EQUILIBRIUM PROBABILITY-CALCULATIONS FOR A DISCRETE-TIME BULK QUEUE MODEL

Many problems in management science and telecommunications can be solv ed by the analysis of a D-X/D-m/1 queueing model. In this paper, we us e the zeros, both inside and outside the unit circle, of the denominat or of the generating function of the model to obtain an explicit close d-form solution for the equilibrium probabilities of the number of cus tomers in the system. The moments of the number of customers in the qu eue or in the system are also studied. When there are infinitely many zeros outside the unit circle, we propose an approximation method usin g polynomials. This method yields correct values for a finite number o f the probabilities, the number depending on the degree of the polynom ial approximation.