Optimal buffer design of an m/g/s queue with finite capacity∗

Abstract

This paper provides an approximate solution of a buffer design problem in an M/G/s queueing system with finite waiting spaces. The buffer design problem is to determine the smallest buffer capacity such that the proportion of lost customers is below an acceptable level. A basic conservation law in the M/G/s queue plus some heuristics yield a simple approximation for the loss probability in the system. The approximation is then applied to the buffer design problem to obtain a simple approximation for the optimal buffer capacity, which has an intimate relation with the well-known Erlang loss formula. As an application of this approximation, two-moment approximations for asymptotic decay rates of tail probabilities are developed for the associated M/G/s queue with infinite capacity