Results

Figure 2 shows an example of how the feedback mechanism works in the Gotthard scenario. The figure shows two ``snapshots'' of the vehicle locations within the queue-based micro-simulation at 9:00 AM. The first image in the figure is a snapshot of the initial (zeroth) iteration of the simulation, and the second is the simulation after 50 iterations via the agent database feedback system described in Sect. 2.3.

Initially the travelers choose routes without any knowledge of the demand (caused by the other travelers), so they all use the fastest links, and tend to select very similar routes, which compose a subset of available routes. However, by driving on the same links, they cause congestion and those links become slower than the next-fastest links which weren't selected. Thus, alternate routes which were marginally slower than the fastest route become, in hindsight, preferred to the routes taken. By allowing some travelers to select new routes using the new information about the network, and others to choose previously tried routes, we allow them to learn about the demand on the network caused by one another.

After 50 iterations between the route selection and the micro-simulation, the travelers have learned what everyone else is doing, and have chosen routes accordingly. Now a more complete set of the available routes is chosen, and overall the travelers arrive to their destination earlier than in the initial iteration. Comparing the usage of the roads, one can see that in the 49th iteration, the queues are shorter overall, and at the same time in the simulation, travelers are, on average, closer to their destination.

Abbildung 2: Example of relaxation due to feedback. TOP: Iteration 0 at 9:00 - all travelers assume the network is empty. BOTTOM: Iteration 49 at 9:00 - travelers take more varied routes to try to avoid one another.

Figure 3 shows another view of the network after about 50 iterations with the queue-based micro-simulation for the Gotthard scenario. The figures show the 15-minute aggregated density of the links in the simulated road network, which is calculated for a given link by dividing the number of vehicles seen on that link in a 15-minute time interval by the length of the link (in meters) and the number of traffic lanes the link contains. In all of the figures, the network is drawn as the set of small, connected line segments, re-creating the roadways as might be seen from an aerial or satellite view of the country. The lane-wise density values are plotted for each link as a 3-dimensional box super-imposed on the 2-dimensional network, with the base of a box lying on top of its corresponding link in the network, and the height above the ``ground'' set relative to the value of the density. Thus, larger density values are drawn as taller boxes, and smaller values with shorter boxes. Longer links naturally have longer boxes than shorter links. Also, the boxes are shaded, with smaller values having lighter shades of gray, and larger values having darker shades of gray. In short, the higher the density (the taller/darker the boxes), the more vehicles there were on the link during the 15-minute time period being illustrated. Higher densities imply higher vehicular flow, up to a certain point (the dark-gray boxes), but any boxes that are black indicate a congested (jammed) link. All times given in the figures are at the end of the 15-minute measurement interval. The Gotthard tunnel is indicated by a circle; the destination in Lugano is indicated by an arrow.

Abbildung 3: Snapshots at 7:00AM, 8:00AM, and 9:00AM of Gotthard Scenario. The circle shows the traffic jam before the Gotthard tunnel. The arrow indicates the destination of all vehicles.

Figure 4 shows a result of the Switzerland scenario during morning rush-hour. This figure is after 50 iterations of the queue micro-simulation, using the agent database. We used as input the origin-destination matrices described in Sect. 3.3, but only the three one-hour matrices between 6:00 AM and 9:00 AM. This means any travelers beginning their trips outside this region of time were not modeled. As one would expect, there is more traffic near the cities than in the country. Jams, are nearly exclusively found in or near Zurich (near the top). This is barely visible in Fig. 4, but can be verified by zooming in (possible with the electronic version of this paper). As of now, it is unclear if this is a consequence of a higher imbalance between supply and demand than in other Swiss cities, or a consequence of a special sensitivity of the queue simulation to large congested networks.

Abbildung 4: Snapshot of Switzerland at 8:00 AM. From the queue micro-simulation, iteration 50.

Fig. 5 shows a comparison between the simulation output of Fig. 4 and field data taken at counting stations throughout Switzerland (see Sec. 3.3 and Bundesamt für Strassen, 2000). The dotted lines outline a region where the simulation data falls within 50% and 200% of the field data. We consider this an acceptible region at this stage since results from traditional static assignments that we are aware of are no better than this (Esser and Nagel, 2001). Only few simulation results are outside this region; investigation of these points is pending.

Abbildung 5: Simulation vs. field data. The x-axis shows the hourly counts from the field data; the y-axis shows throughput on the corresponding link from the simulation. ``7-8'' and ``8-9'' refer to the corresonding hours during the morning rush hour.