The Best and Worst Packet Transmission Policies

We consider the problem of optimizing the order of transmitting and discarding packets for queueing packet networks. The problem gives rise to a queueing system consisting of a finite-capacity buffer, a constant service-time server, and a service policy. We show that for any given sampling function of an input traffic, the LIFO discipline is the best in terms of delays, while FIFO is the worst. We give a comparison of basic performances for LIFO, FIFO, RANDOM, and the PUSH-OUT discipline $d^\ast$. The proof of optimality is given for general input traffic, the delay distribution functions for LIFO, FIFO, RANDOM, and $d^\ast$ are found for stationary memoryless traffic, and a numerical comparison of disciplines is given for the Poisson traffic. We consider discrete-time systems only.