Informatics and Applications
2016, Volume 10, Issue 2, pp 92-97
QUEUEING SYSTEM WITH WORKING VACATIONS AND HYPEREXPONENTIAL INPUT STREAM
Abstract
The time-dependent process in the single server vacation model with hyperexponential input stream is analyzed. The Laplace transform (with respect to an arbitrary point in time) of the joint distribution of server state, queue size, and elapsed time in that state is obtained. The author restricts themselves to a system with exhaustive service (the queue must be empty when the server starts a vacation). The queueing systems with vacations have been well studied because of their applications in modeling the computer networks, communication, and manufacturing systems. For example, in many digital systems, the processor is multiplexed among a number of jobs and, hence, is not available all the time to handle one job type. Besides such an application, theoretical interest in vacation models has arousen with respect to their relationship with polling models.
[+] References (4)
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[+] About this article
Title
QUEUEING SYSTEM WITH WORKING VACATIONS AND HYPEREXPONENTIAL INPUT STREAM
Journal
Informatics and Applications
2016, Volume 10, Issue 2, pp 92-97
Cover Date
2016-05-30
DOI
10.14357/19922264160211
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
hyperexponential input stream; working vacations; single server; queue
Authors
V. G. Ushakov ,
Author Affiliations
Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M.V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, Moscow 119991, GSP-1, Russian Federation
Institute of Informatics Problems, Federal Research Center “Computer Sciences and Control” of the Russian
Academy of Sciences, 44-2 Vavilov Str.,Moscow 119333, Russian Federation
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