A Continuum Model for Route Optimization in Large-Scale Inhomogeneous Multi-Hop Wireless Networks

Abstract

Multi-hop route optimization in large-scale inhomogeneous networks typically requires the use of constrained optimization tools, yielding processing complexity that scales like $O(N^{3}), N$ being the number of relays employed. Here, we propose an alternative approach to route optimization by considering the limit of infinite relay node density to develop a continuum model, which yields an optimized equivalent continuous relay path. The model is carefully constructed to maintain a constant connection density even though the node density scales without bound. This leads to a formulation for minimizing the end-to-end outage probability that can be solved using methods from the calculus of variations. We demonstrate the effectiveness of this new approach and its potential for reducing processing complexity by considering a network subjected to a point source of interference.