Waiting Time of M/M/c/N Queuing System with Balking, Reneging, and Multiple Synchronous Vacations of Partial Servers

The policy of synchronous vacations of partial servers is considered in an multi-server queuing system with balking and reneging. Some fixed partial idle servers take synchronous multiple vacations when these servers become idle at an instant that a customer leaves the system. In this article, by considering the two cases that the partial servers are on vacation and not on vacation, the distributions of the conditional waiting time for customers who join the system when all the available servers are busy and eventually acquire service are obtained. Based on these, the distribution of the conditional waiting time of customers given that they join the system when all available servers are busy and eventually acquire service is derived.