Dynamic road pricing incorporating dynamic traffic assignment - Zhang, Chun Rong (2008)
Road pricing has been widely advocated as an efficient instrument to alleviate traffic congestion. Current static pricing schemes are designed for long term transportation planning as traffic conditions are assumed not to vary dramatically. When dealing with short time period, especially during the peak period, such assumption cannot be valid due to variable conditions of traffic over the whole network. Thus, pricing should be dynamic to accommodate the dynamic traffic evolution. This research aims to develop a theoretical dynamic road pricing model incorporating dynamic traffic assignment. The framework for the optimal road pricing problem incorporating traffic assignment on a network was a Stackelberg game. Road pricing schemes have to be announced firstly and the travellers’ behaviour were assumed to follow the concept of Wardrop’s user equilibrium. This problem can also be expressed as a Mathematical Problem with Equilibrium Constraints (MPEC). Traffic assignment model under fixed tolling level was expressed as the constraint. The toll level was expected to have an effect on travel time. After reviewing various algorithms for the MPEC problems, three different algorithms were tested for a static road pricing problem: Differential Evolutionary (DE), Pattern Search (PS), and Non-linear Problem with Equilibrium Constraints (NLPEC) solver. For this well-defined problem, NLPEC solver showed to be the most efficient in computation time for a given hypothetical nine-node network. To study the dynamic road pricing scheme, promising dynamic traffic evolution should allow for route choosing, departure time selection, and queue size on the network to vary with the tolling level. A suitable dynamic traffic assignment (DTA) model from Huang and Lam (2002) was adopted as the base model. A new procedure to compute some inter-variables was proposed to represent traffic evolution more appropriately. The behaviour of travellers followed the dynamic extension of Wardrop’s user equilibrium, which is based on predictive travel time. First-in-first-out (FIFO) conditions in the dynamic situations are satisfied. Different from the original algorithm from Huang and Lam (2002), a new algorithm based on the projection method was proposed resulting in a smoother traffic flow. The DTA model was set as the equilibrium constraint of the dynamic road pricing problem which was in the form of a dynamic MPEC. For this dynamic road pricing problem with a single objective, Differential Evolutionary (DE) algorithm and Pattern Search (PS) algorithm were tested and DE algorithm was found to be superior as compared to PS algorithm. To evaluate the objective of the MPEC model in the process of applying DE and PS algorithm, the resulting parametric DTA problem was solved using the algorithm based on the projection method proposed in this thesis. In this research, the amount of toll depends on the length of stay on the tolled link. Lastly, multi-objective dynamic road pricing model applying the Non-dominated Sorting Genetic Algorithm (NSGA-II) was successfully illustrated to show how the problem would behave when confronted by the decision maker in reality. The numerical example suggested that when considering queue optimization, the decision maker can take into account the tradeoffs with revenue generation. The results for the dynamic road pricing model and multi-objective dynamic road pricing model were based on the assumptions of the DTA model involved. These assumptions include simplified link travel time function, idealistic travel behaviour modeling, pre-determined input parameters and illustration on a small size network.