Exact dynamical state of the exclusive queueing process with deterministic hopping

TL;DR

This paper derives exact dynamical properties of the exclusive queueing process with deterministic hopping, revealing detailed insights into its spatial and temporal behavior using a matrix product approach.

Contribution

It provides the first exact analysis of the EQP with deterministic hopping, including explicit calculations of the density profile and other dynamical features.

Findings

Exact density profile obtained for p=1

Demonstrated the applicability of matrix product methods

Revealed nontrivial dynamical behavior in the deterministic case

Abstract

The exclusive queueing process (EQP) has recently been introduced as a model for the dynamics of queues which takes into account the spatial structure of the queue. It can be interpreted as a totally asymmetric exclusion process of varying length. Here we investigate the case of deterministic bulk hopping p=1 which turns out to be one of the rare cases where exact nontrivial results for the dynamical properties can be obtained. Using a time-dependent matrix product form we calculate several dynamical properties, e.g. the density profile of the system.