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
GIX/R/1 queue, where
R denotes the class of distributions whose
Laplace–Stieltjes transforms are rational functions (ratios of a
polynomial of degree at most n to a polynomial of degree
n). The analysis is not restricted to generalized
distributions with phases such as Coxian-n
(Cn) 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.
The use of Spitzer's identity in the investigation of the busy period and other quantities in the queue GI/G/1
