Flow thinning (FT) is an active traffic protection mechanism destined for communication networks with variable capacity of links, as for example wireless networks. In FT, end-to-end traffic demands are equipped with dedicated logical tunnels (for example MPLS tunnels) whose maximal capacity is subject to thinning in order to follow the fluctuations of the currently available link capacity. It follows that for each demand the instantaneous traffic realized between its end nodes must accommodate to the current total capacity available on its dedicated tunnels. In the paper we develop an optimization model for network dimensioning for a potentially implementable variant of FT, the so called General Affine Flow Thinning (GAFT), and present a solution algorithm based on the path generation approach. We derive a relevant pricing problem and present a numerical study that illustrates efficiency of the optimization algorithm, as well as compares the network cost for different variants of the flow thinning mechanism.