The Steady State Behaviour Of TheM/Ek/1Queue, With State Dependent Arrival Rates

Abstract

The steady state behaviour of the M/Ek/1 queue, with state dependent arrival rates, is investigated. The method employed is to divide the service time into k phases and derive the probability distribution for the number of phases recursively from its steady equations; then, the distribution of the number of phases recursively from its steady state equations; and finally, the distribution of the number of phases at the time of an arrival is found. Once these two distributions are determined, one can obtain the distribution of the number of elements in the system, the distribution of the actual and virtual waiting time and the sojourn time distribution. A number of interesting relationships between the different distributions are established. A numerical example completes the article.