Congestion Toll Pricing of Tra c Networks

This paper concerns tolling methodologies for tra c networks which ensure that the resultant equilibrium ows are system optimal. A nonnegative vector is de ned to be a valid toll vector, if the set of tolled user equilibrium solutions is a subset of the set of untolled system optimal solutions. The problem of characterizing the toll set T , which is the set of all valid toll vectors, is studied. Descriptions and characterizations of T are given for the cases when either the cost map is strictly monotonic or is a ne monotonic. In the latter case, the cost map is of the form Qv + c, where Q is a not necessarily symmetric matrix and Q+Q is positive semide nite. The results are illustrated with several examples. 1 Support from the NSF grant CCR-9400216 is acknowledged. 2 Current address: Dept. of Mathematics, Linkoping University, Linkoping, Sweden