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arXiv · 1704.02521

Metastability of Queuing Networks with Mobile Servers

F. Baccelli·A. Rybko·S. Shlosman·A. Vladimirov
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Abstract

We study symmetric queuing networks with moving servers and FIFO service discipline. The mean-field limit dynamics demonstrates unexpected behavior which we attribute to the meta-stability phenomenon. Large enough finite symmetric networks on regular graphs are proved to be transient for arbitrarily small inflow rates. However, the limiting non-linear Markov process possesses at least two stationary solutions. The proof of transience is based on martingale techniques.

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F. Baccelli, A. Rybko, S. Shlosman, A. Vladimirov. 2017-04-08. Metastability of Queuing Networks with Mobile Servers. https://doi.org/10.1007/s10955-018-2023-z

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