Analysis of a Priority Controllable Queue MX1,MX2/G1(a,b),G2(a,b)/1 With Multiple Vacations, Setup Times and Closedown Times

In this paper a priority queuing system MX1,MX2/G1(a,b),G2(a,b)/1 with multiple vacations, setup times with N-policy and closedown times has been deduced. Two types of customers, priority and nonpriority, are arrived and are served in this queuing situation. In priority schemes, customers with priority are selected for service ahead of those with nonpriority, independent of their time of arrival into a system, but with no preemption. On completion of service, if each of the number of priority customers ξ1 and the number of nonpriority customers ξ2 in the queue is less than ”a” the server performs closedown work. Following closedown, the server leaves for multiple vacations of random length. When the server returns from a vacation and finds the number of customers of either type in the queue is less than ”N”, he leaves for another vacation and so on, until he finds at least ”N” (N b) customers of either type in the queue waiting for service. Then, he requires a setup time ”R” to start service. After the setup he starts the service with a batch of ”b” from the ”N” priority customers, where b ≥ a. After service, if the number of waiting priority customers ξ1 ≥ a, then the server serves a batch of min (ξ1,b) customers of that type and so on until ξ1 \u3c a, then the server serves non-priority customers in the same way. The probability generating function of the queue size distribution at an arbitrary epoch and various characteristics of the queuing model are derived