### Abstract

Analytical models for wormhole-routed hypercubes with deterministic routing have been widely reported in the literature. A model for the hypercube with fully-adaptive routing has recently been proposed in [1]. It uses M/M/1 queues, and computes a different probability of blocking at each intermediate router along the message path. As a result, the number of equations, and thus the computation steps, to evaluate latency increases with the network size. This paper proposes an alternative model that uses M/G/1 queues, and requires a constant number of computation steps irrespective of the network size. It achieves this by computing only once the mean probability of blocking across the entire path, and using it to determine the blocking time at a given router. Simulation experiments reveal that the model yields accurate latency results.

Original language | English |
---|---|

Pages (from-to) | 111-118 |

Number of pages | 8 |

Journal | Telecommunication Systems |

Volume | 13 |

Issue number | 1 |

Publication status | Published - 2000 |

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### ASJC Scopus subject areas

- Computer Networks and Communications
- Electrical and Electronic Engineering

### Cite this

*Telecommunication Systems*,

*13*(1), 111-118.

**Modelling fully-adaptive routing in hypercubes.** / Loucif, S.; Ould-Khaoua, M.; Mackenzie, L. M.

Research output: Contribution to journal › Article

*Telecommunication Systems*, vol. 13, no. 1, pp. 111-118.

}

TY - JOUR

T1 - Modelling fully-adaptive routing in hypercubes

AU - Loucif, S.

AU - Ould-Khaoua, M.

AU - Mackenzie, L. M.

PY - 2000

Y1 - 2000

N2 - Analytical models for wormhole-routed hypercubes with deterministic routing have been widely reported in the literature. A model for the hypercube with fully-adaptive routing has recently been proposed in [1]. It uses M/M/1 queues, and computes a different probability of blocking at each intermediate router along the message path. As a result, the number of equations, and thus the computation steps, to evaluate latency increases with the network size. This paper proposes an alternative model that uses M/G/1 queues, and requires a constant number of computation steps irrespective of the network size. It achieves this by computing only once the mean probability of blocking across the entire path, and using it to determine the blocking time at a given router. Simulation experiments reveal that the model yields accurate latency results.

AB - Analytical models for wormhole-routed hypercubes with deterministic routing have been widely reported in the literature. A model for the hypercube with fully-adaptive routing has recently been proposed in [1]. It uses M/M/1 queues, and computes a different probability of blocking at each intermediate router along the message path. As a result, the number of equations, and thus the computation steps, to evaluate latency increases with the network size. This paper proposes an alternative model that uses M/G/1 queues, and requires a constant number of computation steps irrespective of the network size. It achieves this by computing only once the mean probability of blocking across the entire path, and using it to determine the blocking time at a given router. Simulation experiments reveal that the model yields accurate latency results.

UR - http://www.scopus.com/inward/record.url?scp=23044520184&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044520184&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:23044520184

VL - 13

SP - 111

EP - 118

JO - Telecommunication Systems

JF - Telecommunication Systems

SN - 1018-4864

IS - 1

ER -