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.
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Dao-Thi, TH., Mairesse, J. (2005). Zero-Automatic Queues. In: Bravetti, M., Kloul, L., Zavattaro, G. (eds) Formal Techniques for Computer Systems and Business Processes. EPEW WS-FM 2005 2005. Lecture Notes in Computer Science, vol 3670. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549970_6
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DOI: https://doi.org/10.1007/11549970_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-28701-8
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