Large-Scale Traffic Signal Offset Optimization

TL;DR

This paper introduces a novel algorithm for large-scale traffic signal offset optimization that guarantees near-global optimality and near-linear runtime on tree-like networks, validated on real-world traffic data.

Contribution

The paper presents a new convex relaxation and randomized rounding approach for traffic signal optimization, with proven approximation guarantees and efficient performance on large networks.

Findings

Algorithm achieves solutions at least 78.5% of optimal value.

Empirical runtime is near-linear with network size.

Solutions are within 99% of the global optimum.

Abstract

The offset optimization problem seeks to coordinate and synchronize the timing of traffic signals throughout a network in order to enhance traffic flow and reduce stops and delays. Recently, offset optimization was formulated into a continuous optimization problem without integer variables by modeling traffic flow as sinusoidal. In this paper, we present a novel algorithm to solve this new formulation to near-global optimality on a large-scale. Specifically, we solve a convex relaxation of the nonconvex problem using a tree decomposition reduction, and use randomized rounding to recover a near-global solution. We prove that the algorithm always delivers solutions of expected value at least 0.785 times the globally optimal value. Moreover, assuming that the topology of the traffic network is "tree-like", we prove that the algorithm has near-linear time complexity with respect to the number of intersections. These theoretical guarantees are experimentally validated on the Berkeley, Manhattan, and Los Angeles traffic networks. In our numerical results, the empirical time complexity of the algorithm is linear, and the solutions have objectives within 0.99 times the globally optimal value.