A polynomial factorization approach for the discrete time GIX/G/1/K queue

This paper proposes a polynomial factorization approach for queue length distribution of discrete time GI(x) /G/1 and GI(x) /G/1/K queues. They are analyzed by using a two-component state model at the arrival and departure instants of customers. The equilibrium state-transition equations of state probabilities are solved by a polynomial factorization method. Finally, the queue length distributions are then obtained as linear combinations of geometric series, whose parameters are evaluated from roots of a characteristic polynomial.