Journal of Applied Mathematics and Decision Sciences
Volume 2005 (2005), Issue 3, Pages 123-135
On vacation queue with two types of
general heterogeneous service
1College of Mathematical Sciences and IT, Ahlia University, P.O. Box 10878, Manama, Bahrain
2Department of Statistics, Faculty of Science, Yarmouk University, Irbid, Jordan
Received 17 March 2003; Revised 1 December 2004
Copyright © 2005 Kailash C. Madan et al. 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.
We analyze a batch arrival queue with a single server
providing two kinds of general heterogeneous service. Just before
his service starts, a customer may choose one of the services and
as soon as a service (of any kind) gets completed, the server may
take a vacation or may continue staying in the system. The
vacation times are assumed to be general and the server vacations
are based on Bernoulli schedules under a single vacation policy.
We obtain explicit queue size distribution at a random epoch as
well as at a departure epoch and also the mean busy period of the
server under the steady state. In addition, some important
performance measures such as the expected queue size and the
expected waiting time of a customer are obtained. Further, some
interesting particular cases are also discussed.