Spatial Fluid Limits for Stochastic Mobile Networks

TL;DR

This paper introduces a PDE-based approach to model large-scale stochastic mobile networks, providing a macroscopic approximation that is computationally efficient and validated against simulations.

Contribution

It proves convergence of Markov models to PDEs for mobile networks, enabling scalable analysis and faster computations compared to traditional methods.

Findings

PDE approximation closely matches discrete simulations

Significant computational speed-ups achieved

Effective modeling even with low node populations

Abstract

We consider Markov models of large-scale networks where nodes are characterized by their local behavior and by a mobility model over a two-dimensional lattice. By assuming random walk, we prove convergence to a system of partial differential equations (PDEs) whose size depends neither on the lattice size nor on the population of nodes. This provides a macroscopic view of the model which approximates discrete stochastic movements with continuous deterministic diffusions. We illustrate the practical applicability of this result by modeling a network of mobile nodes with on/off behavior performing file transfers with connectivity to 802.11 access points. By means of an empirical validation against discrete-event simulation we show high quality of the PDE approximation even for low populations and coarse lattices. In addition, we confirm the computational advantage in using the PDE limit over a traditional ordinary differential equation limit where the lattice is modeled discretely, yielding speed-ups of up to two orders of magnitude.