### Abstract

A class of discrete-time closed cyclic networks is analyzed, where queues at each node have ample waiting room and have independent geometric service times with possibly unequal means. If each node has a single server or if there are sufficiently many parallel servers at each node to accommodate all jobs, equilibrium vectors of product form are obtained. For some other cases, equilibrium vectors of product form need not exist. For the single-server model, a normalization constant is computed and used to determine the queue-length distribution at a node.

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

Pages (from-to) | 117-132 |

Number of pages | 16 |

Journal | Queueing Systems |

Volume | 18 |

Issue number | 1-2 |

DOIs | |

State | Published - Mar 1 1994 |

### Fingerprint

### Keywords

- cyclic queueing network
- Discrete-time queue
- normalization constant
- product form

### ASJC Scopus subject areas

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

### Cite this

**Features of some discrete-time cyclic queueing networks.** / Pestien, Victor; Ramakrishnan, Subramanian.

Research output: Contribution to journal › Article

*Queueing Systems*, vol. 18, no. 1-2, pp. 117-132. https://doi.org/10.1007/BF01158777

}

TY - JOUR

T1 - Features of some discrete-time cyclic queueing networks

AU - Pestien, Victor

AU - Ramakrishnan, Subramanian

PY - 1994/3/1

Y1 - 1994/3/1

N2 - A class of discrete-time closed cyclic networks is analyzed, where queues at each node have ample waiting room and have independent geometric service times with possibly unequal means. If each node has a single server or if there are sufficiently many parallel servers at each node to accommodate all jobs, equilibrium vectors of product form are obtained. For some other cases, equilibrium vectors of product form need not exist. For the single-server model, a normalization constant is computed and used to determine the queue-length distribution at a node.

AB - A class of discrete-time closed cyclic networks is analyzed, where queues at each node have ample waiting room and have independent geometric service times with possibly unequal means. If each node has a single server or if there are sufficiently many parallel servers at each node to accommodate all jobs, equilibrium vectors of product form are obtained. For some other cases, equilibrium vectors of product form need not exist. For the single-server model, a normalization constant is computed and used to determine the queue-length distribution at a node.

KW - cyclic queueing network

KW - Discrete-time queue

KW - normalization constant

KW - product form

UR - http://www.scopus.com/inward/record.url?scp=21844482547&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844482547&partnerID=8YFLogxK

U2 - 10.1007/BF01158777

DO - 10.1007/BF01158777

M3 - Article

AN - SCOPUS:21844482547

VL - 18

SP - 117

EP - 132

JO - Queueing Systems

JF - Queueing Systems

SN - 0257-0130

IS - 1-2

ER -