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demand when the simulation was verified to be working properly. The simulation results included a small number of links with travel times exceeding 1 h. One feature of Vista that facilitates postsimulation analysis is that all the input data and most of the results are stored in a database that can be evaluated by using the language of databases, SQL. It was easy, for example, to query all the link records that experienced such a high travel time and to plot their locations with a geographic information sys- tem (GIS). The first explanation that came to mind was that there must be a coding error in the network or that a centroid link must be dumping a lot of trips into these areas. Detailed inspection of the problem areas revealed no evidence that either of these explanations was correct. With another query of the database, it was possible to collect all of the vehicle arrivals at one of the excessive time links. On the basis of the arrival time at the link and the arrival time at the downstream link, it was possible to plot a timeâspace diagram of the vehicles arriving at these links and derive their propagation along cells defined for the links. The next section shows an example of how congestion might develop on network links. ILLUSTRATING CONGESTION ON LINKS IN CTM MODEL Figure 1 shows a set of vehicle trajectories on a timeâspace diagram to illustrate the evolution of conges- tion occurring in the CTM. In Figure 1, the horizontal axis is space, as shown by Link 1 Link 2 Link 3, and the vertical axis shows time increasing from the top to the bottom of the dia- gram. The diagram shows that Link 1 has two cells, each with capacity for six vehicles; Link 2 has three cells, each with capacity for two vehicles; Link 3 has one cell with capacity for two vehicles. At time 0 s, vehicle a arrives at the first cell of Link 1. One should notice that there is a reduction in capacity from Link 1 to Link 2, and this reduction will result in congestion, as will be seen later. At time 6 s, vehicle a moves to Cell 2 of Link 1 and vehicles b and c arrive at Link 1. At time 12 s, vehicle a moves on to Link 2; vehicles b and c move to Link 1, Cell 2; and vehicles d, e, and f arrive at Link 1. It is relatively easy to follow the arrival of vehicles at Link 1 with 20 total vehicles (aâs) arriving in 60 s (ten 6-s intervals from time 0 to time 54). One might expect delays to occur on Links 2 and 3, given their reduced capacity and the clear excess overca- pacity of the flow trying to use those links, but from the diagram it can be seen that each vehicle moves through the cells in Links 2 and 3 at constant, free- flow speed of one cell per 6 s. This is true for vehicle a, vehicles b and c, vehicles d and e, and so forth. There is no congestion at all in this diagram for Links 2 and 3. The congestion occurs prior to (upstream of) the capacity reduction at Link 2. In other words, the congestion, identified by time delay incurred by vehicles, appears on Link 1. Consider time 18 s at Link 1. Four new vehicles arrive at Cell 1 and three vehicles move from Cell 1 to Cell 2. In the next time step, 24 s, vehicles d, e, and f want to move to Link 2, but there is only room for two, so only d and e move, and f waits for the next time step. Also in that time step, the four new vehicles at Cell 1 move to Cell 2 and join f. At time step 30 s, vehicle f finally arrives at Link 2. The 105DYNAMIC TRAFFIC ASSIGNMENT MODEL BREAKDOWN Time (s) Link 1 Link 2 Link 3 Link 1 Link 2 Link 3 1 2 1 2 3 1 0 a 6 b c a 12 d e f b c a 18 g h i j d e f b c a 24 k l m n f g h i j d e b c a 30 n o h i j k l m f g d e b c a 36 p j k l m n o h i f g d e b c 42 q l m n o p j k h i f g d e 48 r n o p q l m j k h i f g 54 s p q r n o l m j k h i 60 t r s p q n o l m j k FIGURE 1 Timeâspace diagram of vehicles on a simple network.