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This paper presents a new mathematical and simulative framework for quantifying the overhead of a broad class of reactive routing protocols, such as DSR and AODV, in wireless variable topology (ad-hoc) networks. We focus on situations where the nodes are stationary but unreliable, as is common in the case of sensor networks. 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 sensor network is modelled by an unreliable regular Manhattan (i.e. degree four) grid, and expressions for various components of the routing overhead are derived. Results are compared against ns-2 simulations for regular and random topologies, which corroborate the essential characteristics of the analytical results. One of the key insights that can be drawn from the mathematical results of this paper is that it is possible to design infinitely scalable reactive routing protocols for variable topology networks by judicious engineering of the traffic patterns to satisfy the conditions presented in this paper.