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Abstract

We examine a queueing inventory model with single server which can offer two types of inventory items: main item (commodity I) and complementary item (commodity II). We assume both commodities have a finite capacity Si, i = 1, 2. Customers reach the system by following the Markovian arrival process (MAP). The service times are considered to be phase-type (PH) distribution. We have considered no customer in the system, even inventory level is positive; the server will start the working vacation, and any customer that arrives during working vacation, the server provides slow service. If an item is not available, the customer will stay in the waiting line. When the server is affected by a breakdown during normal busy period, the server will move on to the repair process, considered an essential repair. The server then has the option to move on to another repair process, going for another optional repair with probability p, or return to the service system with probability q. Utilising the matrix-analytic method, we examined our model and investigated the stability condition of our model. We have also carried out the cost analysis for our model. At the end, some numerical results are presented for clear insight into our model.

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