Transient workload distribution in the M/G/1 finite-buffer queue with single and multiple vacations

A finite-buffer M / G / 1 -type queueing system with exhaustive service and server vacations is considered. The single and multiple vacation policies are investigated separately. In the former case a single vacation is being initialized every time when the system becomes empty. After the vacation th...

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Bibliographic Details
Published in:Annals of operations research 2016-04, Vol.239 (2), p.381-400
Main Author: Kempa, Wojciech M.
Format: Article
Language:English
Subjects:
Buffers
Business and Management
Combinatorics
File servers
Integral equations
Laplace transforms
Management
Methods
Operations research
Operations Research/Decision Theory
Policies
Query processing
Queuing theory
Scheduling (Management)
Theory of Computation
Vacations
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Summary:A finite-buffer M / G / 1 -type queueing system with exhaustive service and server vacations is considered. The single and multiple vacation policies are investigated separately. In the former case a single vacation is being initialized every time when the system becomes empty. After the vacation the server waits on standby for packets to start the service process. In the multiple vacation policy the server begins successive single vacation periods until at least one packet is present in the system. For both vacation policies systems of integral equations for the transient virtual waiting time v ( t ) distributions, conditioned by the numbers of packets present in the system at the start epoch, are found. The representations for the twofold Laplace transforms of the conditional distributions of v ( t ) are obtained and written in compact forms, convenient in numerical treatment. From these formulae stationary distributions of v ( t ) and their means can be computed via usual operations on transforms. Some numerical illustrations of theoretical results are attached as well.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-015-1804-x