Brooke Shrader

Stability in Random Access Networks

In this talk we describe past and recent efforts towards characterizing the queueing stability region of a wireless network in which source nodes randomly and independently access the channel. We begin by describing some of the tools used in these problems: a Markov chain representing the queue lengths, the stability conditions for a single queue, and parallel dominant systems in which the queue length stochastically dominates that of the original system. We then proceed to describe work on the stability of a network with a single destination node. The methodology and results for the collision channel model as well as the multipacket reception channel are reviewed. We also outline an interesting connection between the stability and the Shannon capacity. Next, we examine the stability region for a network with multiple destination nodes and broadcast transmission. The broadcast service process is described through use of a Markov chain representing which destinations have received the packet currently undergoing transmission. We compare the broadcast stability region with the stability region for a single destination. We point to open research problems in this area throughout the talk and conclude by describing possiblities for future work.

This is joint work with Anthony Ephremides.