Evolution of local computing time in parallel modeling of mobile networks

Abstract

Introduction: The study concerns the properties of a parallel discrete-event simulation (PDES) model, namely a simple mobile network model known as a personal communication service (PCS) model. In this type of parallel computing, each process has its own computation time, known as local virtual time. The local virtual times change during the simulation process, forming a complex profile similar to the surface growth profile in physics.Methods: We apply the scaling theory of statistical physics to study the properties of the PCS model. We construct a simple local virtual time evolution algorithm for the PCS model and compare this theoretical time evolution model to a standard parallel mobile network implementation in Rensselaer’s Optimistic Simulation System (ROSS).Results: We show that the value of the critical exponent for the mobile network system is close to the value in the theoretical local virtual time profile model. A roughening transition is found in the LVT–PCS model, which belongs to the universality class of directed percolation in dimension 2 + 1.Discussion: We believe that the analogies we found can be useful for preliminary analyses of scalability, process desynchronization, and possible deadlocks in a wide class of parallel discrete-event simulation models.