Infinitesimal perturbation analysis of stochastic hybrid systems: Application to congestion management in traffic-light intersections

Abstract

Abstract-This paper presents a new approach to congestion management at traffic-light intersections. The approach is based on controlling the relative lengths of red/green cycles in order to have the congestion level track a given reference. It uses an integral control with adaptive gains, designed to provide fast tracking and wide stability margins. The gains are inverseproportional to the derivative of the plant-function with respect to the control parameter, and are computed by infinitesimal perturbation analysis. Convergence of this technique is shown to be robust with respect to modeling uncertainties, computing errors, and other random effects. The framework is presented in the setting of stochastic hybrid systems, and applied to a particular traffic-light model. This is but an initial study and hence the latter model is simple, but it captures some of the salient features of traffic-light processes. The paper concludes with comments on possible extensions of the proposed approach to traffic-light grids with realistic flow models.

Congestion management in traffic-light intersections via Infinitesimal Perturbation Analysis**Research supported in part by the NSF under Grant CNS-1239225.

“…We point out that the rate-terms in (13) can be measured in real time by detecting the speed of passing vehicles. For details of these derivations please see Wardi and Seatzu (2014).…”

“…Reference Wardi and Seatzu (2014), considering only a singlequeue system, derived the following result for the term ∂xi ∂θi . For t lying in the interior of an empty period in queue i, ∂xi ∂θi (t, θ i ) = 0.…”

Estimating the Critical Density of Road Transportation Networks using Infinitesimal Perturbation Analysis of Hybrid Systems

“…In these works, the on-line gradient estimators are used to iteratively adjust the optimum light cycle lengths over an average traffic congestion metric with respect to the controllable variables that in turn define the green and red cycle phases. The work in [13] tries to control the red/green phases over a signalizing intersection thus to regulate congestion under a given reference level (queue length). The major advantage of these approaches is that vehicles flow rates are measured on-line only when specific events occur with the gradient estimators obtained only by counting the traffic light switchings.…”