Transient analysis of two heterogeneous servers queueing system with differentiated vacations subject to system disaster, server repair

This research paper examines the dynamic behavior of a heterogeneous two-server queuing model that incorporates differentiated vacation periods. Additionally, the model accounts for the possibility of a disaster occurring during busy periods and vacations, with immediate initiation of the repair pro...

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Bibliographic Details
Published inSankhyā. Series B (2008) Vol. 86; no. 2; pp. 751 - 776
Main Authors Karthick, Venugopal, Suvitha, Vaidhiyanathan, Sudhesh, Ramupillai
Format Journal Article
LanguageEnglish
Published New Delhi Springer India 01.11.2024
Subjects
Mathematics and Statistics
Statistics
Differentiated vacation
Transient probabilities
Heterogeneous servers
System disaster
Repairable server
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Summary:This research paper examines the dynamic behavior of a heterogeneous two-server queuing model that incorporates differentiated vacation periods. Additionally, the model accounts for the possibility of a disaster occurring during busy periods and vacations, with immediate initiation of the repair process. The motivation for this study stems from the two types of power-saving mechanisms found in IEEE 802.16E. The paper presents explicit expressions, obtained using generating functions, for the time-dependent probabilities of system size, expressed in terms of modified Bessel functions. To further validate the theoretical findings, numerical illustrations have been included.
ISSN:0976-8386
0976-8394
DOI:10.1007/s13571-024-00339-7