Metastability of Queuing Networks with Mobile Servers

F. Baccelli, A. Rybko, S. Shlosman, A. Vladimirov

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1227-1251
Number of pages25
JournalJournal of Statistical Physics
Volume173
Issue number3-4
DOIs
Publication statusPublished - 1 Nov 2018

Keywords

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

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