### Abstract

In [4], we treated the problem of passage through a discrete‐time clock‐regulated multistage queueing network by modeling the input time series {a_{n}} 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(a_{n}) ≦ 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 language | English (US) |
---|---|

Pages (from-to) | 685-693 |

Number of pages | 9 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 43 |

Issue number | 5 |

DOIs | |

State | Published - 1990 |

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### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*43*(5), 685-693. https://doi.org/10.1002/cpa.3160430506

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

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 43, no. 5, pp. 685-693. https://doi.org/10.1002/cpa.3160430506

}

TY - JOUR

T1 - Queue length distributions in a markov model of a multistage clocked queueing network

AU - Percus, Ora E.

AU - Percus, Jerome

PY - 1990

Y1 - 1990

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990575176&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990575176&partnerID=8YFLogxK

U2 - 10.1002/cpa.3160430506

DO - 10.1002/cpa.3160430506

M3 - Article

VL - 43

SP - 685

EP - 693

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 5

ER -