Zero-Automatic Queues

  • Thu-Ha Dao-Thi
  • Jean Mairesse
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3670)

Abstract

We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic queues are characterized by a special buffering mechanism evolving like a random walk on some infinite group or monoid. The salient result is that all 0-automatic queues are quasi-reversible. When considering the two simplest and extremal cases of 0-automatic queues, we recover the simple M /M /1 queue, and Gelenbe’s G-queue with positive and negative customers.

Keywords

M /M /1 queue G-queue quasi-reversibility product form 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Thu-Ha Dao-Thi
    • 1
  • Jean Mairesse
    • 1
  1. 1.LIAFA, CNRS-Université Paris 7France

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