A M/G/1 Priority Queue

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Abstract
A M/G/1 queue with discretionary priority is considered. There are two priority classes. An arriving high priority customer interrupts a low priority customer in service, if the remaining service time of the latter exceeds a constant d. Otherwise it is not found necessary to make an interruption. The equilibrium joint distribution of the number of type 1 and type 2 customers present is studied, using remaining service time of both the customer in service and the interrupted one (if any) as supplementary variables. The generating functions for the distributions of queue length (both at an arbitrary time and at various imbedded points) are obtained. It is observed that there are simple connections between these generating functions. The Laplace- Stieltjes transforms of the waiting time and some related variables follow easily. The means of all these variables are also calculated.

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