### Abstract

We analyze a discrete‐time network of queues. The unit element of the network is the 2 × 2 buffered switch, which we regard as a system of two queues working in parallel. We show how to transform transition probability information from the output of one switch, or network stage, to the input of the next one. This is used to carry out a Markov time series input model to predict mean queue length at every stage of the system. Another model considered is a renewal process time series model, which we use to find the mean queue length of the second stage of the network. Numerical simulations fall within the narrow band spanned by the two models.

Original language | English (US) |
---|---|

Pages (from-to) | 273-289 |

Number of pages | 17 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 43 |

Issue number | 2 |

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*(2), 273-289. https://doi.org/10.1002/cpa.3160430205

**Models for queue length in clocked queueing networks.** / Percus, Ora E.; Percus, Jerome.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 43, no. 2, pp. 273-289. https://doi.org/10.1002/cpa.3160430205

}

TY - JOUR

T1 - Models for queue length in clocked queueing networks

AU - Percus, Ora E.

AU - Percus, Jerome

PY - 1990

Y1 - 1990

N2 - We analyze a discrete‐time network of queues. The unit element of the network is the 2 × 2 buffered switch, which we regard as a system of two queues working in parallel. We show how to transform transition probability information from the output of one switch, or network stage, to the input of the next one. This is used to carry out a Markov time series input model to predict mean queue length at every stage of the system. Another model considered is a renewal process time series model, which we use to find the mean queue length of the second stage of the network. Numerical simulations fall within the narrow band spanned by the two models.

AB - We analyze a discrete‐time network of queues. The unit element of the network is the 2 × 2 buffered switch, which we regard as a system of two queues working in parallel. We show how to transform transition probability information from the output of one switch, or network stage, to the input of the next one. This is used to carry out a Markov time series input model to predict mean queue length at every stage of the system. Another model considered is a renewal process time series model, which we use to find the mean queue length of the second stage of the network. Numerical simulations fall within the narrow band spanned by the two models.

UR - http://www.scopus.com/inward/record.url?scp=84990623981&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990623981&partnerID=8YFLogxK

U2 - 10.1002/cpa.3160430205

DO - 10.1002/cpa.3160430205

M3 - Article

VL - 43

SP - 273

EP - 289

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 2

ER -