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

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

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
Volume40
Issue number3
DOIs
StatePublished - Dec 1 2002

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Random variables
Byproducts
Servers
Monotonicity
Queue
Discrete-time
Node

Keywords

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

ASJC Scopus subject areas

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

Cite this

Monotonicity and asymptotic queue-length distribution in discrete-time networks. / Pestien, Victor; Ramakrishnan, Subramanian.

In: Queueing Systems, Vol. 40, No. 3, 01.12.2002, p. 313-331.

Research output: Contribution to journalArticle

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