Equilibrium analysis of macroscopic traffic oscillations

Using a simple network model with two parallel links connecting a diverge and a merge, this paper studies under what conditions traffic oscillations may be initiated and propagated in a traffic stream, specially at freeway bottlenecks. Drivers are assumed to minimize either the experienced or instantaneous travel times, and in doing so, they settle at a Wardrop (day-to-day) equilibrium or a Boston (within-day) traffic equilibrium, respectively. We prove that the path travel time function in our model is not monotone, and show that this property leads to multiple Wardrop equilibria, of which only one is both stable and efficient. The paper shows that periodic traffic oscillations do not arise from Wardrop equilibria. Trivial oscillations exist at Boston equilibria, which are caused by drivers' overreaction to traffic conditions. However, periodic oscillations are likely to emerge when (1) transitions between stable and unstable equilibria take place, and more importantly, (2) drivers make decisions based on out-of-date information of traffic conditions. The latter finding is useful in guiding control practice at freeway bottlenecks and work zones to prevent traffic oscillations.