Random Access Channel with Retransmission Gain

An analysis of the throughput and stability region of random access systems is currently of interest in research and industry. This study evaluated the performance of a multiuser random access channel with a retransmission gain. The channel was composed of a media access control (MAC) determined by the transmission probabilities and a multiuser communication channel characterized by the packet reception probabilities as functions of the number of packet transmissions and the collision status. The analysis began with an illustrative two-user channel, and was extended to a general multiuser channel. For the two-user channel, a sufficient condition was derived, under which the maximum throughput was achieved with a control-free MAC. For the channel with retransmission gain, the maximum steady throughput was obtained in a closed form. The condition under which the random access channel can acquire retransmission gain was also obtained. The stability region of the general random access channel was derived. These results include those of the well-known orthogonal channel, collision channel and slotted Aloha channel with packet reception as a special instance. The analytical and numerical results showed that exploiting the retransmission gain can increase the throughput significantly and expand the stability region of the random access channel. The analytical results predicted the performance in the simulations quite well.