Overload analysis of the PH/PH/1/K queue and the queue of the M/G/1/K type with very large K

We consider the PH/PH/1/K queue and the queue of M/G/1 type with very large buffer size K and operating in overload condition. By rotating the resulting transition matrix through 180° we turn it into a queue with underload condition. By approximating the latter queue by an infinite buffer system we are able to study it using the matrix-geometric method. A procedure for estimating the blocking probabilities is presented. We apply the procedure to a telephone system with both patient and impatient customers.