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