Stability and Delay of Finite-User Slotted ALOHA With Multipacket Reception

Abstract

The effect of Multipacket Reception (MPR) on stability and delay of slotted ALOHA based random access systems is considered. A general asymmetric MPR model is introduced and the MAC capacity region is specified. An explicit characterization of the ALOHA stability region for the two user system is given. It is shown that the stability region undergoes a phase transition from a concave region to a convex region bounded by lines as the MPR capability improves. It is also shown that after this phase transition, slotted ALOHA is optimal i.e., the ALOHA stability region coincides with the MAC capacity region. Further, it is observed that there is no need for transmission control when ALOHA is optimal i.e., ALOHA with transmission probability one is optimal. These results are extended to a symmetric N > 2 user ALOHA system, where it is shown that for a large class of symmetric MPR channels no transmission control is optimal from a stability viewpoint. This finding suggests that if the physical layer is even reasonably good, there is no need for sophisticated Medium Access Control protocols.Next, sufficient conditions for stability of slotted ALOHA for the asymmetric N > 2 case are provided.Finally, a complete characterization of average delay in capture channels for the two user system is given. In cases with non-zero capture probability, no transmission control is found to minimize delay for a subset of stable arrival rates. It is shown that in certain capture scenarios, no transmission control is delay-optimal for all stable arrival rates. Further, it is also shown that no transmission control is optimal for stability and delay simultaneously in the two user capture channel.

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