A steady-state analysis of an M/G/1 queue with a finite capacity (K) and a finite population (N) of customers is given. The queue size distribution in this M/G/1/K/N system can be derived from the known queue size distribution in the corresponding M/G/1//N system. The system throughput, the mean response time, and the blocking probability are then calculated. The joint distributions of the queue size and the remaining service times are used to obtain the distributions of the unfinished work in the service facility and the waiting time of an accepted customer.
