Analysis of the queue-length distribution for the discrete-time batch-service Geo/G(a,Y)/1/K queue

In this paper, we consider a discrete-time finite-capacity queue with Bernoulli arrivals and batch services. In this queue, the single server has a variable service capacity and serves the customers only when the number of customers in system is at least a certain threshold value. For this queue, we first obtain the queue-length distribution just after a service completion, using the embedded Markov chain technique. Then we establish a relationship between the queue-length distribution just after a service completion and that at a random epoch, using elementary 'rate-in = rate-out' arguments. Based on this relationship, we obtain the queue-length distribution at a random (as well as at an arrival) epoch, from which important performance measures of practical interest, such as the mean queue length, the mean waiting time, and the loss probability, are also obtained. Sample numerical examples are presented at the end. (c) 2006 Elsevier B.V. All rights reserved.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2007-09
Language
ENG
Keywords

BULK-SERVICE

Citation

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, v.181, pp.787 - 792

ISSN
0377-2217
DOI
10.1016/j.ejor.2006.08.016
URI
http://hdl.handle.net/10203/1338
Appears in Collection
IE-Journal Papers(저널논문)
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