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In this paper we study the stationary probability distribution of a system consisting of a finite capacity buffer connected to  N  equal customers with bursty on-off demands. We assume that the buffer is filled up at a constant rate and we analyze the case when this filling rate satisfies an optimization condition according to the customer demands. First, we consider semi-Markov on-off demands for the case  N  = 2 and we model the dynamics of the system using a semi-Markov evolution environment. We show that we can use the phase merging algorithm to reduce the problem to a Markov evolution environment case. Then, we generalize the results for any  N  using a birth-and-death process.

Stationary probability distribution of a system with N equal customers with bursty demands connected to a single buffer