Lee, Seungjae; (1995) Mathematical programming algorithms for equilibrium road traffic assignment. Doctoral thesis (Ph.D), University of London.

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Abstract

The equilibrium approach to representing interactions between the supply and demand sides of traffic assignment has been used widely in the estimation of traffic flows on road networks. Although this approach is quite reasonable, there is a considerable gap between the observed and modelled values of cost and flow. This gap can be reduced by relaxing some of the restrictive assumptions behind the models used in order to enhance their realism. This study investigates the solutions of various advanced road traffic assignment models. Priority and signal controlled junctions are modelled in traffic assignment in order to enhance the realism of junction analysis. A multiclass assignment is modelled to represent different groups of users. These problems are known to be non-separable because traffic cannot be segmented in such a way that the costs incurred by any one segment vary only with the flow within that segment. Existence, uniqueness and stability properties of solutions to these problems are investigated. These analyses are important to know the reliability and repeatability of any solutions that are calculated. Analyses of these properties lead to some guidelines for using these detailed models. A number of new solution algorithms are developed to solve the resulting traffic assignment problems. These algorithms belong to the general category of simplicial decomposition which solves the problem by dividing it into two subproblems: a linear and a master subproblem which are solved alternately. One of the advantages of these algorithms is that they operate in a lower dimensional space than that of original feasible region and hence allow large-scale problems to be solved with improved accuracy and speed of convergence. These improved algorithms give many choices to the traffic management studies. Two substantial networks have been used to compare the performance of new algorithms on the various models developed. They have performed favourably by comparison with existing algorithms. A small example network has been used to investigate existence, uniqueness and stability properties using the models. In a priority controlled model, a unique stable solution has been obtained using the model whilst in a signal controlled model, multiple and unstable solutions have been obtained. In a multiclass model, a unique solution has been obtained in terms of the total class flow whilst multiple solutions have been obtained in terms of each class flow. These results correspond well to the theoretical analyses of these models, which has shown to have indeterminate behaviour and by the nature of these models assumed, the degree of non-separability is ordered according to priority controlled, multiclass and signal controlled models.

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