Critical behavior of the exclusive queueing process

TL;DR

This paper studies the critical behavior of the exclusive queueing process, a generalized queue model linked to TASEP, analyzing phase transitions and diffusive properties under different update rules and parameters.

Contribution

It provides a detailed analysis of the phase diagram and critical dynamics of the EQP with parallel and backward-sequential updates, highlighting nonuniversal behavior and transition types.

Findings

Diffusive behavior for eta<eta_c

Sub-diffusive, nonuniversal behavior for eta>eta_c

Transition characteristics depend on update rule and hopping parameter p

Abstract

The exclusive queueing process (EQP) is a generalization of the classical M/M/1 queue. It is equivalent to a totally asymmetric exclusion process (TASEP) of varying length. Here we consider two discrete-time versions of the EQP with parallel and backward-sequential update rules. The phase diagram (with respect to the arrival probability \alpha\ and the service probability \beta) is divided into two phases corresponding to divergence and convergence of the system length. We investigate the behavior on the critical line separating these phases. For both update rules, we find diffusive behavior for small output probability (\beta<\beta_c). However, for \beta>\beta_c it becomes sub-diffusive and nonuniversal: the exponents characterizing the divergence of the system length and the number of customers are found to depend on the update rule. For the backward-update case, they also depend on the hopping parameter p, and remain finite when p is large, indicating a first order transition.