Statistical properties of the simulated time horizon in conservative parallel discrete-event simulations

We investigate the universal characteristics of the simulated time horizon of the basic conservative parallel algorithm when implemented on regular lattices. This technique [1, 2] is generically applicable to various physical, biological, or chemical systems where the underlying dynamics is asynchronous. Employing direct simulations, and using standard tools and the concept of dynamic scaling from non-equilibrium surface/interface physics, we identify the universality class of the time horizon and determine its implications for the asymptotic scalability of the basic conservative scheme. Our main finding is that while the simulation converges to an asymptotic nonzero rate of progress, the statistical width of the time horizon diverges with the number of PEs in a power law fashion. This is in contrast with the findings of Ref. [3]. This information can be very useful, e.g., we utilize it to understand optimizing the size of a moving "time window" to enforce memory constraints.

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