June 1984 LIDS - P - 1387 DISCRETE - TIME PRIORITY QUEUES WITH PARTIAL INTERFERENCE

A class of discrete time priority queueing systems with partial interference is considered. Packet-radio communication networks that use a certain mode of operation fall into this class. In these systems N nodes share a common channel to transmit their packets. One node uses random access scheme while the other nodes use the channel according to prescribed priorities. Packet arrivals are modeled as a discrete-time batch processes, and packets are forwarded through the network according to fixed prescribed probabilities. Steady-state analysis of the class of systems under consideration is provided. In particular, we present a recursive method for the derivation of the joint generating function of the queue lengths distribution at the nodes in steady-state. The condition for steady-state is-also derived. A simple example demonstrates the general analysis and provides some insights into the behavior of systems with partial interference. *This research was carried out at the Massachusetts Institute of Technology, Laboratory for Information and Decision Systems with partial support provided by the National Science Foundation under grant NSF-ECS-8310698. **Moshe Sidi is with the Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel. He is currently a Post-Doctoral Associate at the Laboratory for Information and Decision Systems, M.I.T., Cambridge, MA 02139, USA. Introduction The survey paper by Kobayashi and Konheim [1] discusses many models of discrete-time queueing systems. Such systems have been receiving increased attention in recent years, [2-4] due to their usefulness in modelling and analyzing various types of communication systems. Packet-switched communication networks with point-to-point links between the nodes and fixed length data packets motivated most of these models. The models in [2-4] are of tandem nature since in point-to-point networks the transport of a packet from its source to its destination involves the transmission of the packet over a succession of links. The fixed packet length assumption induces the discrete-time nature of the models. In this paper we consider a class of discrete-time priority queueing systems with partial interference. Consideration of these systems have been primarily motivated by the class of packet-switched communication networks called the multi-access/broadcast networks, or packet-radio networks. In these communication networks all nodes share a common channel through which they transmit their packets and from which they extract packets destined to them, hence the multi-access nature of these networks. In addition, when a node transmits a packet through the shared channel, all nodes that are within its transmission range hear this transmission, hence the broadcast nature of the systems. We assume that the channel time axis is slotted into intervals of size equal to the transmission time of a packet. All packets are assumed to be of fixed and equal size. The nodes are synchronized so that they may start transmission of a packet only at the beginning of a slot, hence the discretetime nature of the system. All nodes are assumed to have infinite buffers.