A real-time road pricing system: The case of a two-link parallel network

A real-time road pricing system in the case of a two-link parallel network is proposed in this paper. The system that is based on a combination of Dynamic Programming and Neural Networks makes “on-line” decisions about road toll values. In the first phase of the proposed model, the best road toll sequences during certain time period are calculated off-line for many different patterns of vehicle arrivals. These toll sequences are computed using Dynamic Programming approach. In the second phase, learning from vehicle arrival patterns and the corresponding optimal toll sequences, neural network is trained. The results obtained during on-line tests are close to the best solution obtained off-line assuming that the arrival pattern is known.