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 were not 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.

Figure 3 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. 3, but can be verified by zooming in (possible with the electronic version of this paper, on the TRB CD-ROM or at sim.inf.ethz.ch/papers/ch). 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: Snapshot of Switzerland at 8:00 AM. From the queue micro-simulation, iteration 50.

Abbildung: Comparison to Field Data. (a) Simulation vs. field data for the 50th iteration. The x-axis shows the hourly counts between 7am and 8am from the field data; the y-axis shows throughput on the corresponding link from the simulation. (b) VISUM assignment vs. field data. The x-axis is the same as (a); the y-axis shows the volume obtained from the assignment model.

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Figure 4 shows a comparison between the simulation output of Fig. 3 and field data taken at counting stations throughout Switzerland (see Sec. 3.3 and 26). The dotted lines, drawn above and below the central diagonal line, outline a region where the simulation data falls within 50% and 200% of the field data. We consider this an acceptable region at this stage since results from traditional assignment models that we are aware of are no better than this (Fig. 4(b); see also (27)).

Figure 4(b) shows a comparison between the traffic volumes obtained by IVT using VISUM assignment against the same field data. Visually one would conclude that the simulation results are at least as good as the VISUM assignment results. Table 1 confirms this quantitatively. Mean absolute bias is $\mede {q_{sim} - q_{field}}$, mean absolute error is $\mede {\vert q_{sim} - q_{field}\vert}$, mean relative bias is $\mede {(q_{sim} - q_{field})/q_{field}}$, mean relative error is $\mede {\vert q_{sim} - q_{field}\vert/q_{field}}$, where $\mede {.}$ means that the values are averaged over all links where field results are available.

Tabelle: Bias and Error of Simulation and VISUM Results Compared to Field Data

	Simulation		VISUM		.
Mean Abs. Bias:	$-$64	.	60	$+$99	.	02
Mean Rel. Bias:	$-$5	.	26%	$+$16	.	26%
Mean Abs. Error:	263	.	21	308	.	83
Mean Rel. Error:	25	.	38%	30	.	42%

For example, the ``mean relative bias'' numbers mean that the simulation underestimates flows by about 5%, whereas the VISUM assignment overestimates them by 16%. The average relative error between the field measurement and the simulation is 25%, between the VISUM assignment and reality 30%. These numbers state that the simulation result is better than the VISUM assignment result; also, the simulation results are better than what we obtained with a recent (somewhat similar) simulation study in Portland/Oregon (27); conversely, the assignment values in Portland were better than the ones obtained here.

What makes our result even stronger is the following aspect: The OD matrices were actually modified by a VISUM module to make the assignment result match the counts data as well as possible. These OD matrices were then fed into the simulation, without further adaptation. It is suprising that even under these conditions, which seem very advantageous for the VISUM assignment, the simulation generates a smaller mean error.