A Class of Stable Transmission Algorithms for Varying User Models.

Abstract : We consider a broadcast packet radio network with independent and identical users (LID). We require that the time of the transmission channel be slotted, and that transmissions be then synchronous (each packet transmission may only start at the beginning of some slot). We assume ternary feedback per slot (empty versus success versus collision), full feedback sensing by each user, no propagation delays and also that collision results in full destruction of all the involved packets; thus retransmission is then necessary. This report proposed and analyzes a class of stable transmission algorithms whose operation is independent of the number of users in the system and the arrival process per user, as long as the latter is IID. The algorithms in the class are a combination of a random access and a reservation techniques, they are synchronous, and they are studied in the full sensing broadcast environment. For any finite number of independent users in the system, and any IID arrival process per user, their throughput is one. Given some IID arrival process per user, given some algorithm in the class, its limit throughput, when user population tends to infinity, is lowered bounded by its limit throughput, in the presence of the limit Poisson user model. The latter throughput is also attainable; it coincides with the limit throughput, when the users are Poisson. Due to the above, it is concluded that the limit Poisson user model is an indispensable vehicle in the study of the algorithms in the class.