# Stochastic Flow Models with Delays and Applications to Multi-Intersection Traffic Light Control

## TL;DR

This paper extends Stochastic Flow Models to include delays, applying them to multi-intersection traffic light control, and uses gradient-based methods to optimize cycle lengths for better traffic congestion management.

## Contribution

It introduces a delay-inclusive SFM framework for traffic control and develops new IPA-based gradient estimates for adaptive optimization.

## Key findings

- Inclusion of delays improves traffic congestion modeling.
- Gradient-based optimization effectively adapts light cycles.
- New cost metrics better capture congestion effects.

## Abstract

We extend Stochastic Flow Models (SFMs), used for a large class of discrete event and hybrid systems, by including the delays which typically arise in flow movement. We apply this framework to the multi-intersection traffic light control problem by including transit delays for vehicles moving from one intersection to the next. Using Infinitesimal Perturbation Analysis (IPA) for this SFM with delays, we derive new on-line gradient estimates of several congestion cost metrics with respect to the controllable green and red cycle lengths. The IPA 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. We introduce two new cost metrics to better capture congestion and show that the inclusion of delays in our analysis leads to improved performance relative to models that ignore delays.