Advances in Decision Sciences
Volume 2005 (2005), Issue 3, Pages 123-135
doi:10.1155/JAMDS.2005.123
On Mx/(G1G2)/1/G(BS)/Vs vacation queue with two types of general heterogeneous service
Kailash C. Madan1
, Z.R. Al-Rawi2
and Amjad D. Al-Nasser2
1College of Mathematical Sciences and IT, Ahlia University, P.O. Box 10878, Manama, Bahrain
2Department of Statistics, Faculty of Science, Yarmouk University, Irbid, Jordan
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.