Traditionally, to implement the first-best marginal cost pricing scheme in a traffic network requires the information on the exact demand function or true origin-destination demand, which, however, is rarely available in practice. To overcome this dilemma, the trial-and-error method has been proposed to find the marginal cost toll through an iterative process using the observed traffic volumes. This method guarantees the convergence of tolls and flows to the system optimal state under the assumption of deterministic traffic conditions. However, in reality, the uncertainty of transportation network has been recognized well that induces the variability of link flow and travel time. Therefore, this paper proposes an evolutionary implementation method that iteratively finds the first-best marginal cost toll pattern according to the observed stochastic link flow information and the known travel time functions. The proof of the convergence of the iterative algorithm is presented. The paper also analyzes the effect of the sampling error of the link flow data on the convergence of the algorithm and shows that the biases from the flow observation will not affect the convergence. The numerical tests are provided for the illustration of the algorithm.
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