Computational analysis of stationary waiting-time distributions of GIx/R/1 and GIx/D/1 queues

In this article, we obtain, in a unified way a closed-form analytic expression, in terms of roots of the so-called characteristic equation of the stationary waiting-time distribution for the Gl/(x)/R/1 queue, where R denotes the class of distributions whose Laplace-Stielijes transforms are rational functions (ratios of a polynomial of degree at most it to a polynomial of degree it). The analysis is not restricted to generalized distributions with phases such as Coxian-n (C-n) but also covers nonphase-type distributions such as deterministic (D). In the latter case, we get approximate results. Numerical results are presented only for (1) the first two moments of waiting time and (2) the probability that waiting time is zero. It is expected that the results obtained from the present study should prove to be useful not only for practitioners but also for queuing theorists who would like to test the accuracies of inequalities. bounds. or approximations.