Traffic Assignment Problem With Capacity Constraints Under Uncertainty

Traffic assignment problem(TAP)is one of the basic problems for urban traffic planning and management,which is also a hot topic in the interdisciplinary of mathematics and management science.The traffic assignment problem with link capacity constraint is a further expansion of the conventional TAP.This thesis studies the problem of traffic assignment problem with link capacity constraints under network uncertainty.Chapter 1 introduces the background and the importance of the traffic assignment problem for urban road networks with capacity constraints under uncertainty.The corresponding literature review includes the traffic assignment problems under uncertainty,traffic assignment problems with capacity constraints and traffic network design problems under uncertainty.Chapter 2 introduces the following preliminaries of this thesis: mathematical model of traffic assignment problems with capacity constraints and its two widely used solution algorithms,the mathematical model and the bi-level programming model of traffic assignment problems under uncertainty.In chapter 3,a new mathematical model of traffic assignment problem with capacity constraints under uncertainty is proposed.The model extends the conventional traffic assignment model with capacity constraint considering the stochastic property of traffic flow.Firstly,the link flow is defined as a random variable.Secondly,the mathematical model can be obtained with the consideration of the link capacity constraints under the probabilistic condition.The mathematical formula of delays resulted from the capacity constraints is deduced under uncertainty.Then,a solution algorithm is designed according to the mathematical property of the proposed new model.Finally,the numerical example is used to demonstrate the properties of the model.Chapter 4 proposes a transportation network design model with link capacity constraints under uncertainty.The model can be formulated as a bi-level programming problem.The objective function in upper-level of the proposed model is to minimize the sum of the total system travel times and the delays.The lower-level problem is the traffic assignment model which is proposed in Chapter 3.Then,a heuristic algorithm for solving the network design problem is provided.It is demonstrated by severalnumerical examples that the results of the proposed network design problem in this chapter can effectively alleviate the traffic congestion under network uncertainty.Chapter 5 concludes this thesis and provides some further studies.