Stability conditions for a discrete-time decentralised medium access algorithm

Seva Shneer, Alexander Stolyar

Research output: Contribution to journalArticle

Abstract

We consider a stochastic queueing system modelling the behaviour of a wireless network with nodes employing a discrete-time version of the standard decentralised medium access algorithm. The system is unsaturated-each node receives an exogenous flow of packets at the rate of λ packets per time slot. Each packet takes one slot to transmit, but neighbouring nodes cannot transmit simultaneously. The algorithm we study is standard in the following sense: A node with an empty queue does not compete for medium access; the access procedure by a node does not depend on its queue length as long as it is nonzero. Two system topologies are considered, with nodes arranged in a circle and in a line. We prove that, for either topology, the system is stochastically stable under the condition λ<2/5. This result is intuitive for the circle topology as the throughput each node receives in the saturated system (with infinite queues) is equal to the so-called parking constant, which is larger than 2/5. (This fact, however, does not help us to prove the result.) The result is not intuitive for the line topology as in the saturated system some nodes receive a throughput lower than 2/5.

Original languageEnglish (US)
Pages (from-to)3600-3628
Number of pages29
JournalAnnals of Applied Probability
Volume28
Issue number6
DOIs
StatePublished - Dec 2018

Keywords

  • Carrier-sense multiple access
  • Discrete parking process
  • Medium access protocols
  • Nonmonotone process
  • Queueing networks
  • Stochastic stability
  • Wireless systems

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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