On the throughput, capacity and stability regions of random multiple access over standard multi-packet reception channels

This paper studies finite-terminal random multiple access over a standard multi-packet reception (MPR) channel. In the first part of the paper, we show that if the MPR channel is standard, the throughput region of random multiple access is co-ordinate convex. We then study the information capacity region of multiple access without code synchronization and feedback. We show that the asymptotic capacity region is identical to the throughput region. In the second part of the paper, we study the stability region of ALOHA multiple access. For a class of packet arrival distributions, we show that the stationary distribution of the queues possesses the positive and strong positive correlation properties; and this consequently gives an outer bound to the stability region. We also show that if a conjectured "sensitivity monotonicity" property can be shown for the stationary distribution of the queues, then the equivalence between the closure of the stability region and the throughput region follows as a direct consequence, irrespective of the packet arrival distributions