Congestion pricing in the absence of demand functions

This paper enhances a trial-and-error implementation scheme of marginal-cost pricing on a transportation network, in the absence of explicit expression of the demand function. Link tolls and link flows are updated for the next trial with the revealed link flows for given current trial toll pattern. The method is quite simple, requiring only some function evaluations. Also, the step size is not required to be square summable, thereby leading to the improvement of the efficiency of the algorithm. The global convergence of the method is proved and some numerical results are reported to illustrate its performance.