p p1 1 (3.20) 2 D D R Ra u f d( ) ( )= − − where Da = adjusted delay (hours of delay per mile); Du = unadjusted (base) delay (hours of delay per mile from the incident rate tables); Rf = reduction in incident frequency expressed as a fraction (with Rf = 0 meaning no reduction, and Rf = 0.30 meaning a 30% reduction in incident frequency); and Rd = reduction in incident duration expressed as a fraction (with Rd = 0 meaning no reduction, and Rd = 0.30 meaning a 30% reduction in incident duration). Changes in incident frequency are most commonly affected by strategies that decrease crash rates. However, as crashes are only about 20% of total incidents, a 30% reduction in crash rates alone would reduce overall inci- dent rates by (0.30 × 0.20) = 0.06. 3. Compute the overall mean TTI, which includes the effects of recurrent and incident delay. Equation 3.9 (TTI = ActualTravelTime/FreeFlowTravel- Time) is a general equation for TTI. TTI can also be com- puted in the following way: FreeFlowSpeed ActualSpeed To be able to use Equations 3.10 through 3.18, we need an estimate of the overall mean TTI from a distribution of TTIs (which are simply converted travel times). The overall mean TTI includes all sources of congestion because the equations were based on a year of data at each location. For simplicity, we assume that the mean TTI has two components: a recurrent mean (from DynusT) and an incident mean (from IDAS). In order to use the IDAS numbers, which are in terms of delay, we need to convert everything into delay and then reconvert to TTI. Rewriting Equation 3.20, we have Equations 3.21A and 3.21B: MeanTTI MeanTravelRate FreeFlowTravelRate (3.21A)= MeanTTI 1 1 (3.21B) v v t t d v d v v v f f f f = = = = From MeanTTI = t t f , MeanTTI = t t f = t t f f + θ is obtained, where q is the total delay (in hours), defined as the additional travel time on top of the free-flow travel time, which is the sum of recurrent delay qr and incident-induced delay qi; that is, q = qr + qi. Consequently, MeanTTI 1 1 1 1 t t t t t t v v f f f f r i f i f = = + θ = + θ = + θ + θ = + θ   The final equation becomes MeanTTI 1 1 v v i f = + θ   This essentially means that MeanTTI is the ratio of the sum of the recurrent congestion-induced travel rate and the incident-induced travel rate to the free-flow travel rate. The term qi is the delay due to incidents (IncidentDelay) and is proposed using the IDAS table (Table 3.8), which esti- mates the vehicle hour of incident delay per vehicle mile based on the v/c ratio for a 2-lane facility, a 3-lane facility, and a 4+-lane facility. Because the L03 equations predict TTI, the travel time can be computed as given by Equation 3.22: pTravel Time TTI FreeFlowSpeed (3.22)= Small et al. (2005) defined unreliability as the difference between the 80th and 50th percentile travel times and found the value of unreliability to be approximately equal to the value of travel time. Based on this result, Equation 3.23 can be applied to calculate link travel time equivalents (TTEs) for a trip: pTTE MTT + 80th%TTI 50th%TTI (3.23)a ( )= − where TTE = link travel time equivalent; MTT = mean travel time (min); a = reliability ratio (using the value obtained from Metro staff survey); 80%TTI = 80th percentile TTI (min); and 50%TTI = 50th percentile TTI (min). Mean travel time and 80th and 50th percentile TTIs were computed with the above equations. Based on currently avail- able information, we recommend a value of 0.8 for a (the reli- ability ratio), but this value may be revised based on future research. TTE is then used as a replacement for the average travel time in the feedback loop to the TDM. TTE is basically an inflated

26 value of travel time over the average that accounts for how trav- elers value reliability. How the TDM, which was calibrated using average travel time, will behave with this inflated travel time value is unknown and was the subject of testing in this project. 3.6.2 Modeling Reliability Measures for Transit Modeling reliability in the transit networks focuses on mea- suring travel time reliability and on using that measurement in the assignment model. We have added a submodel to the existing transit assignment model to estimate the variation in transit travel time and to capture its effect on transit riders’ behavior. The added contributions of this effort compared to all prior efforts, including those in SHRP 2 C10B, were (1) to develop such a model for schedule-based transit networks by using the multimodal assignment model and (2) to use the method on the transit assignment model and the feedback to the other parts of the demand model. In the first step, a general formulation for a transit TTI was proposed to capture the causes and effects of travel time vari- ability. The model separates various sources of “excess” travel time, and based on these additional times, defines TTI. Addi- tional delays imposed on the transit vehicles and thus on the passengers can be categorized into traffic delay, dwell time, holding time (in schedule-based networks), and incidental delay. Using the proposed TTI, different index values may be calculated for similar routes if they operate differently. The advantage of the proposed formulation is that, unlike methods in previous studies, it can accommodate both frequency-based and schedule-based routes. Transit users plan their trips according to the information they receive from transit opera- tors in the form of published schedules, route headways, trip planner advice, and so forth. Therefore, their expectations of travel time may differ in frequency-based versus schedule- based systems. The TTI for a transit route segment is calculated through the dynamic multimodal assignment model. The transit assignment model will calculate the delay due to dwell time, and integration with the dynamic traffic assignment (DTA) model will help in estimating the traffic congestion and the holding time delay. Transit TTI and TTE in schedule-based systems can be expressed as shown in the following equations: TTI Mean Travel Time Scheduled Travel Time = TTE Mean Travel Time + Reliability Timet= ∝ The proposed TTI is then used to calculate the mean travel time, travel time percentiles, and the TTE (tE), similar to the calculation for the automobile network. This information is also used to estimate the distribution of vehicle arrival and departure times at each stop. The impact of transit reliability is considered in relation to the two major components of pas- senger travel time. The first component is in-vehicle travel time, which is modeled by TTE; that is, tE, which is calculated by adding a travel time buffer to the mean travel time, is used by transit users in their decision-making process. The tE is calculated based on the 80th percentile travel time in con- junction with the mean travel time (Van Oort 2011) by using a formula similar to the one used in the automobile network. However, the travel time RR may be different in automobile and transit networks. The second component of travel time affected by transit system reliability is the waiting time. To account for the vehicles’ departure time variation (Hickman 2001), passengers may plan to arrive earlier than the expected vehicle departure time at the stop to minimize their chance of missing the vehicle. The buffer time used for the waiting time is typically based on the 95th percentile of the headway (Van Oort 2011), meaning that there will be little chance of miss- ing the transit vehicle. As a new feature to add to the existing transit assignment model, a submodel was developed to model passenger incidence at the boarding stops. Based on the expected value and variation of the vehicle departures, the passenger incidence submodel can define three types of pas- senger arrival behavior, as well as their proportion among the total demand: random, coordinated with schedule, and coin- cidentally on time (Julliffe and Hutchinson 1975). The pro- posed assignment is achieved using the modified path algorithm in the transit assignment model. In the results, the impact of travel time reliability is captured on each individual passenger’s decision, and the reliability of the transit network can be evaluated at different levels of aggregation, such as a route, a corridor, an O-D pair, or the whole network. • In-vehicle travel time reliability Reliability Time 80th% travel time 50th% travel time= − • Waiting time reliability with schedule-dependent passengers Wait Time 95th% Headway Mean Headway= − • Waiting time reliability with randomly arriving passengers Wait Time Headway 2 =