Opportunistic walks on Random Geometric Networks and their application in scalability analysis

Opportunistic routing is studied as a representative example of location-aware greedy routing schemes. The routing process between an arbitrary source-destination pair is modeled as a directed random walk between the two ends in the underlying graph. The mean number of transmissions as well as the average multi-hop distance between arbitrary nodes are unified under a conceptual measure called expected length of the opportunistic walk in the induced network graph. We model this quantity as the mean time to absorption in a finite-state Markov chain. An explicit closed-form expression is presented to approximate the results and tight bounds are given. The accuracy of the results predicted by the analytical model is verified through simulation experiments. We also demonstrate an application of the foregoing model in defining proximity-based social models and identifying classes of social networks that are scalable.