Existence of uniform link tolls and the efficiency loss of congestion pricing for stochastic system optimization

In stochastic traffic assignment, if the total perceived travel cost of all users is used as the system performance index, the stochastic system optimum (SSO) assignment is then to minimize the total perceived travel cost. In this study, we investigate the existence of nonnegative uniform link tolls and the efficiency loss of congestion pricing of multiclass stochastic user equilibrium (SUE) traffic assignment against SSO assignment. It is shown that there exist nonnegative uniform link tolls to decentralize the SUE into SSO. The efficiency loss of multiclass SUE traffic assignment under congestion pricing against SSO is analytically derived while tolls are considered as part of the system costs. It is shown that the upper bound always depend on the travel time function class, the time-irrelevant travel function class, the users´ socio-economic characteristics and the total experienced travel cost under congestion pricing.