Random Access Channel with Retransmission Gain

This paper analyzes the maximum steady throughput and optimum media access control (MAC) of a multiuse random access system over channels with retransmission gain. The channel is defined by the packet success probability that is determined by the number of transmissions of the packet and the number of collisions with interfering packets. An approach based on multidimensional Markov chain is applied. The performance over a two-user channel is first analyzed. The stationary distribution of transmission states and the maximum steady throughput are obtained in closed form. The conditions that the optimum MAC in terms of maximum throughput is no MAC are obtained for symmetrical and asymmetrical channels, respectively. The orthogonal channel and conventional channel without retransmission gain are shown to be special instances of our results. The approach is then well extended to multiuser symmetric channel and the general multi-user asymmetric channel. Finally, numerical simulation is presented, which confirms with analytical results well.