An Approximation Method for the Analysis of GI/G/1 Queues

We study in this paper an approximation method for the calculation of various performance measures of a GI/G/1 queue. Instead of solving the waiting time directly, we analyze the idle-period distribution as the starting point. The result is then taken as input to many known results to get other performance measures. We show that the distribution of the GI/G/1 idle period satisfies a nonlinear integral equation. This equation directly leads to an accurate approximate solution of the idle-period distribution of the GI/G/1 queue where the interarrival times have a generalized hyperexponential distribution GH. Since all distribution functions can be approximated by a GH distribution at any given accuracy Botta and Harris [Botta, R. F., C. M. Harris. 1986. Approximation with generalized hyperexponential distributions: Weak convergence results. Queueing Systems2 169-190.], the solution method developed in this paper serves as a unified basis for the analysis of GI/G/1 queues.