A Gaussian approximation of the distributed computing process

The authors propose a refinement of the stochastic model describing the dynamics of the Desktop Grid (DG) project with many hosts and many workunits to be performed, originally proposed by Morozov et al. in 2017. The target performance measure is the mean duration of the runtime of the project. To this end, the authors derive an asymptotic expression for the amount of the accumulated work to be done by means of limit theorems for superposed on-off sources that lead to a Gaussian approximation. In more detail, depending on the distribution of active and idle periods, Brownian or fractional Brownian processes are obtained. The authors present the analytic results related to the hitting time of the considered processes (including the case in which the overall amount of work is only known in a probabilistic way), and highlight how the runtime tail distribution could be estimated by simulation. Taking advantage of the properties of Gaussian processes and the Conditional Monte-Carlo (CMC) approach, the authors present a theoretical framework for evaluating the runtime tail distribution.