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Detailed computational analysis of queueing-time distributions of the BMAP/G/1 queue using roots

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  09 December 2016

Gagandeep Singh ,
U. C. Gupta  and
M. L. Chaudhry
Gagandeep Singh*
Affiliation:
Panjab University
U. C. Gupta*
Affiliation:
Indian Institute of Technology, Kharagpur
M. L. Chaudhry*
Affiliation:
Royal Military College of Canada
*
* Postal address: Department of Mathematics, Panjab University, Chandigarh, 160014, India. Email address: rahigs@gmail.com
** Postal address: Department of Mathematics, Indian Institute of Technology, Kharagpur, 721302, India. Email address: umesh@maths.iitkgp.ernet.in
*** Postal address: Department of Mathematics and Computer Science, Royal Military College of Canada, PO Box 17000, STN Forces, Kingston, ON, K7K 7B4, Canada. Email address: chaudhry-ml@rmc.ca
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Abstract

In this paper we present closed-form expressions for the distribution of the virtual (actual) queueing time for the BMAP/R/1 and BMAP/D/1 queues, where `R' represents a class of distributions having rational Laplace‒Stieltjes transforms. The closed-form analysis is based on the roots of the underlying characteristic equation. Numerical aspects have been tested for a variety of arrival and service-time distributions and results are matched with those obtained using the matrix-analytic method (MAM). Further, a comparative study of computation time of the proposed method with the MAM has been carried out. Finally, we also present closed-form expressions for the distribution of the virtual (actual) system time. The proposed method is analytically quite simple and easy to implement.

Keywords

Batch Markovian arrival processBMAProotsqueueing timesystem timevirtual waiting timerational Laplace‒Stieltjes transformmatrix exponentialphase typedeterministic

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 1078 - 1097
Copyright
Copyright © Applied Probability Trust 2016 

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