#
Exact and Approximate Analysis

of ATM Cell Loss Correlation

## Abstract

Cell loss behavior
is analyzed for an ATM switch with homogeneous Markov sources.
While prior work in this regard has focused mainly on measures such as
the steady-state loss probability and conditional loss probability,
we consider a more refined measure, namely the
probability distribution of a cell loss period.
Evaluation is based on a discrete-time, finite-state Markov
process where cell arrivals at
each input port are represented by an *M*+1-state source model
(*M* ON states and one OFF state).
Although we are able to formulate the loss period
distribution exactly, for switches with realistic dimensions, the
associated computational cost is high.
As an alternative, we find that the loss period distribution
is essentially insensitive to the buffer capacity *K*
and, more importantly, its companion tail distribution
can be accurately approximated by
a relatively simple expression.
As evidenced by numerical results, the errors of approximation
are small and indeed, in many instances,
the results obtained are effectively the same as
those of an exact analysis.
**Keywords:** ATM switch, Markov source models, cell loss,
loss period distribution.

**Compressed PostScript File:**
ipds96.ps.zip