Transportation Network Equilibrium Assignment Problem

Network flow assignment is a significant theorical problem and an important research subject in the field of the communication and water resource. In the intelligent transportation system, traffic flow assignment is the core of the traffic regulation and path choice problems. It has attracted many researchers. Based on the others' research in traffic flow assignment, we do some work as follows:In the theory of static traffic flow assignment, we formulate a completely link-based variational inequality (VI) model, whose objective function and constraint conditions do not have the path variables. Since the model is completely link-based, we need not enumerate all the paths to evaluate this model. This model is equivalent to the user equilibrium (UE) condition, that is, for each origin-destination pair, the travel time on all the used paths is equal and minimal; the travel time on the unused paths is greater than or equal to the minimal travel time. We present an optimal path choice algorithm to solve the VI model and determine an optimal path for each vehicle in the traffic network. An example is given to show that the model and the algorithm are right and effective.In the theory of dynamic flow assignment, we present a link-based VI model for the dynamic path choice. This model satisfies the dynamic user optimal condition, i.e., for each Origin-Destination pair, the path travel time experienced by travelers departing during the same interval is equal and minimal. We present the nested diagonalization method. We then put up a dynamic path choice algorithm to determine an optimal path for each vehicle in the traffic network.Since the traffic demand matrix is difficult to obtain, we present a discrete time-dependent maximum entropy (ME) approach to estimate the origin-destination trip matrices in transit network. The Newton method is applied to solve this optimization model of ME model. Then some efficient algorithms and data structures are put up, including the storage and application of the sparse matrix and the evaluation of the reverse matrix. An example is given to show that the origin-destination trip matrices which is gained by the ME model has a high reliability and the data structures and algorithms are very efficient.