#
An Integrated Approach to Evaluating the

Loss Perfomance of ATM Switches

## Abstract

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.

**Compressed PostScript File:**
atm96.ps.zip