Joint MAC and rate control for stability and delay in wireless multi-access channels

In this paper, we investigate the stability and delay issues of a two-user multi-access channel at the bit level. The two users, have the option to transmit at a higher instantaneous rate separately, or to transmit simultaneously but at a lower individual instantaneous rate due to interference caused by concurrent transmissions. Traffic burstiness is considered by modeling random arrivals at the users, and the stability region in terms of bits/slot is derived. Further, we determine the condition under which the maximum stability region is achieved when the users always transmit if their queues are non-empty; in this case, the stability region is shown to be convex. Subsequently, we study the minimum delivery time problem where each user is allocated an initial amount of traffic volume to be sent to the destination. For any initial queue size vector, we explicitly characterize the optimal policy that empties the two users’ queues within the shortest time.