Second best toll pricing within the framework of bounded rationality
The network design problem is usually formulated as a bi level program, assuming the user equilibrium is attained in the lower level program. Given boundedly rational route choice behavior, the lower level program is replaced with the boundedly rational user equilibria (BRUE) The network design problem with boundedly rational route choice behavior is understudied due to non uniqueness of the BRUE. In this study, thus, we mainly focus on boundedly rational toll pricing (BR TP) with affine link cost functions. The topological properties of the lower level BRUE set are first explored. As the BRUE solution is generally non unique, urban planners cannot predict exactly which equilibrium flow pattern the transportation network will operate after a planning strategy is implemented. Due to the risk caused by uncertainty of people's reaction, two extreme scenarios are considered: the traffic flow patterns with either the minimum system travel cost or the maximum, which is the "risk prone" (BR TP RP) or the "risk averse" (BR TP RA) scenario respectively. The upper level BR TP is to find an optimal toll minimizing the total system travel cost, while the lower level is to find the best or the worst scenario. Accordingly BR TP can be formulated as either a min min or a min max program. Solution existence is discussed based on the topological properties of the BRUE and algorithms are proposed. Two examples are accompanied to illustrate the proposed methodology.