Synchronization in Small-World-Connected Computer Networks

Abstract

In this thesis we study synchronization phenomena in natural and artificial coupled multi-component systems, applicable to the scalability of parallel discrete-event simulation for systems with asynchronous dynamics. We analyze the properties of the virtual time horizon or synchronization landscape (corresponding to the progress of the processing elements) of these networks by using the framework of non-equilibrium surface growth. When the communication topology mimics that of the short-range interacting underlying system, the virtual time horizon exhibits Kardar-Parisi-Zhang-like kinetic roughening. Although the virtual times, on average, progress at a nonzero rate, their statistical spread diverges with the number of processing elements, hindering efficient data collection. We show that when the synchronization topology is extended to include quenched random communication links (small-world links) between the processing elements, they make a close-to-uniform progress with a nonzero rate, without global synchronization. We also provide a coarse-grained description for the small-world-synchronized virtual-time horizon and compare the findings to those obtained by simulating the simulations based on the exact algorithmic rules. We also present numerical results for the evolution of the virtual-time horizon on scale-free Barabasi-Albert networks serving as communication topology among the processing elements. Finally, we investigate to what extent small-world couplings (extending the original local relaxational dynamics through the random links) lead to the suppression of extreme fluctuations in the synchronization landscape.