Throughput of Slotted ALOHA with Encoding Rate Optimization and Multipacket Reception

This paper considers a slotted ALOHA random access system where users send packets to a common receiver with multipacket reception capability. A collection of m users access the shared medium independently of each other with probability p and, upon access, they choose an encoding rate. A collision occurs when the sum of the rates of all the users exceeds the capacity of the channel. We analytically characterize as a function of m and p the encoding rate which maximizes the expected global though put of the system. It is shown that for any value of p the throughput converges to one when m tends to infinity, hence there is no loss due to packet collisions. This is in striking contrast with the well known behavior of slotted ALOHA systems in which users cannot adjust the encoding rate. In that case the throughput decreases to zero as the number of users increases. Finally, assuming that users are selfish, we characterize the encoding rate which maximizes the expected individual throughput of each user, and show that the corresponding Nash equilibrium is not globally optimum.