Monte Carlo Approach to the Computation...

This article proposes an approach to the problem of computational capacities analysis of the computing continuum via theoretical framework of equilibrium phase-transitions and numerical simulations. We introduce the concept of phase transitions in computing continuum and show how this phenomena can be explored in the context of workflow makespan, which we treat as an order parameter. We simulate the behavior of the computational network in the equilibrium regime within the framework of the XY-model defined over complex agent network with Barabasi-Albert topology. More specifically, we define Hamiltonian over complex network topology and sample the resulting spin-orientation distribution with the Metropolis-Hastings technique. The key aspect of the paper is derivation of the bandwidth matrix, as the emergent effect of the “low-level” collective spin interaction. This allows us to study the first order approximation to the makespan of the “high-level” system-wide workflow model in the presence of data-flow anisotropy and phase transitions of the bandwidth matrix controlled by the means of “noise regime” parameter η. For this purpose, we have built a simulation engine in Python 3.6. Simulation results confirm existence of the phase transition, revealing complex transformations in the computational abilities of the agents. Notable feature is that bandwidth distribution undergoes a critical transition from single to multi-mode case. Our simulations generally open new perspectives for reproducible comparative performance analysis of the novel and classic scheduling algorithms.