Journal
APPLIED MATHEMATICAL MODELLING
Volume 31, Issue 7, Pages 1321-1337Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2006.02.012
Keywords
balking; busy period and idle period distribution; Markov process; supplemental variable; waiting time distribution
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This paper studies the operating characteristics of an M-[x]/G/1 queueing system under a variant vacation policy, where the server leaves for a vacation as soon as the system is empty. The server takes at most J vacations repeatedly until at least one customer is found waiting in the queue when the server returns from a vacation. If the server is busy or on vacation, an arriving batch balks (refuses to join) the system with probability 1 - b. We derive the system size distribution at different points in time, as well as the waiting time distribution in the queue. Finally, important system characteristics are derived along with some numerical illustration. (c) 2006 Elsevier Inc. All rights reserved.
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