Estimation of Travel Time Distribution and Travel Time Derivatives

With the complexity of transportation systems, generating optimal routing decisions is a critical issue. This thesis focuses on how routing decisions can be made by considering the distribution of travel time and the associated risk. More specifically, the routing decision process is modeled in a way that explicitly considers the dependence between travel time among different links and the risk associated with the volatility of travel time. Furthermore, the computation of this volatility allows for the development of the travel time derivative, which is the financial derivative based on travel time. It serves as a value pricing (also known as congestion pricing) scheme that is based on not only the level of congestion but also its uncertainties. In addition to the introduction (Chapter 1), the literature review (Chapter 2), and the conclusion (Chapter 6), the thesis consists of two major parts: In the first part (Chapters 3 and 4), the travel time distribution for transportation links and paths, conditioned on the latest observations, is estimated to enable routing decisions based on risk. Chapter 3 sets up the basic decision framework by modeling the dependent structure between the travel time distributions for nearby links using the copula method. In Chapter 4, the framework is generalized to estimate the travel time distribution for a given path using Gaussian copula mixture models (GCMM). To explore more information from fundamental traffic conditions, a scenario-based GCMM is studied: A distribution of the path scenario (systematic factor) is defined first; the dependent structure between constructing links in the path is modeled as a Gaussian copula for each scenario, and the scenario-wise path travel time distribution can be obtained based on this copula. The final estimates are calculated by integrating the scenario-wise path travel time distributions over the distribution of the path scenario. In a discrete setting, it is a weighted sum of these conditional travel time distributions. The property of the scenario-based GCMM is studied when the number of scenarios changes. Furthermore, general GCMM are introduced for better finite scenario performance, and extended expectation-maximum algorithms are designed to estimate the model parameters, which introduces an innovative copula-based machine learning method. iii In the second part (Chapter 5), travel time derivatives are introduced as financial derivatives based on road travel time a non-tradable underlying asset and a more flexible alternative for value pricing. The chapter addresses (a) the necessity of introducing such derivatives (that is, the demand for hedging), (b) the market and design of the product, and (c) the pricing schemes. The pricing schemes are designed based on the travel time data from loop detectors, which are modeled as mean reverting processes driven by diffusion processes. The no-arbitrage principle is used to generate the price.