Queue length distributions in a markov model of a multistage clocked queueing network

Ora E. Percus, J. K. Percus

Research output: Contribution to journalArticlepeer-review

Abstract

In [4], we treated the problem of passage through a discrete‐time clock‐regulated multistage queueing network by modeling the input time series {an} to each queue as a Markov chain. We showed how to transform probability transition information from the input of one queue to the input of the next in order to predict mean queue length at each stage. The Markov approximation is very good for p = E(an) ≦ ½, which is in fact the range of practical utility. Here we carry out a Markov time series input analysis to predict the stage to stage change in the probability distribution of queue length. The main reason for estimating the queue length distribution at each stage is to locate “hot spots”, loci where unrestricted queue length would exceed queue capacity, and a quite simple expression is obtained for this purpose.

Original languageEnglish (US)
Pages (from-to)685-693
Number of pages9
JournalCommunications on Pure and Applied Mathematics
Volume43
Issue number5
DOIs
StatePublished - Jul 1990

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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