The Optimal Retry Distribution for Lightly Loaded Slotted Aloha Systems

Most of the analytical work on slotted Aloha has been concerned with maximizing the utilization. The delay experienced by a transmission has not been a primary issue. In this note we take the opposite point of view. It is assumed that the system is operating far below capacity (as is typical in practice), and we concern ourselves with the problem of minimizing packet delay in the event of a collision. The retry distribution that minimizes the average delay is derived. Surprisingly, the optimal retry distribution has finite support, and in fact, one never waits more than three slots before retransmitting.