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We consider parallel simulations for asynchronous systems employing Lprocessing elements that are arranged on a ring. Processors communicate onlyamong the nearest neighbors and advance their local simulated time only if itis guaranteed that this does not violate causality. In simulations with noconstraints, in the infinite L-limit the utilization scales (Korniss et al, PRL84, 2000); but, the width of the virtual time horizon diverges (i.e., themeasurement phase of the algorithm does not scale). In this work, we introducea moving window global constraint, which modifies the algorithm so that themeasurement phase scales as well. We present results of systematic studies inwhich the system size (i.e., L and the volume load per processor) as well asthe constraint are varied. The constraint eliminates the extreme fluctuationsin the virtual time horizon, provides a bound on its width, and controls theaverage progress rate. The width of the window constraint can serve as a tuningparameter that, for a given volume load per processor, could be adjusted tooptimize the utilization so as to maximize the efficiency. This result may findnumerous applications in modeling the evolution of general spatially extendedshort-range interacting systems with asynchronous dynamics, including dynamicMonte Carlo studies.Comment: 14 pages, 11 figure

Algorithmic scalability in globally constrained conservative parallel discrete event simulations of asynchronous systems