Expected path length for angle and distance-based localized routing

We give analytical solutions for the expected path length in ad-hoc wireless networks employing distance-based or angle-based based greedy routing schemes. Such schemes underlay many practical routing protocols for ad-hoc wireless networks in which nodes are aware of their geographical locations and can use that information to simplify (localize) the routing rules. As the two paradigms, i.e., minimizing the distance towards the destination, and minimizing the angular deviation from the straight path towards the destination, lie at the heart of practically all location-based routing protocols, our solutions can be viewed as generic and applicable to a variety of realistic schemes.