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Mathematical Problems in Engineering
Volume 2 (1996), Issue 2, Pages 95-106

Bulk input queues with quorum and multiple vacations

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

Received 17 April 1995

Copyright © 1996 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.


The authors study a single-server queueing system with bulk arrivals and batch service in accordance to the general quorum discipline: a batch taken for service is not less than r and not greater than R(r). The server takes vacations each time the queue level falls below r(1) in accordance with the multiple vacation discipline. The input to the system is assumed to be a compound Poisson process. The analysis of the system is based on the theory of first excess processes developed by the first author. A preliminary analysis of such processes enabled the authors to obtain all major characteristics for the queueing process in an analytically tractable form. Some examples and applications are given.