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40 I N N O VAT I O N S I N T R AV E L D E M A N D M O D E L I N G , V O L U M E 1 capacity using artificial links, splitting a link in two, and els. The first model was a traditional STA model. The using dummy links. second model was the TransCAD approximator, which The analysis conducted in this study indicates that uses analytical, link performance-function-based speed modeling is intertwined with model calibration. approximation to DTA. The third model was VISTA, The results suggest that insensitive speedflow equations which uses a simulation-based DTA approach. give less accurate queue delays, but they tolerate inaccu- The traditional STA models use a steady-state rate capacities, dummy links, and inaccurate link flows. approach, with no concept of time. STA models use total Conversely, sensitive speedflow equations give more demand in a single time period. STA models include link accurate queue delays, but cannot tolerate inaccurate performance functions. The TransCAD DTA approxi- capacities and flows. mator is an add-in to the TransCAD software. It is based To obtain more accurate queue delays, more accu- on an iterative algorithm. It uses link performance func- rate speedflow equations should be used in combina- tions to calculate vehicle delay, which is a major differ- tion with accurate capacities, coding to distinguish ence from the VISTA model. The link performance dummy links, and peak-period analysis. In the future, functions are less computationally intensive, and the using DTA with simulation--including programs such as approximator runs faster than VISTA. It does not model Dynasmart(P), DynaMIT(P), or Dynameq--may address traffic flow at the same level of detail, however. some of the limitations identified in this study. VISTA is network-enabled software that integrates temporal network data and models for a wide range of transportation applications. It is based on a cell trans- A COMPARISON OF STATIC AND DYNAMIC mission model (CTM) that divides links into smaller TRAFFIC ASSIGNMENT UNDER TOLLS IN THE cells, which can be modeled individually at fine resolu- DALLASFORT WORTH REGION tion of approximately 5 to 10 seconds. A key feature of CTM is that flows are explicitly prohibited from exceed- Stephen Boyles, Satish Ukkusuri, S. Travis Waller, ing capacity. If demand for a cell exceeds the available and Kara Kockelman capacity, queues form to maintain flow less than capac- ity. This ability to model queues in a more realistic man- Stephen Boyles discussed the use of static and dynamic ner is a main attraction of VISTA. assignment models in the DallasFort Worth region to The parameters used by the models are different. analyze congestion pricing alternatives. He described a The link performance function used by STA and the DTA study comparing the use of three models: traditional sta- approximator requires that the capacity and free-flow tic traffic assignment (STA), the TransCAD approxima- time for each link be specified. The two calibration pa- tor, and VISTA's simulation-based dynamic traffic rameters must also be specified. The CTM requires the assignment (DTA). Volume 2 includes a paper on this jam density and the length of each cell to be specified. topic.3 The following points were covered in his The two parameters indicating the slopes of the flow- presentation. density curve when flow is increasing or decreasing with volume must also be specified. Use of DTA models provides the capability to Comparing STA and DTA is not easy because of account for time-varying properties of traffic flow. the fundamental differences in the modeling approaches. Although differences exist among DTA models in how The presence of clearance intervals in DTA bias travel traffic flow is modeled and how the mathematical pro- times is low compared with static assignment. Clearance gram is described, all DTA approaches provide the abil- intervals account for vehicles that depart near the end of ity to model traffic flow changes over time. DTA models the model period and arrive at their destination beyond require more input data than STA models, including the model period. No additional vehicles are assigned time-dependent travel demand data. DTA models also during these intervals, but vehicles remaining on the net- introduce other issues, such as ensuring first-in-first-out work are allowed to complete their trips. The result is queuing disciplines. The use of DTA models requires that some links experience flows for longer periods of substantial computational time when applied to a major time than in STA, effectively increasing link capacities. metropolitan area with large networks, such as the Dal- This issue does not occur with STA because of the inabil- lasFort Worth region. ity to distinguish when vehicles depart and assume a A comparison was conducted in the DallasFort steady-static condition. Worth area using three different traffic assignment mod- The three approaches were applied to analyze toll alternatives in the DallasFort Worth metropolitan area. 3 See Boyles, S., S. Ukkusuri, S. T. Waller, and K. Kockelman. A A total of 92 links (of the 56,574 total links) were tolled Comparison of Static and Dynamic Traffic Assignment Under Tolls in in this application. A 3-hour morning peak period from the DallasFort Worth Region. Volume 2, pp. 114117. 6:00 a.m. to 9:00 a.m. was used in the analysis. This