Optimal topology for parallel discrete-event simulations

The effect of shortcuts on the task completion landscape in parallel discrete-event simulation (PDES) is investigated. The morphology of the task completion landscape in PDES is known to be described well by the Langevin-type equation for nonequillibrium interface growth phenomena, such as the Kardar-Parisi-Zhang equation. From the numerical simulations, we find that the root-mean-squared fluctuation of task completion landscape, W(t,N), scales as W(t→∞,N)~N when the number of shortcuts, ℓ, is finite. Here N is the number of nodes. This behavior can be understood from the mean-field type argument with effective defects when ℓ is finite. We also study the behavior of W(t,N) when ℓ increases as N increases and provide a criterion to design an optimal topology to achieve a better synchronizability in PDES.