New Approach for Finding Basic Performance Measures of Single Server Queue

Abstract

Consider the single server queue in which the system capacity is infinite and the customers are served on a first come, first served basis. Suppose the probability density function f(t) and the cumulative distribution function F(t) of the interarrival time are such that the rate f(t)/1-F(t) tends to a constant as t→∞, and the rate computed from the distribution of the service time tends to another constant. When the queue is in a stationary state, we derive a set of equations for the probabilities of the queue length and the states of the arrival and service processes. Solving the equations, we obtain approximate results for the stationary probabilities which can be used to obtain the stationary queue length distribution and waiting time distribution of a customer who arrives when the queue is in the stationary state.