I n this paper, we consider the steady-state queue length of the multiserver finite-capacity GI/G/c/c + r queue.As a result, we first obtain an exact transform-free expression for the steady-state queue-length distribution. Making use of this result, we then present a simple two-moment approximation for the queue-length distribution. From this, approximations for some important performance measures, such as the loss probability, the mean queue length, and the mean waiting time, are also obtained. In addition, we propose an approximation for the minimal buffer size that keeps the loss probability below an acceptable level. Extensive numerical experiments show that our approximation is extremely simple yet fairly good in its performance.
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.
In this paper, we first consider a Geo/G/1 queue with disasters that remove all workloads from the system upon their occurrence. We present the steady-state queue-length distribution of the Geo/G/1 queue with disasters. Using this result, we then analyze the Geo/G/1 queue with multiple working vacations in which the server works at a different rate rather than completely stopping during the vacation period. We also present the steady-state queue-length distribution of the Geo/G/1 queue with multiple working vacations.
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