Homogenization Tools for the Routing Management Problem in Dense Networks With Transmission Defects

The article addresses routing management in large sensors networks when transmission defects occur. Many so-called geographical routing algorithms rely on a continuous approach ruled by a partial differential equation problem, especially for dense wireless sensor networks (WSNs). These algorithms may be supported by different physically inspired points of view and are of course all founded on an optimization criterion, but they typically neglect the potential for transmission defects. The aim of the present article is threefold. First, we show how to derive rigorously the optimal routing taking into account geographically identified transmission defects. Second, when the instability risk is distributed throughout the network, we use homogenization theory for deriving effective optimal models for the information transport that depend on the severity of the defects. Numerical simulations then illustrate that the paths determined from the no-fault model may be far from optimal above a certain transmission defect rate. Third, we explore how the Zermelo navigation’s problem can inspire a new routing approach for limiting the effect of transmission defects in WSNs.