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International Journal of Mathematics and Mathematical Sciences - Volume 15 1992, Issue 1, Pages 189-194



Department of Applied Mathematics, Florida Institute of Technology, Melbourne 32901, FL, USA

Department of Operations Research, Florida Institute of Technology, Melbourne 32901, FL, USA

Received 27 June 1991

Copyright © 1992 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper introduces a bulk queueing system with a single server processing groups of customers of a variable size. If upon completion of service the queueing level is at least r the server takes a batch of size r and processes it a random time arbitrarily distributed. If the queueing level is less than r the server idles until the queue accumulates r customers in total. Then the server capacity is generated by a random number equals the batch size taken for service which lasts an arbitrarily distributed time dependent on the batch size.

The objective of the paper is the stationary distribution of queueing process which is studied via semi-regenerative techniques. An ergodicity criterion for the process is established and an explicit formula for the generating function of the distribution is obtained.





Autor: Jewgeni H. Dshalalow and Lotfi Tadj

Fuente: https://www.hindawi.com/



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