Reliability-based transit assignment : formulations, solution methods, and network design applications

Abstract

Transit assignment, a problem of predicting passengers’ route choices and determining the usage for transit services, is an important research field because the results of transit assignment models are crucial for evaluating the performance of transit networks. Essentially, the passengers’ route choices in transit assignment models depend on the supply of transit networks and a principle describing how passengers select transit routes. This thesis contributes to the literature of transit assignment by incorporating the stochasticity of the supply side of transit networks and proposing the reliability-based user equilibrium conditions that define the passengers’ route choice principle in uncertain transit networks.

This thesis proposes three general frameworks based on the linear programming approach, the complementarity problem approach, and the variational inequality problem approach for modeling and analyzing reliability-based user equilibrium problems. Based on these frameworks, this thesis develops mean standard-deviation and mean-variance formulations wherein either hard capacity constraints or soft capacity constraints are incorporated. Within each of these frameworks, the existence of a solution is guaranteed given continuous cost functions and a convex compact solution set. The properties of these formulations are discussed and illustrated.

To solve the proposed formulations, this thesis develops different algorithms. For the mean standard-deviation formulations, the column generation technique is adopted, while for the mean-variance formulations, the dynamic programming method is used. In particular, this thesis proposes a revised extragradient method. This method only requires a mild assumption for convergence and its computational advantages are demonstrated in a realistic size network.

This thesis also initially investigates the supply side paradox issues in transit area. Two types of paradoxes are pointed out. One is a Braess-like paradox, which is a phenomenon that the system performance deteriorates, in terms of the total effective travel cost, after providing a new line or increasing the frequency of a transit line. The other is a capacity paradox phenomenon that the network throughout reduces after adding a new line or increasing the frequency of a transit line.

Finally, one of the proposed reliability-based transit assignment models is applied into a bilevel framework for solving a transit network design problem. The upper level problem is to determine the frequency setting of transit lines, while the lower level problem is the mean-variance formulation of the transit assignment problem with hard capacity constraints. A decent direction method is developed to solve the bilevel problem. Numerical studies are also provided to investigate the properties of the problem. Future research directions are also pointed out.