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 integr
al control with adaptive gains, designed to provide fast tracking and wide stability margins. The gains are inverse-proportional 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.
When Perturbation Analysis (PA) yields unbiased sensitivity estimators for expected-value performance functions in discrete event dynamic systems, it can be used for performance optimization of those functions. However, when PA is known to be unbiase
d, the complexity of its estimators often does not scale with the systems size. The purpose of this paper is to suggest an alternative approach to optimization which balances precision with computing efforts by trading off complicated, unbiased PA estimators for simple, biased approximate estimators. Furthermore, we provide guidelines for developing such estimators, that are largely based on the Stochastic Flow Modeling framework. We suggest that if the relative error (or bias) is not too large, then optimization algorithms such as stochastic approximation converge to a (local) minimum just like in the case where no approximation is used. We apply this approach to an example of balancing loss with buffer-cost in a finite-buffer queue, and prove a crucial upper bound on the relative error. This paper presents the initial study of the proposed approach, and we believe that if the idea gains traction then it may lead to a significant expansion of the scope of PA in optimization of discrete event systems.
