Multi-intersection Traffic Light Control Using Infinitesimal Perturbation Analysis

Abstract

We address the traffic light control problem for multiple intersections in tandem by viewing it as a stochastic hybrid system and developing a Stochastic Flow Model (SFM) for it. Using Infinitesimal Perturbation Analysis (IPA), we derive on-line gradient estimates of a cost metric with respect to the controllable green and red cycle lengths. The IPA estimators obtained require counting traffic light switchings and estimating car flow rates only when specific events occur. The estimators are used to iteratively adjust light cycle lengths to improve performance and, in conjunction with a standard gradient-based algorithm, to obtain optimal values which adapt to changing traffic conditions. Simulation results are included to illustrate the approach.

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

“…note that this is like one of the functions f j (θ) defined in (14) with the noted exceptions. Let τ i (θ), i = 1, .…”

“…with only the following two possible exceptions: (i) For j = 1, if ξ 1 (θ) = u t (θ), then the left -limit point of the integral in (14) is u t (θ) and not u t (θ) − ; and (ii) for j = p, if η p (θ) = t then the right-limit point of the integral is t and not t + .…”

“…Early techniques developed for these control and optimization problems include dynamic programming [20] and linear complementary algorithms [8], while more recent approaches are based on Markov-decision processes [21], game theory [3], and mixedinteger programming [9]; [19] contains an early survey, and a recent one can be found in [10]. Regarding applications of IPA, early results were presented in [12], [18], and a recent systematic approach has been developed in [13], [14], [15], [10]. This approach defines the traffic-light control problem in the aforementioned setting of stochastic hybrid systems [7], and develops for it effective IPA-based algorithms.…”

Differentiable Agent-Based Simulation for Gradient-Guided Simulation-Based Optimization

“…While gradient-free simulation-based optimization is a time-tested approach, the hypothesis underlying the present paper is that the targeted local search carried out by gradient-based methods may achieve faster convergence or higher-quality solutions for certain agent-based models. An existing method to obtain gradients is Infinitesimal Perturbation Analysis (IPA) [29], which the literature applies by determining derivative expressions by a manual model analysis (e.g., [13,22,33]), limiting its applicability to relatively simple models. Alternatively, gradients can be estimated based on finite differences.…”

Quasi-dynamic Traffic Light Control for a Single Intersection

“…In [12], we studied the TLC problem for a single intersection using a Stochastic Flow Model (SFM) and Infinitesimal Perturbation Analysis (IPA), and extended the method to multiple intersections in [13]. In this prior work, the green/red cycle lengths are viewed as controllable parameters.…”