  We model the performance of an ideal closed chain of L processing elements
that work in parallel in an asynchronous manner. Their state updates follow a
generic conservative algorithm. The conservative update rule determines the
growth of a virtual time surface. The physics of this growth is reflected in
the utilization (the fraction of working processors) and in the interface
width. We show that it is possible to nake an explicit connection between the
utilization and the macroscopic structure of the virtual time interface. We
exploit this connection to derive the theoretical probability distribution of
updates in the system within an approximate model. It follows that the
theoretical lower bound for the computational speed-up is s=(L+1)/4 for L>3.
Our approach uses simple statistics to count distinct surface configuration
classes consistent with the model growth rule. It enables one to compute
analytically microscopic properties of an interface, which are unavailable by
continuum methods.
