MOST LIKELY ORIGIN-DESTINATION LINK USES FROM EQUILIBRIUM ASSIGNMENT

This paper formulates the problem of finding the most likely distribut ion of origin-destination (O-D) specific link volumes (called ''link u ses'') 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 unchange d. Alternative link uses that yield identical aggregate link volumes c an affect O-D specific estimates of fuel consumption, pollution emissi ons or development impacts. Equilibrium assignments found by methods o f linear combinations, such as the Frank-Wolfe algorithm, may not repr esent most likely link uses. The problem of finding maximum entropy li nk uses (MELU) formulated herein is a multi-commodity optimum flow (ma x-flow at min-cost) problem with nonlinear flow-dependent link use cos ts. 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 n etworks. An approximate solution technique is presented that finds lik ely link uses for realistic size problems. The method is to linearly c ombine successive F-W solutions using step sizes that seek a maximum e ntropy mix. The examples include other comparisons of trial link uses that indicate the extent to which they differ.