Queueing process with excluded-volume effect

Abstract

We introduce an extension of the M/M/1 queueing process with a spatial structure and excluded- volume effect. The rule of particle hopping is the same as for the totally asymmetric simple exclusion process (TASEP). A stationary-state solution is constructed in a slightly arranged matrix product form of the open TASEP. We obtain the critical line that separates the parameter space depending on whether the model has the stationary state. We calculate the average length of the model and the number of particles and show the monotonicity of the probability of the length in the stationary state. We also consider a generalization of the model with backward hopping of particles allowed and an alternate joined system of the M/M/1 queueing process and the open TASEP.

9 figures

References in corpus (1)

• Nonequilibrium Steady States of Matrix Product Form: A Solver's Guide

Cited by in corpus (10)

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• Density profiles of the exclusive queueing process
• Effect of walking-distance on a queuing system of totally asymmetric simple exclusion process equipped with functions of site assignments
• Critical behavior of the exclusive queueing process
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• Restricted permutations for the simple exclusion process in discrete time over graphs