Smart agents and non-predictability

A curious aspect of making the agents ``smarter'' is that, when it goes beyond a certain point, it may actually degrade system performance. More precisely, while average system performance may be unaffected, system variance, and thus unpredictability, invariably goes up. An example is Fig. 1.6, which shows average system performance in repeated runs as a function of the fraction $f$ of travelers with within-day replanning capability. While average system performance improves with $f$ increasing from zero to 40%, beyond that both average system performance and predictability (variance) of the system performance degrade. In other words, for high levels of within-day replanning capability, the system shows strong variance between uncongested and congested. From a user perspective, this is often not any better than bad average system performance - for example, for a trip to the airport or to the opera, one usually plans according to a worst case travel time. Also, if the system becomes non-predictable, route guidance systems are no longer able to help with efficent system usage. The system ``fights back'' against efficient utiliziation by reducing predictability.

Results of this type seem to be generic. For example, Kelly reports a scenario where many travelers attempt to simultaneously arrive at downtown for work at 8am [27]. In this case, the mechanism at work is easy to see: If, say, 2000 travelers want to go to downtown, and all roads leading there together have a capacity of 2000 vehicles per hour, then the arrival of the travelers at the downtown location necessarily will be spread out over one hour. Success or failure to be ahead of the crowd will decide if one is early or late, very small differences in the individual average departure time will result in large differences in the individual average arrival time, and because of stochasticity there will be strong fluctuations in the arrival time from day to day even if the departure time remains constant. Ref. [28] reports from a scenario where road pricing is used to push traffic closer towards the system optimum. Also in this case, the improved system performance is accompanied by increased variability. Both results were obtained with day-to-day replanning.

Figure 1.6: Predictability as function of within-day rerouting capabilities. The result was obtained in the context of a simulation study of route guidance systems. The x-axis shows the fraction of equipped vehicles; the y-axis shows average travel time of all vehicles in the simulation. For each value of market saturation, five different simulations with different random seeds were run. When market saturation increases from zero to 40%, system performance improves. Beyond that, the average system performance, and, more importantly, also the predictability (variance) of the system performance degrade. From [13].