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The congestion pricing has been discussed as a practical tool for traffic management on urban transport networks. The traffic congestion is defined as an external diseconomy on the network in transport economics. It has been proposed that the congestion pricing would be used to reduce the traffic on the network. This paper investigates the cordon-based second-best congestion-pricing problems on road networks, including optimal selection of both toll levels and toll locations. A road network is viewed as a directed graph and the cutest concept in graph theory is used to describe the mathematical properties of a toll cordon by examining the incidence matrix of the network. Maximization of social welfare is sought subject to the elastic-demand traffic equilibrium constraint. A mathematical programming model with mixed (integer and continuous) variables is formulated and solved by use of two genetic algorithms for simultaneous determination of the toll levels and cordon location on the networks. The model and algorithm are demonstrated in the road network of Mashhad CBD.

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This paper proposes a new hybrid method namely SA-IP including simulated annealing and interior point algorithms to find the optimal toll prices based on level of service (LOS) in order to maximize the mobility in urban network. By considering six fuzzy LOS for flows, the tolls of congested links can be derived by a bi-level fuzzy programming problem. The objective function of the upper level problem is to minimize the difference between current LOS and desired LOS of links. In this level, to find optimal toll, a simulated annealing algorithm is used. The lower level problem is a fuzzy flow estimator model with fuzzy link costs. Applying a famous defuzzification function, a real-valued multi-commodity flow problem can be obtained. Then a polynomial time interior point algorithm is proposed to find the optimal solution regarding to the estimated flows. In pricing process, by imposing cost on some links with LOS F or E, users incline to use other links with better LOS and less cost. During the iteration of SA algorithm, the LOS of a lot of links gradually closes to their desired values and so the algorithm decreases the number of links with LOS worse than desirable LOS. Sioux Falls network is considered to illustrate the performance of SA-IP method on congestion pricing based on different LOS. In this pilot, after toll pricing, the number of links with LOS D, E and F are reduced and LOS of a great number of links becomes C. Also the value of objective function improves 65.97% after toll pricing process. It is shown optimal toll for considerable network is 5 dollar and by imposing higher toll, objective function will be worse.