The Poisson Multiple-Access Conflict Resolution Problem
The major thrust of system theory research in recent years has been directed at multiterminal, or decentralized, problems. These are characterized by the fact that system functions — such as coding, routing, control, decision, and estimation — are effected simultaneously at several physically distinct sites within the system. The information available differs, in general, from site to site. This necessitates the development of distributed algorithms aimed at cooperatively achieving optimum, or near-optimum, performance in the face of topologically complex information patterns. In previous lectures at CISM, several investigators including myself have treated multiterminal information theory problems involving distributed algorithms for encoding and decoding. In these lectures I concentrated instead on an intriguing problem in multiterminal communication theory, the conflict resolution problem in packet-switched communication networks. After stating the problem, we recast it as one of “fishing in a Poisson stream with a weak net”. The slotted ALOHA protocol is described ana analyzed. Gallager’s improvement on Capetanakis’s algorithm is then treated in considerable detail; a closed-form expression for its efficiency is derived. Recursive equations developed by the Russian and French schools are presented as an alternative means of analyzing this algorithm and others. Then we present Pippenger’s and Molle’s upper bounds to the maximum efficiency attainable. We conclude with what we feel to be a convincing case for our belief that Molle’s method can be improved upon to yield an upper bound of 0.5254 which is only 0.0377 above the efficiency of 0.4877 achieved by the optimized version of Gallager’s algorithm.
KeywordsSlot Aloha Fishing Strategy Poisson Stream Poisson Limit Geneous Poisson Process
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