Abstract

Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of indistinguishable drivers commuting between a common origin/destination pair in an acyclic transportation network. The drivers' route choices are affected by their, relatively infrequent, perturbed best responses to global information about the current network congestion levels, as well as their instantaneous local observation of the immediate surroundings as they transit through the network. A novel model is proposed for the drivers' route choice behavior, exhibiting local consistency with their preference toward globally less congested paths as well as myopic decisions in favor of locally less congested paths. The simultaneous evolution of the traffic congestion on the network and of the aggregate path preference is modeled by a system of coupled ordinary differential equations. The main result shows that, if the frequency of updates of path preferences is sufficiently small as compared to the frequency of the traffic flow dynamics, then the state of the transportation network ultimately approaches a neighborhood of the Wardrop equilibrium. The presented results may be read as a further evidence in support of Wardrop's postulate of equilibrium, showing robustness of it with respect to non-persistent perturbations. The proposed analysis combines techniques from singular perturbation theory, evolutionary game theory, and cooperative dynamical systems. Comment: 21 pages, 2 figures, submitted

Abstract

The concept of resilience can be realized in natural and engineering systems, representing the ability of system to adapt and recover from various disturbances. Although resilience is a critical property needed for understanding and managing the risks and collapses of transportation system, an accepted and useful definition of resilience for urban traffic as well as its statistical property under perturbations is still missing. Here we define city traffic resilience based on the spatio-temporal clusters of congestion in real traffic, and find that the resilience follows a scale free distribution in two-dimensional city road networks and one-dimensional highways, with different exponents, but similar exponents in different days and different cities. The traffic resilience is also revealed to have a novel scaling relation between the cluster size of the spatio-temporal jam and its recovery duration, independent of microscopic details. Our findings of universal traffic resilience can provide indication towards better understanding and designing these complex engineering systems under internal and external disturbances. Comment: 6 pages, 4 figure Document type: Article

Abstract

"jats:p"In this paper, we consider a kinetic description of follow-the-leader traffic models, which we use to study the effect of vehicle-wise driver-assist control strategies at various scales, from that of the local traffic up to that of the macroscopic stream of vehicles. We provide theoretical evidence of the fact that some typical control strategies, such as the alignment of the speeds and the optimisation of the time headways, impact on the local traffic features (for instance, the speed and headway dispersion responsible for local traffic instabilities) but have virtually no effect on the observable macroscopic traffic trends (for instance, the flux/throughput of vehicles). This unobvious conclusion, which is in very nice agreement with recent field studies on autonomous vehicles, suggests that the kinetic approach may be a valid tool for an organic multiscale investigation and possibly the design of driver-assist algorithms. Document type: Article