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Exclusive Queueing Process with Discrete Time

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Abstract

In a recent study (Arita in Phys. Rev. E 80(5):051119, 2009), an extension of the M/M/1 queueing process with the excluded-volume effect as in the totally asymmetric simple exclusion process (TASEP) was introduced. In this paper, we consider its discrete-time version. The update scheme we take is the parallel one. A stationary-state solution is obtained in a slightly arranged matrix product form of the discrete-time open TASEP with the parallel update. We find the phase diagram for the existence of the stationary state. The critical line which separates the parameter space into regions with and without the stationary state can be written in terms of the stationary current of the open TASEP. We calculate the average length of the system and the average number of particles.

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Authors and Affiliations

  1. Faculty of Mathematics, Kyushu University, Fukuoka, 819-0395, Japan

    Chikashi Arita

  2. Research Center for Advanced Science and Technology, The University of Tokyo, Tokyo, 153-8904, Japan

    Daichi Yanagisawa

  3. Japan Society for the Promotion of Science, Tokyo, 102-8472, Japan

    Daichi Yanagisawa

Authors
  1. Chikashi Arita
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  2. Daichi Yanagisawa
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Correspondence to Chikashi Arita.

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Arita, C., Yanagisawa, D. Exclusive Queueing Process with Discrete Time. J Stat Phys 141, 829–847 (2010). https://doi.org/10.1007/s10955-010-0075-9

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  • DOI: https://doi.org/10.1007/s10955-010-0075-9

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