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

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: 19 January 2005
Accepted: 5 May 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.