Most likely origin-destination link uses from equilibrium assignment

This paper formulates the problem of finding the most likely distribution of origin-destination (O-D) specific link volumes (called "link uses") from equilibrium assignment. Although an equilibrium assignment is unique in terms of aggregate link volumes, trips between different O-D pairs assigned to alternative paths between any node pair can be swapped among these paths such that total link volumes remain unchanged. Alternative link uses that yield identical aggregate link volumes can affect O-D specific estimates of fuel consumption, pollution emissions or development impacts. Equilibrium assignments found by methods of linear combinations, such as the Frank-Wolfe algorithm, may not represent most likely link uses. The problem of finding maximum entropy link uses (MELU) formulated herein is a multi-commodity optimum flow (max-flow at min-cost) problem with nonlinear flow-dependent link use costs. MELU does not require path enumeration or knowledge of used paths between zones, but it is NP-hard to solve and very sizable for large networks. An approximate solution technique is presented that finds likely link uses for realistic size problems. The method is to linearly combine successive F-W solutions using step sizes that seek a maximum entropy mix. The examples include other comparisons of trial link uses that indicate the extent to which they differ.