The Fixed-Cycle Traffic-Light queue with multiple lanes and temporary blockages

TL;DR

This paper extends the Fixed-Cycle Traffic-Light queue model to include multiple lanes and pedestrian-induced blockages, providing a more realistic analysis of traffic flow and delays at intersections.

Contribution

It introduces a generalized FCTL queue model incorporating pedestrian blockages and simultaneous vehicle departures, using advanced analytical techniques.

Findings

Pedestrian blockages significantly increase vehicle delays.

Multiple lanes and simultaneous departures affect queue length distributions.

The model offers insights into optimizing traffic light cycles.

Abstract

Traffic-light modelling is a complex task, because many factors have to be taken into account. In particular, capturing all traffic flows in one model can significantly complicate the model. Therefore, several realistic features are typically omitted from most models. We introduce a mechanism to include pedestrians and focus on situations where they may block vehicles that get a green light simultaneously. More specifically, we consider a generalization of the Fixed-Cycle Traffic-Light (FCTL) queue. Our framework allows us to model situations where (part of the) vehicles are blocked, e.g. by pedestrians that block turning traffic and where several vehicles might depart simultaneously, e.g. in case of multiple lanes receiving a green light simultaneously. We rely on probability generating function and complex analysis techniques which are also used to study the regular FCTL queue. We study the effect of several parameters on performance measures such as the mean delay and queue-length distribution.