Routing problems in stochastic time-dependent networks with applications in dynamic traffic assignment

Abstract

Stochasticity is prevalent in transportation networks in general, and traffic networks in particular. The overall objective of this thesis is to study implications and significance of stochasticity in the development of models and algorithms for dynamic traffic flows in road networks. There are two major parts in this thesis. We first study the best routing policy problems in stochastic and time-dependent networks, and then develop policy-based stochastic dynamic traffic assignment models and algorithms. Routing problems are not only useful to develop dynamic traffic assignment (DTA) methods, but are also fundamental network optimization problems with a wider application domain. We define the problem in general and give a framework, which we believe is the first in the literature. We give a comprehensive taxonomy and an indepth discussion of most of the variants of the problem. We study in detail a variant pertinent to the traffic in road networks. We give an exact solution algorithm to this variant, analyze its running time complexity and point out the importance of finding good approximation algorithms. We then present several approximations, and study their effectiveness against the exact algorithm, both theoretically and computationally. We proceed to develop a policy-based stochastic dynamic traffic assignment model. We give a conceptual framework and then develop models for users' choice of policies and the dynamic network loading problem. These models are two major components of the overall DTA model. We give solution algorithms for these models, and present a heuristic algorithm to solve the proposed policy-based DTA model. Using an example, we show that policy-based DTA models have solutions that are different in expected travel times than the path-based models.