\(GI/M/1\) queue with set-up period and working vacation and vacation interruption. (English) Zbl 1184.90054
Summary: We consider a \(GI/M/1\) queue with set-up period and working vacation and working interruption. We introduce set-up time and vacation interruption policy: the server can come back to the set-up period once there are customers after a service completion during the vacation period, thus the server may not accomplish vacation. Using matrix-geometric solution method, we obtain the steady-state distribution for the number of customers in the system at arrival epochs, and the distribution of the waiting time. Furthermore, we also present the stochastic decomposition properties of queue length.
MSC:
90B22 | Queues and service in operations research |