Random Access Broadcast: Stability and Throughput Analysis

A wireless network in which packets are broadcast to a group of receivers through use of a random access protocol is considered in this work. The relation to previous work on networks of interacting queues is discussed and subsequently, the stability and throughput regions of the system are analyzed and presented. A simple network of two source nodes and two destination nodes is considered first. The broadcast service process is analyzed assuming a channel that allows for packet capture and multipacket reception. It is proved that the stability and throughput regions coincide in this small network. The same problem for a network with N sources and M destinations is considered next. The channel model is simplified in that packet capture and multipacket reception is no longer permitted. Bounds on the stability region are developed using the concept of stability rank and the throughput region of the system is compared to the bounds. Our results show that as the number of destination nodes increases, the stability and throughput regions diminish. Additionally, a previous conjecture that the stability and throughput regions coincide for a network of arbitrarily many sources is supported for a broadcast scenario by the results presented in this work.