Equilibrium probability calculations for a
discrete-time bulk queue model
Many problems in management science and telecommunications
can be solved by the
analysis of a DX/Dm/1 queueing model.
In this paper, we use the zeros,
both inside and outside the unit circle,
of the denominator of the generating function of the model
to obtain an explicit closed-form solution for the
equilibrium probabilities of the number of customers in the system.
The moments
of the number of customers in the queue or in the system
are also studied.
When there are infinitely many zeros outside the unit circle, we propose
an approximation method using polynomials. This method yields correct
values for a finite number of the probabilities, the number depending
on the degree of the polynomial approximation.
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