The virtual waiting time in a finite-buffer queue with a single vacation policy

Authors:
Wojciech M. Kempa
Affiliations:
Institute of Mathematics, Silesian University of Technology, Gliwice, Poland
Venue:
ASMTA'12 Proceedings of the 19th international conference on Analytical and Stochastic Modeling Techniques and Applications
Year:
2012

Citing 4
Cited 0

A finite-capacity queue with exhaustive vacation/close-down/setup times and Markovian arrival processes

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A vacation queue with setup and close-down times and batch Markovian arrival processes

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Departure process in finite-buffer queue with batch arrivals

ASMTA'11 Proceedings of the 18th international conference on Analytical and stochastic modeling techniques and applications
On departure process in the batch arrival queue with single vacation and setup time

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Abstract

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.