This article analyzes an inventory system for service facilities where there is limited waiting space for customers. For service facilities, typically inventory is used during the provision of service. We consider a system with Poisson arrivals, arbitrarily distributed service times and zero leadtimes. Optimal value of the maximum allowable inventory that minimizes the long-run expected cost rate is obtained in an elegant manner. Various examples of service distributions and optimal values for maximum inventory in each of these cases is also presented. Our analysis also yields a closed form expression of the stationary distribution for the embedded Markov chain of an M / G / l finite capacity queue.

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