Fast mixing of parallel glauber dynamics and low-delay csma scheduling

Libin Jiang, Mathieu Leconte, Jian Ni, R. Srikant, Jean Walrand

Research output: Contribution to journalArticle

Abstract

Glauber dynamics is a powerful tool to generate randomized, approximate solutions to combinatorially difficult problems. It has been recently used to design distributed carrier-sense multiple-access (CSMA) scheduling algorithms for multihop wireless networks. In this paper, we derive bounds on the mixing time of a generalization of Glauber dynamics where multiple links update their states in parallel and the fugacity of each link can be different. The results are used to prove that the average queue length (and hence, the delay) under the parallel-Glauber-dynamics-based CSMA grows polynomially in the number of links for wireless networks with bounded-degree interference graphs when the arrival rate lies in a fraction of the capacity region. Other versions of adaptive CSMA can be analyzed similarly. We also show that in specific network topologies, the low-delay capacity region can be further improved.

Original languageEnglish (US)
Article number6214604
Pages (from-to)6541-6555
Number of pages15
JournalIEEE Transactions on Information Theory
Volume58
Issue number10
DOIs
StatePublished - 2012

Keywords

  • Carrier-sense multiple-access (CSMA)
  • Glauber dynamics
  • Markov chain
  • delay performance
  • mixing time
  • scheduling algorithm

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

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