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

Ora E. Percus, Jerome Percus

Research output: Contribution to journalArticle

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 - 1990

Fingerprint

Queue Length Distribution
Queueing networks
Queueing Networks
Queue Length
Markov Model
Queue
Time series
Markov processes
Probability distributions
Predict
Hot Spot
Transition Probability
Locus
Markov chain
Exceed
Discrete-time
Probability Distribution
Transform
Approximation
Modeling

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

Queue length distributions in a markov model of a multistage clocked queueing network. / Percus, Ora E.; Percus, Jerome.

In: Communications on Pure and Applied Mathematics, Vol. 43, No. 5, 1990, p. 685-693.

Research output: Contribution to journalArticle

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