D/M/1 Queue: Policies and Control

Equilibrium G/M/1-FIFO waiting times are exponentially distributed, as first proved by Smith (1953). For other client-sorting policies, such generality is not feasible. Assume that interarrival times are constant. Symbolics for the D/M/1-LIFO density are completely known; numerics for D/M/1-SIRO arise via an unpublished recursion due to Burke (1967). Consider a weighted sum of two costs, one from keeping clients waiting for treatment and the other from having the server idle. With this in mind, what is the optimal interarrival time and how does this depend on the choice of policy?