## Abstract

In this paper we investigate a certain class of systems containing dependent discrete time queues. This class of systems consists of N nodes transmitting packets to each other or to the outside of the system over a common shared channel, and is characterized by the fact that access to the channel is assigned according to priorities that are preassigned to the nodes. To each node a given probability distribution is attached, that indicates the probabilities that a packet transmitted by the node is forwarded to one of the other nodes or to the outside of the system. Using extensively the fact that the joint generating function of the queue lengths distribution is an analytic function in a certain domain, we obtain an expression for this joint generating function. From the latter any moment of the queue lengths and also average time delays can be obtained. The main motivation for investigating the class of systems of this paper is its applicability to several packet-radio networks. We give two examples: The first is a certain access scheme for a network where all nodes can hear each other, and the second is a three-node tandem packet-raido network.

Original language | English |
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Pages (from-to) | 265-275 |

Number of pages | 11 |

Journal | Performance Evaluation |

Volume | 3 |

Issue number | 4 |

DOIs | |

State | Published - Nov 1983 |

Externally published | Yes |

## Keywords

- Dependent Arrivals
- Dependent Queues
- Discrete-Time Queues
- Packet-Radio Networks
- Priority Queueing Systems
- Queueing Networks
- Random Routing
- Shared Channel
- Tandem Networks