### Abstract

For a discrete-time, closed, cyclic queueing network, where the nodes have independent, geometric service times, the equilibrium rate of local progress is determined. Faster nodes are shown to have a capacity depending only on the service probabilities. A family of such networks, each with the same number of types of nodes, is analyzed. If the number of nodes approaches infinity, and if the ratio of jobs to nodes has a positive limit and each node type has an asymptotic density, then for a given node type, the limits of the proportion of occupied nodes and the expected queue length are calculated. These values depend on the service parameter and on the asymptotic rate of local progress. The faster nodes can attain their capacity only when the limiting density of nodes of slowest type is zero.

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

Pages (from-to) | 327-357 |

Number of pages | 31 |

Journal | Queueing Systems |

Volume | 31 |

Issue number | 3-4 |

State | Published - Jul 1 1999 |

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### Keywords

- Asymptotic analysis
- Cyclic network
- Discrete-time queue
- Equilibrium distribution
- Queue length

### ASJC Scopus subject areas

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

### Cite this

**Queue length and occupancy in discrete-time cyclic networks with several types of nodes.** / Pestien, Victor; Ramakrishnan, Subramanian.

Research output: Contribution to journal › Article

*Queueing Systems*, vol. 31, no. 3-4, pp. 327-357.

}

TY - JOUR

T1 - Queue length and occupancy in discrete-time cyclic networks with several types of nodes

AU - Pestien, Victor

AU - Ramakrishnan, Subramanian

PY - 1999/7/1

Y1 - 1999/7/1

N2 - For a discrete-time, closed, cyclic queueing network, where the nodes have independent, geometric service times, the equilibrium rate of local progress is determined. Faster nodes are shown to have a capacity depending only on the service probabilities. A family of such networks, each with the same number of types of nodes, is analyzed. If the number of nodes approaches infinity, and if the ratio of jobs to nodes has a positive limit and each node type has an asymptotic density, then for a given node type, the limits of the proportion of occupied nodes and the expected queue length are calculated. These values depend on the service parameter and on the asymptotic rate of local progress. The faster nodes can attain their capacity only when the limiting density of nodes of slowest type is zero.

AB - For a discrete-time, closed, cyclic queueing network, where the nodes have independent, geometric service times, the equilibrium rate of local progress is determined. Faster nodes are shown to have a capacity depending only on the service probabilities. A family of such networks, each with the same number of types of nodes, is analyzed. If the number of nodes approaches infinity, and if the ratio of jobs to nodes has a positive limit and each node type has an asymptotic density, then for a given node type, the limits of the proportion of occupied nodes and the expected queue length are calculated. These values depend on the service parameter and on the asymptotic rate of local progress. The faster nodes can attain their capacity only when the limiting density of nodes of slowest type is zero.

KW - Asymptotic analysis

KW - Cyclic network

KW - Discrete-time queue

KW - Equilibrium distribution

KW - Queue length

UR - http://www.scopus.com/inward/record.url?scp=0033243597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033243597&partnerID=8YFLogxK

M3 - Article

VL - 31

SP - 327

EP - 357

JO - Queueing Systems

JF - Queueing Systems

SN - 0257-0130

IS - 3-4

ER -