Optimal topology for parallel discrete-event simulations

Fluctuations in complex networks with variable dimensionality and heterogeneity

Synchronizing individual activities is essential for the stable functioning of diverse complex systems. Understanding the relation between dynamic fluctuations and the connection topology of substrates is therefore important, but it remains restricted to regular lattices. Here we investigate the fluctuation of loads, assigned to the locally least-loaded nodes, in the largest-connected components of heterogeneous networks while varying their link density and degree exponents. The load fluctuation becomes finite when the link density exceeds a finite threshold in weakly heterogeneous substrates, which coincides with the spectral dimension becoming larger than 2 as in the linear diffusion model. The fluctuation, however, diverges also in strongly heterogeneous networks with the spectral dimension larger than 2. This anomalous divergence is shown to be driven by large local fluctuations at hubs and their neighbors, scaling linearly with degree, which can give rise to diverging fluctuations at small-degree nodes. Our analysis framework can be useful for understanding and controlling fluctuations in real-world systems.

Parallel discrete-event simulation schemes with heterogeneous processing elements

To understand the effects of nonidentical processing elements (PEs) on parallel discrete-event simulation (PDES) schemes, two stochastic growth models, the restricted solid-on-solid (RSOS) model and the Family model, are investigated by simulations. The RSOS model is the model for the PDES scheme governed by the Kardar-Parisi-Zhang equation (KPZ scheme). The Family model is the model for the scheme governed by the Edwards-Wilkinson equation (EW scheme). Two kinds of distributions for nonidentical PEs are considered. In the first kind computing capacities of PEs are not much different, whereas in the second kind the capacities are extremely widespread. The KPZ scheme on the complex networks shows the synchronizability and scalability regardless of the kinds of PEs. The EW scheme never shows the synchronizability for the random configuration of PEs of the first kind. However, by regularizing the arrangement of PEs of the first kind, the EW scheme is made to show the synchronizability. In contrast, EW scheme never shows the synchronizability for any configuration of PEs of the second kind.