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106 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 2 time difference for vehicle f, and therefore its travel time earlier. Where there is a large variability in vehicle travel on Link 1, is 30 12 = 18 s. All the vehicles before f, ae, times over movements through a link, the result might be have travel times of 12 s on Link 1, which is the free-flow that the congested link appeared to the route generator travel time for Link 1. Therefore, vehicle f has 6 s of to be suitable long after it was congested due to the aver- delay on Link 1. Following similar trajectories for the aging. In such an instance, one should use movement- other vehicles indicates that the most delay occurs for based times in TDSP, at least in problematic areas, to vehicle n on Link 1 (30 s). address the problem described here. Movement-based times would cause the route through the congested link pair to be considered much differently from the link pair EFFECT OF CONGESTION ON ATLANTA that shares a common link but has essentially free-flow DTA RESULTS times. It is more resource intensive to do movement- based TDSP, which is why the default is to use link-based The above exercise illustrates clearly that with the simul- TDSP, but it is possible to identify a select number of taneous arrival of too many vehicles, only some could locations for which movement-based times should be continuously move along, while others had to wait. The used. In general, in dynamic network models, one must number allowed to move at each time step was deter- be aware of problems that could be caused by highly mined by the saturation flow rate defined for the link, variable movement travel times exiting links. which determines the number of vehicles that can occupy It was believed that high variability in exiting link a cell during any time step. The number of time steps times can be used to identify the locations requiring that elapsed before the vehicles could completely tra- movement-based times. A query of vehicles arriving at verse the link determined the total delay experienced on links during the same time period but destined for differ- the link. ent downstream links, where the vehicles have much dif- For the entire Atlanta network, once cells became sat- ferent downstream arrival times, identified those links. urated while vehicles continued to arrive, the cell satura- By using the GIS, a spatial correlation between links with tion effect moved upstream. The original overcongested high variability in movement times and links with exces- link caused many more links upstream of it to become sive travel times was confirmed. Only a couple dozen oversaturated. When propagation of congestion affected such locations were identified, and the changes necessary a freeway link, routes between origins and destinations for Vista to consider movement-based times in TDSP spanning nearly the entire region became affected, and were easily made. the simulation broke down. It was not possible, due to the excessive times on important links, for all the vehi- cles to complete their trips during the simulation period. SOME PRELIMINARY VISTA SUMMARY RESULTS With many vehicles having route attributes associated with incomplete trips, the dynamic user-equilibrium Calibration of the Vista DTA model of the Atlanta region results and subsequent route-generation steps were is still in progress, but some preliminary results can be suspect. described. Table 1 shows the link summary statistics for The dynamics of a traffic jam produced by the simu- the Vista model for the 6:00 to 7:00 a.m. demand period. lation results showed that the software was responding The number of links, total observed count, and total esti- the way it was intended but did not provide any expla- mated flow are listed for volume ranges, along with rel- nation for why so many arrivals occurred at these links. ative error and percent root mean square error statistics. The next course of action was to look more carefully at Figure 2 shows the scatter plot of the same DTA results. the set of vehicle arrivals at this congested link, ordering The results were determined from the DTA model run them by their arrival time. Doing so revealed that some resulting from the first traffic signal setting retime fol- of the vehicles exiting a link in question were exiting at lowing the initial Vista DTA model results. essentially free-flow speed while others exiting the same Table 2 and Figure 3 show the DTA results after four link at the same time but toward a different downstream iterations of retiming traffic control settings and running link were exiting with times in the 2,000+ s range. Even- the DTA model to solve for dynamic user-equilibrium. tually, all vehicles regardless of their downstream link The results after the first iteration show a good fit would experience huge travel times, but initially as con- with observed data. The results after the fourth iteration gestion built up on this one link, there was a large vari- show an even better fit. Results from the second and ability in exiting travel times, or in other words, a large third iteration, not shown here, had successively better variability in movement times passing through a given fit, leading up to the fourth iteration results. link at a given time. The iterations involved figuring traffic control set- Routes are determined on the basis of the link time tings, solving for an equilibrium-based distribution of averaged over the link time aggregation period as defined vehicles to routes, updating the traffic control settings,