A retrial inventory system with priority customers and second optional service. (English) Zbl 1360.90013
Summary: In this paper, we investigate a single server \((s, Q)\) perishable inventory model consisting of two priority customers, say, type-1 and type-2. The customers arrival flows are independent Poisson processes, and the service times of the type 1 and type 2 customers are exponentially distributed. The server offers two different types of services – first with ordinary service (essential service) and the second with optional service. The idle server first gives ordinary service to the arriving customers (type 1/type 2). Upon first essential service completion, then the server gives additional service (second optional) only to the type 1 customers. We assume that the type 1 customers have both types of priorities (non-preemptive priority and preemptive priority) over the type 2 customers. We discussed retrial concepts only for type-2 customers. The stationary probability distribution of the inventory level, status of the server, number of customer in the orbit and number of customers in the waiting line are obtained by matrix methods and some numerical illustrations are provided.
Keywords:
mixed priority; \((s, Q)\) policy; Markov process; service facility; ordinary and additional serviceReferences:
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