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An investigation of an $ M^{\theta}/G/1/m$ queueing system with service mode switching


Author: K. Yu. Zhernovyĭ
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 86 (2012).
Journal: Theor. Probability and Math. Statist. 86 (2013), 65-78
MSC (2010): Primary 60K25; Secondary 60K20
DOI: https://doi.org/10.1090/S0094-9000-2013-00889-8
Published electronically: August 20, 2013
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Abstract | References | Similar Articles | Additional Information

Abstract: We consider an $ \mathrm {M^{\theta }/G/1/m}$ queueing system with two service modes. The server switches between the modes when the number of customers present at the beginning of service is larger than $ h$. Laplace transforms for the distributions of the number of customers in the system during the busy period and for the distribution function of the busy period are found. The average duration of the busy period is obtained. Formulas for the stationary distribution of the number of customers in the system and for the stationary characteristics of the system are established.


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Additional Information

K. Yu. Zhernovyĭ
Affiliation: Department of Higher Mathematics, Faculty for Mathematics and Mechanics, National Ivan Franko University, Universytets’ka Street, 1, L’viv, 79000, Ukraine
Email: k{\textunderscore}zhernovyi@yahoo.com

DOI: https://doi.org/10.1090/S0094-9000-2013-00889-8
Keywords: $\mathrm{M^{\theta}/G/1/m}$ queueing system with two service modes, distribution of the number of customers, distribution function of a busy period, method of potential
Received by editor(s): May 16, 2011
Published electronically: August 20, 2013
Article copyright: © Copyright 2013 American Mathematical Society