A Real-World Scenario

While the previous sections have discussed general design issues for multi-agent transportation simulations, this section will describe results of a particular scenario. Since this is work in progress, the implementation does not use all the modules described earlier. It will however provide some intuition how multi-agent models can be used in this context, and how they perform when compared to more conventional approaches. The scenario consists of approximately 1 million agents traveling throughout Switzerland during an average week-day morning rush hour, from 6:00 AM to 9:00 AM.

The ``Switzerland'' Scenario

The street network that is used was originally developed for the Swiss regional planning authority (Bundesamt für Raumentwicklung), and covered Switzerland. It was extended with the major European transit corridors for a railway-related study (Vrtic et al., 1999). The network has the fairly typical number of 10564 nodes and 28622 links. Also fairly typical, the major attributes on these links are type, length, speed, and capacity constraint. From Sec. 2.2, one can see that this is enough information for the queue simulation.

Our starting point for demand generation is a 24-hour origin-destination matrix from the Swiss regional planning authority (Bundesamt für Raumentwicklung). The original 24-hour matrix is converted into 24 one-hour matrices using a three step heuristic (Vrtic and Axhausen, 2002). These hourly matrices are then disaggregated into individual trips. That is, we generate individual trips such that summing up the trips would again result in the given OD matrix. The starting time for each trip is randomly selected between the starting and the ending time of the validity of the OD matrix.

This leads to a list of approximately 5 million trips, or about 1 million trips between 6:00 AM and 9:00 AM. Since the origin-destination matrices are given on an hourly basis, these trips reflect the daily dynamics. Intra-zonal trips are not included in those matrices, as by tradition.

Simulation models

The above scenario was fed into two different models: First, into a VISUM (PTV, www.ptv.de) assignment which is a relatively standard assignment (Sheffi, 1985) except that it is dynamic on an hourly basis (Vrtic and Axhausen, 2002), and second into an agent-based micro-simulation based on the principles described earlier. For the agent-based simulation, neither a synthetic population nor activities were used, since demand was given by the OD matrix. An initial set of routes was generated using a fastest path algorithm based on free speeds given by the network data. These routes were then run through the queue micro-simulation (Sec. 2.2). The simulation collected link travel times in 15-min time bins. These time-dependent link travel times formed the basis for the next route calculation, which was done for 10% of the travelers. These routes were then merged with the pre-existing routes by the other travelers, and that set of routes was run again through the simulation. These iterations are repeated until the system is relaxed, which takes about 50 iterations.

As a major difference to many other implementations of similar systems, our system remembers all routes ever tried by an agent. That is, new routes keep coming in at a rate of 10% new routes per iteration, but even the remaining 90% of agents are adaptive in every iteration: They keep scores (trip times) $T_i$ for each route, and select a route with probability

$$p_i \propto e^{-\beta T_i} ,$$

where $\beta$ tunes the amount of randomness. The use of the agent database makes the software system considerably more robust against artifacts of the router module: ``Bad'' routes are tried out once by the agent and subsequently ignored. Artifacts of the router module may not just be due to implementation errors, but also due to inherent limitations, such as the one caused by the binning of the travel times (Raney and Nagel, 2003). The agent database also moves the implementation closer to a true agent-interpretation of the traveler, meaning that in such an implementation the agent is an autonomous entity in the system capable of adaptation and learning.

Results

Figure 5 shows a result of the Switzerland morning rush-hour scenario. 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. 5.1, 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. 5, but can be verified by zooming in (possible with the electronic version of this paper; see also 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.

Figure 5: Snapshot of Switzerland at 8:00 AM. From the queue micro-simulation, iteration 50.

Figure 6: Comparison of link volumes for 7:00-8:00 AM from (a) Simulation (iter. 50) or (b) VISUM assignment model, vs. corresponding hourly counts from field data.

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Fig. 6(a) shows a comparison between the simulation output of Fig. 5 and field data taken at counting stations throughout Switzerland (see Sec. 5.1 and Bundesamt für Strassen, 2000). 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. 6(b); see also Esser and Nagel, 2001). Fig. 6(b) shows a comparison between the traffic volumes obtained using the VISUM assignment (Vrtic and Axhausen, 2002) 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 $\left\langle q_{sim} - q_{field}\right\rangle$, mean absolute error is $\left\langle\vert q_{sim} - q_{field}\vert\right\rangle$, mean relative bias is $\left\langle(q_{sim} - q_{field})/q_{field}\right\rangle$, mean relative error is $\left\langle\vert q_{sim} - q_{field}\vert/q_{field}\right\rangle$, where $\left\langle.\right\rangle$ means that the values are averaged over all links where field results are available. 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 of the simulation is 25%, compared to 30% for the VISUM assignment. 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 (Esser and Nagel, 2001); 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 surprising that even under these conditions, which seem very advantageous for the VISUM assignment, the simulation generates a smaller mean error.

Table 1: 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%