Journal of Applied Mathematics and Decision Sciences
Volume 2005 (2005), Issue 3, Pages 123-135

On Mx/(G1G2)/1/G(BS)/Vs vacation queue with two types of general heterogeneous service

Kailash C. Madan,1 Z. R. Al-Rawi,2 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

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.