Boundedly Rational User Equilibrium with Restricted Unused Routes

A boundedly rational user equilibrium model with restricted unused routes (R‐BRUE) considering the restrictions of both used route cost and unused route cost is proposed. The proposed model hypothesizes that for each OD pair no traveler can reduce his/her travel time by an indifference band by unilaterally changing route. Meanwhile, no route is unutilized if its travel time is lower than sum of indifference band and the shortest route cost. The largest and smallest used route sets are defined using mathematical expression. We also show that, with the increase of the indifference band, the largest and smallest used route sets will be augmented, and the critical values of indifference band to augment these two path sets are identified by solving the mathematical programs with equilibrium constraints. Based on the largest and smallest used route sets, the R‐BRUE route set without paradoxical route is generated. The R‐BRUE solution set can then be obtained by assigning all traffic demands to the corresponding generated route set. Various numerical examples are also provided to illustrate the essential ideas of the proposed model and structure of R‐BRUE route flow solution set.