Detailed computational analysis of queueing-time distributions of the BMAP/G/1 queue using roots. (9th December 2016)

• Record Type: Journal Article
• Authors: Singh, Gagandeep; Gupta, U. C.; Chaudhry, M. L.
• Is Part Of: Journal of applied probability. Volume 53:Number 4(2016)
• Page Start: 1078
• Page End: 1097
• Publication Date: 2016-12-09
• Subjects: Batch Markovian arrival process, -- BMAP, -- roots, -- queueing time, -- system time, -- virtual waiting time, -- rational Laplace‒Stieltjes transform, -- matrix exponential, -- phase type, -- deterministic; Primary 60K25, -- Secondary 90B22; 519.2
• DOI: 10.1017/jpr.2016.66
• Languages: English
• ISSNs: 0021-9002

Abstract

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.