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