Stability and delay of finite-user slotted ALOHA with multipacket reception

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 medium-access control (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 polyhedral region 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. Next, these results are extended to a symmetric N>2 user ALOHA system. Finally, a complete characterization of average delay in capture channels for the two-user system is given. It is shown that in certain capture scenarios, ALOHA with transmission probability one is delay optimal for all stable arrival rates. Further, it is also shown that ALOHA with transmission probability one is optimal for stability and delay simultaneously in the two-user capture channel.