A finite-buffer queueing system with Poisson arrivals and generally distributed service times is considered. Every time when the system empties, a single vacation is initialized, during which the service process is blocked. A system of integral equations for the transient distributions of the virtual waiting time v(t) at a fixed moment t, conditioned by the numbers of packets present in the system at the opening, is derived. A compact formula for the 2-fold Laplace transform of the conditional distribution of v(t) is found and written down using a special-type sequence called a potential. From this representation the stationary distribution of v(t) as t → ∞ and its mean can be easily obtained. Theoretical results are illustrated by numerical examples as well. © 2012 Springer-Verlag.
CITATION STYLE
Kempa, W. M. (2012). The virtual waiting time in a finite-buffer queue with a single vacation policy. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7314 LNCS, pp. 47–60). https://doi.org/10.1007/978-3-642-30782-9_4
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