Stability, bounds and approximation in asymmetric buffered aloha-type systems

Random access protocols have been studied since 1970 when Norman Abramson proposed the simplest version of the protocol called ALOHA protocol. Since that time ALOHA-type protocols have received a tremendous amount of attention, both from theoreticians and from engineers. Three types of problems have been always associated with the protocol, namely: stability, (exact) analysis and approximations. The behavior of the original ALOHA protocol with unbuffered users is more or less understood, however, there are still some open problems. In this paper we focus our attention on an asymmetric buffered ALOHA system, i.e., we assume that users have buffers of infinite capacity. So far a good analytical model for the protocol is not available. The stability problem (ergodicity of the associated Markov chain) is still open, however, some progress has been noticed recently. The queue length and waiting time analyses are very scarce, and only some approximations and bounds are known. This paper is a limited survey paper on stability problems, bounds and approximation in the asymmetric buffered ALOHA system.