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Innovations in Travel Demand Modeling, Volume 2: Papers (2008)

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Suggested Citation:"T57054 txt_104.pdf." National Academies of Sciences, Engineering, and Medicine. 2008. Innovations in Travel Demand Modeling, Volume 2: Papers. Washington, DC: The National Academies Press. doi: 10.17226/13678.
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they traverse their routes. The propagation depends on the posted speed for the links, saturation flow rates, and jam density for links. The values specified for these link properties define a speed–flow–density relationship for the link to which simulated vehicles adhere. The result- ing effect is that at a link level, vehicles exhibit proper traffic flow theory properties in that they form queues, and queues may spill back to other links. Link travel times therefore consist of time required to traverse a link at posted speed plus time spent delayed in queues and time delayed by traffic control devices. Once the vehicle simulation has finished, it is possible to compute link travel times at any aggregation interval desired. A typical Vista application would include a sim- ulation time step of 6 s, meaning that the position of vehicles in cells is updated every 6 s. The travel times on links could then be computed for every link at every 6-s interval, or they could be computed at longer intervals where an average of the 6-s times would be calculated and stored. Given time- dependent (by link aggregation interval) link travel times, a TDSP algorithm can be used to calcu- late routes through the network. The TDSP algorithm works much like the conventional shortest- path algo- rithms used in static traffic assignment methods, except that the link times have a time index. At each step in the algorithm, as a link is being considered for inclusion in the shortest path, the criteria used includes the travel time on the link at the current accumulated time along the path. In other words, for a specific assignment interval, if a link is 60 s of accumulated link time from the origin along the shortest path, the link is evaluated for inclusion in the shortest path based on the link time associated with the aggregate time interval that corresponds with 60 s past the beginning of the assignment interval. The result of the TDSP is a set of routes between every origin and destina- tion zone starting in every assignment time interval. With the capability to simulate traffic and compute time- dependent link travel times and TDSP, a DTA model can compute a dynamic network equilibrium solution. Typically, for planning studies, a dynamic user equilibrium is the desired outcome. For intelligent trans- portation system applications, one might be more inter- ested in a dynamic system- equilibrium solution. The dynamic equilibrium is usually defined by extension of the static user- equilibrium principle that states that no used route between an origin and a destination may have a higher travel time than any unused route. By extending this principle to the time- dependent case, one arrives at a similar condition: at no time along a route from an ori- gin to a destination can a traveler change to a different route and lower his or her travel time. In other words, the travel times for all used routes between an origin and a destination starting during the same time interval are all equal at equilibrium. In most DTA models, the equilibrium solution is determined by first identifying a feasible or reasonable path set, then allocating flow between those paths to cause the path times to be equal as per the definition given above. In Vista, a reasonable path set is determined by solving the dynamic user- optimal equilibrium prob- lem with the method of successive averages (MSA) pro- cedure. This involves iteratively solving the CTM and TDSP, then averaging the time- dependent flow solution with the solutions from previous iterations. The weight of the most recently calculated flows is 1/N, where N is the iteration number, and the weight of the previous averaged flows is (1 – 1/N). The MSA solution converges very slowly toward an equilibrium solution, but each iteration provides the opportunity for new routes to be determined subject to traffic conditions established as the combined effect of the other iterations. Once the reasonable path set is determined, an alloca- tion mechanism can be used to achieve a more exact equilibrium solution over the fixed set of reasonable paths. Vista uses a methodology called simplicial decom- position, which, for any origin–destination–time interval set, causes flows from higher travel- time routes to be apportioned to lower travel- time routes, and conversely, lower travel- time flows shifted to higher travel- time routes. The solution procedure results in a set of time- dependent link flows and route times corresponding to the dynamic user- optimal conditions. (The solution is not a pure equilibrium solution. Routes with shorter travel times may exist that were not identified in the MSA procedure. However, the solution is probably nearly an equilibrium, and it is thought to be adequately close.) The implementation described here involved itera- tively building a reasonable route set and solving the dynamic user- equilibrium for that route set. Following each dynamic user- equilibrium solution, routes that had previously received vehicles but no longer did were pruned from the route set and new reasonable routes were determined with the approximate MSA solution procedure. This was followed by solving for the more precise dynamic user- equilibrium solution for the route set. When one of these iterations produced only a small number of new routes, the model was said to have con- verged sufficiently. ANALYSIS OF VISTA RESULTS FOR ATLANTA A DTA model of the Atlanta region is a large problem to solve. Most DTA results published to date are for much smaller problems. An attempt was made to reduce the problem size by limiting the demand loaded on the net- work. At first trips were simulated beginning between 6:00 and 7:00 a.m. with the intention of increasing 104 INNOVATIONS IN TRAVEL DEMAND MODELING, VOLUME 2

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TRB Conference Proceedings 42, Innovations in Travel Demand Modeling, Volume 2: Papers includes the papers that were presented at a May 21-23, 2006, conference that examined advances in travel demand modeling, explored the opportunities and the challenges associated with the implementation of advanced travel models, and reviewed the skills and training necessary to apply new modeling techniques. TRB Conference Proceedings 42, Innovations in Travel Demand Modeling, Volume 1: Session Summaries is available online.

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