This article presents a perishable stochastic inventory system under continuous review at a service facility in which the waiting hall for customers is of finite size M. The service starts only when the customer level reaches N (< M), once the server has become idle for want of customers. The maximum storage capacity is fixed as S. It is assumed that demand for the commodity is of unit size. The arrivals of customers to the service station form a Poisson process with parameter λ. The individual customer is issued a demanded item after a random service time, which is distributed as negative exponential. The items of inventory have exponential life times. It is also assumed that lead time for the reorders is distributed as exponential and is independent of the service time distribution. The demands that occur during stock out periods are lost.The joint probability distribution of the number of customers in the system and the inventory levels is obtained in steady state case. Some measures of system performance in the steady state are derived. The results are illustrated with numerical examples.