Deadlocks and waiting times in traffic jam

TL;DR

This paper models traffic jams as band formations in a city with right and up-moving cars, revealing how deadlocks form and that waiting times follow a power law, indicating no characteristic jam duration.

Contribution

It introduces a model showing how small numbers of left-moving cars can cause deadlocks and analyzes the power law distribution of waiting times in traffic jams.

Findings

Deadlocks are caused by a small number of left-moving cars.

Waiting times at signals follow a power law distribution.

The same exponent applies to both band and deadlock scenarios.

Abstract

In a city of right moving and upmoving cars with hardcore constraint, traffic jam occurs in the form of bands. We show how the bands are destroyed by a small number of strictly left moving cars yielding a deadlock phase with a rough edge of left cars. We also show that the probability of waiting time at a signal for a particular tagged car has a power law dependence on time, indicating the absence of any characteristic time scale for an emergent traffic jam. The exponent is same for both the band and the deadlock cases. The significances of these results are discussed.