Wardropian Cycles: fair and optimal traffic assignment concept for compliant connected autonomous vehicles.

Abstract

We show how System Optimal assignment can be User Equilibrated and both Wardop principles can be reached at the same time. System Optimal traffic assignment is unfair as travel times of drivers using different routes connecting the same OD pair typically differ. Considering a finite sequence of days, however, the average travel times can be equilibrated for all the drivers on a given OD pair. We call such a sequence of daily assignments of drivers to routes a Wardropian Cycle and demonstrate that it always exists. We introduce analytical methods to identify such Cycles, along with a greedy algorithm which every day assigns users to routes so as to minimize the inequity. Cyclical User Equilibrium (that we introduce) allows to remove Price of Anarchy (and save of up to 670 hours of travel time in our Barcelona case).