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December 2016 Detailed computational analysis of queueing-time distributions of the BMAP/G/1 queue using roots
Gagandeep Singh, U. C. Gupta, M. L. Chaudhry
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J. Appl. Probab. 53(4): 1078-1097 (December 2016).

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.

Citation

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Gagandeep Singh. U. C. Gupta. M. L. Chaudhry. "Detailed computational analysis of queueing-time distributions of the BMAP/G/1 queue using roots." J. Appl. Probab. 53 (4) 1078 - 1097, December 2016.

Information

Published: December 2016
First available in Project Euclid: 7 December 2016

zbMATH: 1356.60158
MathSciNet: MR3581243

Subjects:
Primary: 60K25
Secondary: 90B22

Rights: Copyright © 2016 Applied Probability Trust

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Vol.53 • No. 4 • December 2016
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