Chapter

Formal Techniques for Computer Systems and Business Processes

Volume 3670 of the series Lecture Notes in Computer Science pp 64-78

Zero-Automatic Queues

  • Thu-Ha Dao-ThiAffiliated withLancaster UniversityLIAFA, CNRS-Université Paris 7
  • , Jean MairesseAffiliated withLancaster UniversityLIAFA, CNRS-Université Paris 7

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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