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Journal of Statistical Physics

, Volume 173, Issue 3–4, pp 1227–1251 | Cite as

Metastability of Queuing Networks with Mobile Servers

  • F. BaccelliEmail author
  • A. Rybko
  • S. Shlosman
  • A. Vladimirov
Article

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 metastability 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.

Keywords

Mean-field limit Non-linear Markov process Random walks on graphs Martingale 

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • F. Baccelli
    • 4
    Email author
  • A. Rybko
    • 3
  • S. Shlosman
    • 1
    • 2
    • 3
  • A. Vladimirov
    • 3
  1. 1.Skolkovo Institute of Science and TechnologyMoscowRussia
  2. 2.Aix Marseille Université, Université de ToulonMarseilleFrance
  3. 3.Inst. of the Information Transmission ProblemsRASMoscowRussia
  4. 4.Department of MathematicsUT AustinAustinUSA

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