Dynamical analysis of the exclusive queueing process

TL;DR

This paper investigates the dynamic behavior of an exclusive queueing process modeled as a TASEP with varying system length, analyzing phase transitions and validating predictions with simulations.

Contribution

It provides a detailed dynamical analysis of the EQP using analytical, phenomenological, and simulation methods, extending previous stationary state results.

Findings

Identifies two main phases: convergence and divergence.

Quantitative agreement of domain wall theory with simulations in the convergent phase.

Partial agreement in the divergent phase, only for particle number.

Abstract

In a recent study [C Arita and D Yanagisawa: J. Stat. Phys. 141, 829 (2010)] the stationary state of a parallel-update TASEP with varying system length, which can be regarded as a queueing process with excluded-volume effect (exclusive queueing process, EQP), was obtained. We analyze the dynamical properties of the number of particles $< N_t>$ and the position of the last particle (the system length) $< L_t>$, using an analytical method (generating function technique) as well as a phenomenological description based on domain wall dynamics and Monte Carlo simulations. The system exhibits two phases corresponding to linear convergence or divergence of $< N_t>$ and $< L_t>$. These phases can both further be subdivided into high-density and maximal-current subphases. The predictions of the domain wall theory are found to be in very good agreement quantitively with results from Monte Carlo simulations in the convergent phase. On the other hand, in the divergent phase, only the prediction for $< N_t>$ agrees with simulations.