Delay distributions of slotted ALOHA and CSMA

In this paper, we derive the closed-form delay distributions of slotted ALOHA and nonpersistent carrier sense multiple access (CSMA) protocols under steady state. Three retransmission policies are analyzed. We find that under a binary exponential backoff retransmission policy, finite average delay and finite delay variance can be guaranteed for G < 2S and G < 4S/3, respectively, where G is the channel traffic and S is the channel throughput. As an example, in slotted ALOHA, S < In 2/2 and S < 3 (In 4 - In 3) /4 are the operating ranges for finite first and second delay moments. In addition, the blocking probability and delay performance as a function of r(max) (maximum number of retransmissions allowed) is also derived.