Monotonicity and asymptotic queue-length distribution in discrete-time networks

Victor Pestien, S. Ramakrishnan

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


For closed, cyclic, discrete-time networks with one server per node and with independent, geometric service times, in equilibrium, the joint queue-length distribution can be realized as the joint distribution of independent random variables, conditionally given their sum. This tool helps establish monotonicity properties of performance measures and also helps show that the queue-length random variables are negatively associated. The queue length at a node is asymptotically analyzed through a family of networks with a fixed number of node types, where the number of nodes approaches infinity, the ratio of jobs to nodes has a positive limit, and each node type has a limiting density. The queue-length distribution at any node is shown to converge, in a strong sense, to a distribution that is conditionally geometric. As a by-product, this approach settles open issues regarding occupancy proportion and average queue length at a node type.

Original languageEnglish (US)
Pages (from-to)313-331
Number of pages19
JournalQueueing Systems
Issue number3
StatePublished - 2002


  • Asymptotic analysis
  • Cyclic network
  • Discrete-time network
  • Monotonicity
  • Negative association
  • Queue-length distribution

ASJC Scopus subject areas

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


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