UC Davis

Understanding the relationship between demand and traffic network flows under an uncertain setting is gaining more and more attention in the transportation science community. In this dissertation, we establish new theorems and methods for understanding the input-output relation of traffic network equilibrium problems under uncertainty. Approaching the problem from a fresh geometrical perspective, we provide new understanding of the uncertainty propagation process in the problem of traffic equilibrium. We first introduce a minimum norm solution mapping (MNSM) between travel demand and network flows and explore its mathematical properties in terms of well-defined, continuity, induced partition and connectivity. Under the linearity assumption of the link cost function, we provide a stable analytic formula of the MNSM together with the criterion of partition region determination. We then extend those results to more general cost functions by using epi-splines to incorporate more realistic situation of nonlinear link cost under congestion. The new results can also maintain good geometric inherent characteristics. After completing these fundamental analysis, we demonstrate how the MNSM can help understand the uncertainty propagation process through the push-forward measure induced by the MNSM and we prove that the approximation process maintains strong convergence of the push-forward measure. We also provide an effective algorithm to compute the MNSM which avoids massive enumeration. Several important application examples are provide in the end to demonstrate how the new analytical and numerical methods established in the dissertation can be used to provide engineering and policy insights for transportation network planning and management.