Poisson hypothesis for open networks at low load

A. Rybko, Senya Shlosman, A. Vladimirov

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

Abstract

We study large communication networks of the mean-field type. The input flows to the nodes of the network are supposed to be stationary and with low rate. We show that such a network is ergodic, i.e., it goes to the stationary state, which does not depend on the initial state of the network. This is in contrast with the high load regime, when the large time behavior of the network might depend on its initial state. Our technique is based on the coupling construction, which couples two Non-Linear Markov Processes.

Original languageEnglish
Pages (from-to)145-160
Number of pages16
JournalMoscow Mathematical Journal
Volume17
Issue number1
DOIs
Publication statusPublished - 2017

Keywords

  • Mean-field
  • Non-linear Markov process
  • Queuing theory

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