An Integrated Approach to Evaluating the
Loss Perfomance of ATM Switches

S. Montagna, R. Paglino, and J. F. Meyer


This work addresses model-based evaluation of cell loss probabilities for an ATM switching element with a shared output buffer. The incoming traffic to the switch is represented by the superposition of N bursty input sources, each of which is modeled as a two-state (ON/OFF) Markov chain. In the ON state the sources transmit cells whose addresses are uniformly distributed over R output ports. For such systems, we consider an integrated approach to their evaluation that employs both exact and approximate solutions. The exact method is based on a reduced Markov model obtained by lumping the states according to certain symmetries of the traffic model. However, even with such reduction, numerical solutions are feasible only if the switch dimensions involved, particularly the number of output ports, are reasonably small. We then introduce a new approximate solution algorithm that can be applied to larger switches. By comparing the results obtained with those of the exact method, we find that the errors of approximation are relatively small. Moreover, due to the iterative nature of the approximate solution algorithm, the two methods can be integrated so as to yield even more accurate results with less execution time. Finally, relative to a specified admissible cell loss probability, we use this approach to compare the capacities required for shared vs. dedicated buffering. This, in turn, suggests a heuristic for estimating required shared-buffer capacity in the case of very low admissible cell loss probabilities.

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