A highway problem is a cost sharing problem that arises if the common resource is an ordered set of sections with fixed costs such that each agent demands consecutive sections. We provide axiomatizations of the core, the prenucleolus, and the Shapley value on the class of TU games associated with highway problems. However, the simple and intuitive properties employed in the results are exclusively formulated by referring to highway problems rather than games. The main axioms for the core and the nucleolus are consistency properties, while the Shapley value is characterized by requiring that the fee of an agent is determined by the highway problem when truncated to the sections she demands. An alternative characterization is based on the new contraction property. Finally it is shown that the games that are associated with generalized highway problems in which agents may demand non-connected parts are the positive cost games, i.e., nonnegative linear combinations of dual unanimity games.