The multi server \(M/M/(s,S)\) queueing inventory system. (English) Zbl 1325.90028
Summary: We consider a multiserver Markovian queuing model where each server provides service only to one customer. Arrival of customers is according to a Poisson process and whenever a customer leaves the system after getting service, that server is also removed from the system. Here the servers are considered as an inventory that will be replenished according to the standard \((s,S)\) policy. Behavior of this system is studied using a two dimensional QBD process. The condition for checking ergodicity, the steady state solutions and average inventory cycle time are obtained using matrix analytic methods. Also we have studied an optimization problem that minimizes the total cost induced by the waiting cost of arrivals, holding cost of the inventory of servers and ordering cost. Some numerical illustrations are provided.
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