Discrete-time GeoX/G(a,b)/1/N queues with single and multiple vacations

Authors:
S. K. Samanta;M. L. Chaudhry;U. C. Gupta
Affiliations:
Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India;Department of Mathematics and Computer Science, Royal Military College of Canada, P.O. Box 17000, STN Forces, Kingston Ontario, Canada K7K 7B4;Department of Mathematics, Indian Institute of Technology, Kharagpur-721302, India
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2007

Citing 5
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Abstract

In this paper, we consider a discrete-time single-server finite-buffer batch arrival queue in which customers are served in batches according to a general bulk-service rule, that is, at least 'a' customers are needed to start a service with a maximum serving capacity of 'b' customers. The server takes a (single and multiple) vacation as soon as the queue length falls below 'a' at the completion of service. The interarrival times of batches are assumed to be independent and geometrically distributed. The service times of the batches and vacation times of the server are generally distributed and their durations are integral multiples of slot duration. We obtain queue length distributions at service completion, vacation termination, arbitrary, and prearrival epochs. Finally, we discuss various performance measures and numerical results.