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139 Walk-Accessibility Accessibility is a general concept in travel modeling that typically refers to the ability of people to reach various desti- nations. It measures both the degree of development activity and the travel time needed to get to those activities. It was theorized that accessibility is a primary factor influencing the number of pedestrian trips made. Population and employ- ment density are sometimes used to reflect the closeness of travel opportunities, but given the extremely small size of the TAZs used in this model (i.e., a single block face), density was not a credible measure. Accessibility is a zone-based measure and can be cal- culated from a matrix of zone-to-zone travel times and a vector of zonal âopportunitiesâ. For the purposes of this study, a fairly conventional definition of accessibility was used: [ ]( ) ( ) ( )( ) = âAcc i Opp j F i,j summed across all zones j Where: Acc(i) = accessibility of zone i Opp(j) = opportunities in zone jâgenerally either employ- ment or households F(i,j) = an inverse function of travel time between zones i and j (as time increases, F becomes smaller); for this purpose, a gamma function is used: F t e1.5 0.1t= ââ â Where: t = walk time between zones i and j, minutes (computed as the distance along the sidewalk at a speed of 3 mph) e = base of natural logarithms (2.71828 . . . ) Trip Generation For each trip purpose, a trip production model of the following type was estimated: ( ) = â â â â + â TR ACCMFM ACCEMP ACCRET D LOW E HIGH A B C Where: TR = trip rate (trips/HH for HB purposes, trips/ KSF floor space for NHB purposes) ACCMFM = accessibility to MFDUs ACCEMP = accessibility to total employment ACCRET = accessibility to retail employment LOW = low income dummy (= 1 if the zonal average HH income < $41,000, else 0) HIGH = high income dummy (= 1 if the zonal average HH income â¥ $41,000, else 0) A, B, C, D, E = calibrated coefficients (Note: for the NHB purposes, the âDâ and âEâ coefficients were set equalâthere is no influence of income) The models were calibrated using the method of least squares. For each district, the estimated trip rate was compared to the surveyed rate. The coefficients were adjusted so as to minimize the overall sum of the squared error. A P P E N D I X D Baltimore PedContext Model10 10 Urbitran Associates. Pedestrian Flow Model for Prototypical Maryland Cities. Final Report. For Maryland Department of Transportation, Division of High- way Safety Programs, and University of Maryland, National Center for Smart Growth (2004)
140 Trip Attractions were determined through the following equations: Trip Distribution Trip productions and attractions are converted to origin- destination trips through a âgravity modelâ, which propor- tions the number of trips between zone i and zone j to the number of trips produced in zone i, the number of trips attracted to zone j, and inversely proportional to the imped- ance separating the two zones: â= âT P A F A F ij i j ij j ij j Where: Tij = trips from zone i to zone j Pi = trips produced in zone i Aj = trips attracted to zone j Fij = impedance function, i to j And: â âF = a t eb gt Where: F = impedance t = perceived walk time, minutes a, b, g = calibrated coefficients e = base of natural logarithms (2.71828 . . . )
141 Impedances The accessibility calculations that underlie the previously described demand model, and the path-finding that under- lies the trip assignment model, all are based on travel times and impedances derived from the pedestrian network. Travel (walk) times are computed for each link in the networkâ sidewalks, intersection crosswalks and mid-block jay walks, doorways / load points, and other types. Then these times are weighted by various factors to produce a set of impedances for each link that govern path-finding. Basic sidewalk walk time is based on walking speed and distance. Average walk speed can be defaulted, or can be specified by the user. The default value for sidewalk walk speed is 3.5 mph. Sidewalk quality factors are applied to modify the walk time to reflect perceived quality. For example, a high-quality sidewalk would receive a quality factor of 1.0, whereas a poor-quality or non-existent sidewalk might receive a quality factor of 2.0. These factors can be set or over- ridden by the user. Default quality factors are as follows: Time Factors for Sidewalk Quality Sidewalk Quality Time Factor High quality 1.0 Marginal quality 1.3 Poor quality 2.0 On-street walk 1.7 Other walkway types 1.0
142 A path set with minimum perturbation, used by such trip purposes as walking to work, is essentially the minimum path, and typically results in minor variations to jaywalk Default Sidewalk Types for Street Facility Types: Freeway None Arterial Marginal Collector High Local High Alleyway On-Street Other Marginal At intersection crosswalks and mid-block jay walks, basic crosswalk times are based on walking speed (specified sepa- rately and typically faster than sidewalk walk speed), distance based on street width, and step-off conditions. Additional time is added to account for wait times for gaps in uninter- rupted traffic (a function of the traffic volume), and wait times at signals (a function of signal timing and pedes- trian phasing). Default crossing time parameters are shown below: Crosswalk Time Parameters Parameter Value Crosswalk Walk Speed 4.5 mph Reaction/Step-off Time 1.0 sec Speed Risk Allowance 0.05 sec/mph Crossing time factor if Pedestrian Phase at Signal 0.6 Crossing time factor if Pedestrian Actuation at Signal 0.8 Further adjustments are applied to increase walk time to account for crossing risk. Jay walks, for example, are riskier than intersection crossings. High traffic speeds are more risky than low speed streets. These risk factors and acceptable gap times are computed based on the facility type, speed, and volume. Adopted defaults are shown below: Street Volume and Speed Defaults Traffic Volume (Veh/hour/lane) Facility Type Speed (mph) Peak Off-Peak Freeway 60 1,200 850 Arterial 45 900 600 Collector 35 350 200 Local-1 25 150 80 Local-2 15 0 0 Local-3 15 0 0 Alleyway 15 0 0 Other 15 0 0 Network Assignment Pedestrian trips from each block face to all other block faces are estimated by the pedestrian travel demand model. Paths are then found through the pedestrian network accord- ing to the above travel impedances, and the pedestrian trips are assigned to those paths. While moving from the same origin to the same destination, a group of pedestrians will use various pathsâsome efficient with respect to time or impedance, some not so. To emulate this phenomenon the assignment method needs to find mul- tiple paths from each origin to each destination and to propor- tionally load the trips along those paths. Because the pedestrian network built by this model con- tains a multitude of short links that prevent alternative paths from being qualified and assigned, it was concluded that standard stochastic assignment methods could not be used for this pedestrian model. An alternative approachâthe Pseudo-Stochastic Network Impedance Modelâwas deemed more able to deal with specialized traffic assignment issues. This construct uses an iterative path-finding and assignment process, but randomly perturbates the link impedances before finding paths to emulate the random ways in which users per- ceive or react to actual impedances. After several iterations with these perturbated times, a family of paths was generated for each origin-to-destination movement that were found to be a reasonable representation of multi-path assignment. The implementation of this model in TP+ found nine sepa- rate sets of perturbated paths for each origin-to-destination movement. These sets are developed as three random variants (A through C) of three levels of perturbation (1 through 3). Each trip purpose follows a perturbation level as shown below.
143 instead of using intersection crosswalks. A set with maxi- mum perturbation, used by such trip purposes as leisure, will show a high level of variation and can typically result in going entirely around a block or finding another street to walk on. The variations in travel impedances that comprise these perturbations are computed in one of two ways that can be selected by the user: Either the overall total impedance on a link can be perturbated, or the individual components of travel time (walk time, crossing time, crossing wait time, traffic speed penalties) can be perturbated. It appears that the individual component approach is more sensitive and delivers more appropriate paths, but further experimenta- tion is needed in this regard. The median values of each component, and of the total overall impedance, are computed using the defaults described above or user data if provided. Then for each of the nine impedance sets (1A through 3C in the preceding table) the values are randomly varied, using a normal distribution with standard deviations that can be specified by the user. Sug- gested standard deviations that have been defined through practice are shown below. The matrix containing 24-hour pedestrian trips is assigned to the pedestrian network using the TP+ program HWYLOAD. One iteration of all-or-nothing assignment is used, with each trip purpose set assigned according to the three perturbated impedances comprising each set as shown in the table of standard deviations above. Each set is then weighted with the following fractions. For any set (minimum, medium, or maximum), the fractions sum to 1.00. The product of this step is a loaded network containing estimated 24-hour pedestrian volumes on all links in the net- work: sidewalks, intersection crosswalks, jay walks, and door links/load points.