Analyzing discrete-time bulk-service Geo/Geob/m queue

Issue		RAIRO Oper. Res. Volume 40, Number 3, July-September 2006


Page(s)		267 - 284
DOI		10.1051/ro:2006021
Published online		08 November 2006

RAIRO Oper. Res. 40 (2006) 267-284
DOI: 10.1051/ro:2006021

Analyzing discrete-time bulk-service Geo/Geo^b/m queue

Veena Goswami¹, Umesh C. Gupta² and Sujit K. Samanta²

¹ Department of Computer Science, Kalinga Institute of Industrial Technology, Bhubaneswar-751024, India; veena_goswami@yahoo.com
² Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India; umesh@maths.iitkgp.ernet.in; sujit.samanta@rediffmail.com

(Received January 19, 2005. Accepted May 5, 2006. Published online 8 November 2006.)

Abstract
This paper analyzes a discrete-time multi-server queue in which service capacity of each server is a minimum of one and a maximum of b customers. The interarrival- and service-times are assumed to be independent and geometrically distributed. The queue is analyzed under the assumptions of early arrival system and late arrival system with delayed access. Besides, obtaining state probabilities at arbitrary and outside observer's observation epochs, some performance measures and waiting-time distribution in the queue have also been discussed. Finally, it is shown that in limiting case the results obtained in this paper tend to the continuous-time counterpart.

Key words: Bulk-service, discrete-time, multi-server, queueing, waiting-time.

© EDP Sciences 2006

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