This post aims to introduce different ways in which road traffic can be modeled. I will focus on outlining the conceptional differences between what I call choice-based and action-based models of traffic and look at two particularly interesting papers in detail.
Most publications do primarily focus on the "choose-a-route" problem, meaning that road traffic and congestion as a macroscopic emergence of the system are primarily influenced by the route choices of individuals. This assumes that it is mainly the density of traffic (i.e. the ratio of the number of travelers on over the capacity of a particular route) that gives rise to congestions and traffic jams. In other words, once you chose a particular road, there is not much left to be done in terms of decision-making (i.e. driving behavior) in order to avoid getting stuck in a jam. This appears sensible, as it serves the intuition that every individual driver is intrinsically dependent on the behavior of other drivers and that his influence on the overall system should be very limited.
Yet, it is also interesting to observe how, given a certain density-level, different driving styles can yield very different outcomes in terms of efficiency of the traffic system. Kai Nagel has done some interesting work on life-times of simulated traffic jams that might become particular relevant when we try to draw conclusions about the business cycles, i.e. which policies might be most effective when trying to get the economy out of a recession, say.
For now, I want to introduce two papers. The first paper "Individual Apaption in a path-based simulation of the freeway network of Northrhine-Westfalia" by Kai Nagel aims to examine how individuals learn and adapt their route-choices, based on the past performance of their respective choices and how the system evolves accordingly. The second paper "How Individuals take turns: Emergence of alternating cooperation in a congestion game and the prisoner's dilemma" by Dirk Helbing, Martin Schoenhof, Hans-Ulrich Stark and Janusz A. Holyst takes a game-theoretical approach to observe how people's choices in a two and higher dimensional set-up might or might not yield socially efficient equilibria. Both papers give a nice intuition about how we might want to model the choose-a-route problems associated with road traffic.
Here is the basic set-up of the choice-based models. All roads can be thought of as having a certain comfort limit L. If the number of cars on the road exceeds this comfort limit L, the road gets uncomfortable to be on, i.e. jam or at the very least traffic delays occur. Drivers choose particular routes, essentially trying to outguess everyone else. The essential bit is that they won't know that the correct decision, i.e. the route that minimizes the travel time from A to B, is until it is too late.
Nagel's paper introduces a similar set-up. Using the freeway network of the German Land Northrhine-Westfalia, a simulation is built, where there are many travelers with different origin-destination pairs. Each traveler has a choice between 10 different paths (or routes) that connect his origin with his destination. In the course of the simulation, each driver tries every single route and from then on on a daily basis choses the route that has performed best in the past (i.e. the route that minimized the time to get from A to B). The simulation runs 6000 iterations where each iteration consists of a preparation phase, where each traveler chooses his path for the day according to past performances, and a traffic microsimulation phase, where the daily traffic dynamics are simulated and macroscopic phenomena like jams are recorded.
The results of these simulations are somehow surprising. Nagel finds that the network performance decreases as drivers optimize their individual route and settle down on a route which is most convenient for themselves. In other words as individuals learn and adapt strategies that optimize their own performance, the aggregate system performs worse. This is partly due to the fact that jams are "equilibrated" , meaning that fastest ways around congested areas tend to vanish over time.
Dirk Helbing et al take a different approach and yet, they draw somehow similar conclusions.
Helbing et al conducted experiments where the test persons were instructed to choose between route 1 which corresponded to a freeway and route 2 that represented a side road. Participants were told that if more than half of the participants would choose route 1, everyone would receive 0 points. If on the other hand half would choose route 1, they would receive the maximum average of 100 points, but 1-choosers would profit at the cost of 2-choosers. This paper introduces the route-choice game as a "multi-stage symmetrical N-person single commodity congestion game". What exactly does this mean?
Multi-stage: The game is played several times.
"Symmetrical": Refers to the fact that the payoffs associated with a certain strategy do only depend on the other strategies that are played and not on who plays them.
"single commodity ": the single available commodity is space on the road
"congestion game": The payoff for each player depends on the resource that he choses and the number of players choosing the same resource.
Previous research on congestion games has shown that there always exists a Wardrop equilibrium. This is characterized by the property that no driver can decrease her travel time by choosing a different route and that travel times on all used routes is roughly the same. Yet, the Wardrop equilibrium does not generally reach the system optimum, i.e. minimize the overall travel time. According to Braess paradox additional streets might even increase the overall travel time. Note that this can be seen to correspond to Nagel's findings.
Nevertheless Helbing et al find that oscillatory cooperation (the notion of taking turns in order to maximize the system outcome) "can still emerge in route choice games with more than 2 players after a long period (rarely within 300 iterations)". They also find though that "emergent cooperation is unlikely to appear in real traffic systems" under the current conditions. The paper suggests that an automated route guidance system where drivers get individual and on average fair route choice recommendations based on the current traffic situation might help to reach the system optimum.
So looking at two papers that model road traffic from complexity science's point of view, we learn that the system might actually become less efficient as travelers adapt strategies that optimize their individual performance . Game theory tells us that the introduction of more space might actually further worsen the system's performance. All this might have very interesting consequences for our study of aggregate economic behavior. The next step is to look at models that try to measure how the behavior of individuals once they chose a particular road might affect the efficiency of the overall traffic system. Bringing both perspectives together will hopefully give us an idea of the key factors that yield traffic inefficiencies, which in turn will help us when comparing it to other systems that exhibit complex behavior as well, such as the behavior of ants and birds.
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