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This paper presents a mathematical and simulative framework for quantifying the overhead of reactive routing protocols, such as dynamic source routing and ad hoc on-demand distance vector, in wireless variable topology (ad hoc) networks. A model of the routing-layer traffic, in terms of the statistical description of the distance between a source and a destination, is presented. The model is used to study the effect of the traffic on the routing overhead. Two network models are analyzed; a Manhattan grid model for the case of regular node placement, and a Poisson model for the case of random node placement. We focus on situations where the nodes are stationary but unreliable. For each network model, expressions of various components of the routing overhead are derived as a function of the traffic pattern. Results are compared against ns-2 simulations, 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.