  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 $n^{\Theta(\log n)}$ 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.
