Journal of Applied Mathematics and Decision Sciences
Volume 2005 (2005), Issue 3, Pages 123-135
doi:10.1155/JAMDS.2005.123
Abstract
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.