Volume 104, Number 3, November 2013
|Number of page(s)||6|
|Published online||04 December 2013|
Critical behavior of the exclusive queueing process
1 Institut de Physique Théorique, CEA Saclay - F-91191 Gif- sur-Yvette, France
2 Theoretische Physik, Universität des Saarlandes - D-66041 Saarbrücken, Germany
3 Institut für Theoretische Physik, Universität zu Köln - D-50937 Köln, Germany
Received: 9 August 2013
Accepted: 5 November 2013
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 α and the service probability β) 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 service probability . However, for it becomes sub-diffusive and nonuniversal: the critical 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.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 02.50.-r – Probability theory, stochastic processes, and statistics / 05.70.Fh – Phase transitions: general studies
© EPLA, 2013
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