Range of User-equilibrium Route Flow with Applications

The route-flow-nonuniqueness problem is a well-known limitation of user-equilibrium (UE) traffic assignment. The concerned maximum entropy user equilibrium solution is stable and repeatable that could make a plausible reference point, but is not sufficient in many cases. It is an improvement of exploring all solutions by constructing the range of UE route flow solutions. In this paper, based on the range of UE route flow solutions (ROUE), all route flow solutions can be divided into several ranges according to their constitutions. We provide two new ways to analyze the range of UE route flow solutions, which are then used in different practical applications. By dividing the range of UE route flow solutions, sensitivity of the equilibrium traffic network is analyzed in different ranges. Solutions from the same range have the same effect on sensitivity analysis. So the traditional constraints for route flow solution in sensitivity analysis can be promoted to conditions for route constitutions, and finally define a domain for all feasible solutions. In addition, the range of UE route flow solutions is used to construct an optimization model for identifying the best reference route flow for bus line configuration. We also get the unique route flow solution can be obtained according to our model. From the numerical experiment, we found bus frequency on each line should refer to the route flows. The acquired route flow solution may also be useful for locations of other traffic facilities or implementation of overall traffic management.