``Average case performance'' is an oft-cited motivation for self-timed
design.
In self-timed designs, computations procede according to handshakes,
and these handshakes can reflect the actual time required for operations
rather than the worst-case time.
The intuitive argument is that this should lead to systems whose performance
reflects the average-case performance of their components.
This paper shows that such intuition is often wrong.
This paper describes a connection between self-timed circuits and
percolation networks.
Percolation networks are a class of infinite graphs originally used to
model critical phenomena arising from fluid flows in porous media.
This paper shows how these techniques can be used to show the frequent
existence of long chains of slow operations in self-timed designs.
These chains can give rise to performance that is closer to
worst-case than average-case.
This paper makes three contributions.
First, it describes a fundamental connection between percolation networks
and self-timed circuits.
Second, it presents novel methods for studying the percolation networks
that arise in the analysis of self-timed circuits.
Third, it describes how these results can be applied during the design process.
