A Mathematical Model for Latency Constrained Self-Organizing Application Placement in the Edge

The highly dynamic and heterogeneous environment that characterizes the edge of the Cloud/Edge Continuum calls for new intelligent methods for tackling the needs of such a complex scenario. In particular, adaptive and self-organizing decentralized solutions have been advanced for optimizing the placement of applications at the Edge. In this paper, we propose a probabilistic mathematical model that allows to describe one of such solutions. The goal of the model is twofold: i) to make it possible to demonstrate the convergence of the proposed solution; ii) to study the impact of the self-organizing solution without the need of an actual implementation or simulation of the system, allowing to evaluate the suitability of the solution in specific contexts. The paper presents the mathematical formulation of the proposed solution as well as the validation of the proposed model against a simulation of the system.