A comprehensive study on the queue-size distribution in a finite-buffer system with a general independent input flow

A finite-buffer GI/M/1/N−type queueing model is considered. The explicit formula for the Laplace transform of the transient queue-size distribution, conditioned by the number of packets present in the system at the starting time, is derived. The shape of the formula allows for finding the stationary distribution by applying the key renewal theorem. Moreover, the convergence rate of the transient queue-size distribution to the stationary one is determined with the constant value given explicitly. Numerical example is attached as well.