On channel sharing in discrete-time, multi-access broadcast communication

Abstract : The major contribution is the novel techniques to solve a variety of distributed resource sharing problems arising in Packet Radio Networks (PRNETs). Some are applicable to a large class of resource sharing problems in computer communication networks. The results are (1) Problems of adaptive channel sharing algorithms: There are two major contributions falling under this category: (a) A novel distributed adaptive channel-access scheme, the Urn scheme, has been derived mathematically. (b) A novel mathematical approach to decentralized optimal resource sharing is developed. Using this approach, a very general characterization of optimal distributed access schemes for multi-hop networks is derived. (2) Problems of interfering queueing processes: Queueing processes may interfere with each other through their arrival processes (e.g., join the shortest queue routing) or through their service processes (e.g., destructive collisions in PRNETs). We develop novel analytical solutions, exact and approximate, to problems of interfering queues in PRNETs. (3) Capacity of multi-hop networks: We compute the capacity of tandems and show that in the limit, when the length of the tandem increases to infinity, the capacity converges to 4/27 of the bandwidth. A novel phenomena of singular topologies (i.e., where topology helps reduce interference) in PRNETs is explored.