Density profiles of the exclusive queuing process - Kölner UniversitätsPublikationsServer

Arita, Chikashi and Schadschneider, Andreas ORCID: 0000-0002-2054-7973 (2012). Density profiles of the exclusive queuing process. J. Stat. Mech.-Theory Exp.. BRISTOL: IOP PUBLISHING LTD. ISSN 1742-5468

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DOI:10.1088/1742-5468/2012/12/P12004

Abstract

The exclusive queuing process (EQP) incorporates the exclusion principle into classic queuing models. It is characterized by, in addition to the entrance probability alpha and exit probability beta, a third parameter: the hopping probability p. The EQP can be interpreted as an exclusion process of variable system length. Its phase diagram in the parameter space (alpha, beta) is divided into a convergent phase and a divergent phase by a critical line which consists of a curved part and a straight part. Here we extend previous studies of this phase diagram. We identify subphases in the divergent phase, which can be distinguished by means of the shape of the density profile, and determine the velocity of the system length growth. This is done for EQPs with different update rules (parallel, backward sequential and continuous time). We also investigate the dynamics of the system length and the number of customers on the critical line. They are diffusive or subdiffusive with non-universal exponents that also depend on the update rules.

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Journal Article

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