Cluster-based routing overhead in networks with unreliable nodes

While several cluster based routing algorithms have been proposed for ad hoc networks, there is a lack of formal mathematical analysis of these algorithms. Specifically, there is no published investigation of the relation between routing overhead on one hand and route request pattern (traffic) on the other. This paper provides a mathematical framework for quantifying the overhead of a cluster-based routing protocol. We explicitly model the application-level traffic in terms of the statistical description of the number of hops between a source and a destination. The network topology is modelled by a regular two-dimensional grid of unreliable nodes, and expressions for various components of the routing overhead are derived. The results show that clustering does not change the traffic requirement for infinite scalability compared to flat protocols, but reduces the overhead by a factor of O(1/M) where M is the cluster size. The analytic results are validated against simulations of random network topologies running a well known (D-hop max-min) clustering algorithm.