Assessment of Adherence to the Condition of Proportionality in User Equilibrium Traffic Assignments with Uniquely Determined Route Flows

Abstract

The standard formulation of the static deterministic user equilibrium (UE) traffic assignment problem based on the criterion of Wardrop provides a unique solution in terms of link flows; however, route flows are not determined uniquely. Analyses based on an arbitrary choice among the infinite number of possible route flow solutions could cause inconsistencies or even controversies in applications. In 2010, a computationally efficient algorithm named Traffic Assignment by Paired Alternative Segments (TAPAS) was successfully implemented to identify UE route flows uniquely. To date, no study has examined to what extent solutions adhere to the condition of proportionality in UE traffic assignments with uniquely determined route flows. In this paper, TAPAS is applied to obtain proportional UE route flows for the Chicago, Illinois, regional network in three highly precise solutions. Various assessments of adherence to proportionality are performed for a selected pair of alternative segments. The results show that route and link flows determined by TAPAS correspond closely to expected proportionality. Only inconsequential differences are found between the expected and computed proportional UE route flows. Systematic characteristics of the plots for the two segments ensure that TAPAS behaves properly according to the condition of proportionality. Insights from these empirical results may help transportation planning professionals to become aware of the magnitude of differences in UE route flows based on proportionality and in distinguishing uniqueness from nonuniqueness of route flows in UE traffic assignments. The results may also be useful to software developers in seeking improved adherence to proportionality of route flow solutions.