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We present a proof that the number of breakpoints in the arrival function between two terminals in graphs of treewidth w is n O(log 2 w) when the edge arrival functions are piecewise linear. This is an improvement on the bound of n Θ(log n) by Foschini, Hershberger, and Suri for graphs without any bound on treewidth. We provide an algorithm for calculating this arrival function using star-mesh transformations, a generalization of the wye-delta-wye transformations.