Computer-controlled queuing system with constant-access cycle and general service times

Abstract

A computer-controlled single-server queue with Poisson input, first-come-first-served queue discipline and general service times is considered. In statistical equilibrium, the mean queue size, mean waiting time of subscribers and the Laplace-Stieltjes transforms are obtained. Furthermore, a necessary and sufficient condition for the existence of statistical equilibrium of the computer-controlled queuing system is derived. It is shown that, in the limiting case when the access cycle becomes zero, the necessary and sufficient condition for the existence of statistical equilibrium reduces to that of the conventional queuing system.