Random Walks on Digraphs: A Theoretical Framework for Estimating Transmission Costs in Wireless Routing

Abstract

In this paper we develop a unified theoretical framework for estimating various transmission costs of packet forwarding in wireless networks. Our framework can be applied to the three routing paradigms, best path routing, opportunistic routing, and stateless routing, to which nearly all existing routing protocols belong. We illustrate how packet forwarding under each paradigm can be modeled as random walks on directed graphs (digraphs). By generalizing the theory of random walks that has primarily been developed for undirected graphs to digraphs, we show how various transmission costs can be formulated in terms of hitting times and hitting costs of random walks on digraphs. As representative examples, we apply the theory to three specific routing protocols, one under each paradigm. Extensive simulations demonstrate that the proposed digraph based analytical model can achieve more accurate transmission cost estimation over existing methods.