Estimating the minimal revenue tolls in large-scale roadway networks using the dynamic penalty function method

•The dynamic penalty function method is used to estimate a toll vector that guarantees the SO flows in the network.•Numerical results show that this toll vector is a good estimation for the MinRev optimal solution.•The proposed method is fast and memory effect for large-scale implementations.•We used the method for sensitivity analysis on MinRev tolled links.•More practical solutions were explored for two large networks using sensitivity analysis.

Congestion toll pricing is an inexpensive management way to mitigate the traffic congestion and reduce the delay in the network. One of the models that were proposed for toll pricing is the minimum toll revenue (MinRev) problem. The objective of this model is to find link-tolls that simultaneously cause users to efficiently use the network and to minimize the total toll revenues to be collected. Although it can be written as a linear model, when applied to road networks in practice, this model is difficult to be solved optimally in a reasonable time, due to its large size. This paper proposes a method to approximately estimate the minimal revenue tolls in large-scale roadway networks. The method was implemented for four real network ranged from medium to large, and two large random networks. Implementation of this method indicated that this technique can find an approximate toll vector that is within 0.5% of the optimal solution after just a few seconds. Furthermore, this method allows to perform sensitivity or trade-off analysis between the total collected tolls, the number of tolled links and the desired network improvement, which could suggest implementing more practically efficient solutions with substantially fewer tolled links and even quicker solution time at a negligible additional network cost.