This slim monograph presents a novel approach to understanding the behavior of the M/M/1 queue and of other Markovian queues with finite capacity. The basic idea is to construct a two-dimensional model of the queueing system, where the two dimensions represent the number of customers who have arrived to the system, and the number of customers who have departed. A closed-form solution is then obtained for this model, from which various performance measures of interest can be derived. The author also presents transient analysis of certain Markovian queues based on this same approach.
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