Message sojourn time for TDM schemes with any buffer capacity

In this paper we deal with a queueing model based on TDM schemes. Many results concerning this kind of model can be found in literature, but a large part of these results only concerns particular cases. Our main concern is to provide a general solution for the exact message sojourn time in the queue that should be available whatever the storage capacity may be. First, the probability distribution function as well as the Laplace transform of the message sojourn time in the buffer are derived, assuming Poisson fixed-length message arrivals, multiple output and finite buffer capacity. Second, taking advantage of these results, we provide the expected value of the message sojourn time and compare our results with those obtained by many authors. The formulas stated here are available for various particular cases especially for unlimited buffer capacity. Finally, we point out that the work done is directly usable for performance evaluation of many communication systems such as real-time networks, multiplexers and ATM links. Therefore, our results are both of theoretical and practical interests.