Throughput limits from the asymptotic profile of cyclic networks with state-dependent service rates

Research output: Contribution to journalArticle

2 Scopus citations

Abstract

We consider networks where at each node there is a single exponential server with a service rate which is a non-decreasing function of the queue length. The asymptotic profile of a sequence of networks consists of the set of persistent service rates, the limiting customer-to-node ratio, and the limiting service-rate measure. For a sequence of cyclic networks whose asymptotic profile exists, we compute upper and lower bounds for the limit points of the sequence of throughputs as functions of the limiting customer-to-node ratio. We then find conditions under which the limiting throughput exists and is expressible in terms of the asymptotic profile. Under these conditions, we determine the limiting queue-length distributions for persistent service rates. In the absence of these conditions, the limiting throughput need not exist, even for increasing sequences of cyclic networks.

Original languageEnglish (US)
Pages (from-to)191-219
Number of pages29
JournalQueueing Systems
Volume58
Issue number3
DOIs
StatePublished - Mar 1 2008

Keywords

  • Asymptotic queue length
  • Convergence of throughput
  • Cyclic networks
  • Product form
  • State-dependent service

ASJC Scopus subject areas

  • Statistics and Probability
  • Computer Science Applications
  • Management Science and Operations Research
  • Computational Theory and Mathematics

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