Abstract
AbstractIn this paper, we consider a single-server queueing inventory model with two types of customers, say, type-1 and type-2. The queue formed by the type-1 customer is infinite. The queue formed by the type-2 customer can accommodate a maximum of N customers. Even though the same server provides service to both types of customers, type-1 customers are served one by one, while type-2 customers are served in batches of varying sizes. The service is initiated only when inventory is available and the service time is assumed to be positive. If at least one item is available in the inventory and the server is idle, an arriving type-1 customer can directly enter into the service. The service of the type-2 customer is initiated either upon realization of a random clock that started ticking with the arrival of the first type-2 customer or by the accumulation of N type-2 customers, whichever occurs first. The arrivals follow a Marked Markovian process. Service time distribution of both type-1 and type-2 customers follow two different phase-type distribution. Replenishment of inventory follows the (s, S) policy having a positive lead time. It is assumed that N is less than s. Steady-state analysis, as well as evaluation of some performance measures, have been done. The model is analyzed numerically and graphically.KeywordsLead timePositive service timeMMAPPhase type distribution
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