### Abstract

In this paper we present a new algorithm for evaluating queueing networks with multi-rate traffic. The detailed state space of a node is evaluated by explicit formulæ. We consider reversible nodes with multi-rate traffic and find the state probabilities by taking advantage of local balance. Theory of queueing networks in general, presumes that we have product form between the nodes. Otherwise, we have the state space explosion. Even so, the detailed state space of each node may become very large because there is no product form between chains inside a node. A prerequisite for product form is reversibility which implies that the arrival process and departure process are identical processes, for example state-dependent Poisson processes. This property is equivalent to reversibility. Due to product form, an open network with multi-rate traffic is easy to evaluate by convolution algorithms because the nodes behave as independent nodes. For closed queueing networks with multiple servers in every node and multi-rate services we may apply multidimensional convolution algorithm to aggregate the nodes so that we end up with two nodes, the aggregated node and a single node, for which we can calculate the detailed performance measures.

Original language | English |
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Journal | Advances in Electronics and Telecommunications |

Volume | 2 |

Issue number | 3 |

Pages (from-to) | 3-7 |

ISSN | 2081-8580 |

Publication status | Published - Sep 2011 |

### Keywords

- Multi-rate traffic
- Reversibility
- Convolution algorithm
- Product form
- Insensitivity
- Queueing networks

## Cite this

Iversen, V. B., & Ko, K-T. (2011). Algorithm for queueing networks with multi-rate traffic.

*Advances in Electronics and Telecommunications*,*2*(3), 3-7. http://advances.et.put.poznan.pl/issues/3/ATE_issue3_p0091.pdf