Abstract
We consider a multi-server Markovian queuing model where the servers can be considered as an inventory with standard (r, Q) policy and positive lead time. The demands are considered as arrivals and the time for serving the inventory is considered as the service time. Here we consider the model in which a fixed order quantity Q is ordered each time when the on hand inventory reaches the reorder point r. Behaviour of this system is studied using a two state quasi birth and death (QBD) process. Condition for checking ergodicity, the steady state solutions, the distribution of inventory recycle time and an optimisation problem are presented. Numerical illustrations are also given.
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