Exclusive Queueing Processes and their Application to Traffic Systems

TL;DR

This paper reviews the Exclusive Queueing Process (EQP), a microscopic model for queues that captures internal density profiles and complex phase behavior, with applications to traffic and pedestrian systems.

Contribution

It provides a comprehensive overview of the EQP, highlighting its complex phase diagram, dependence on update procedures, and potential applications in traffic modeling.

Findings

EQP exhibits a rich, nonuniversal phase diagram.

Behavior on phase transition lines is more complex than fixed-length TASEP.

The model's properties depend strongly on update procedures.

Abstract

The dynamics of pedestrian crowds has been studied intensively in recent years, both theoretically and empirically. However, in many situations pedestrian crowds are rather static, e.g. due to jamming near bottlenecks or queueing at ticket counters or supermarket checkouts. Classically such queues are often described by the M/M/1 queue that neglects the internal structure (density profile) of the queue by focussing on the system length as the only dynamical variable. This is different in the Exclusive Queueing Process (EQP) in which the queue is considered on a microscopic level. It is equivalent to a Totally Asymmetric Exclusion Process (TASEP) of varying length. The EQP has a surprisingly rich phase diagram with respect to the arrival probability alpha and the service probability beta. The behavior on the phase transition line is much more complex than for the TASEP with a fixed system length. It is nonuniversal and depends strongly on the update procedure used. In this article, we review the main properties of the EQP. We also mention extensions and applications of the EQP and some related models.