Estimation of Travel Time Distribution and Travel Time Derivatives

Abstract

Given the complexity of transportation systems, generating optimal routing decisions is a critical issue. This thesis focuses on how routing decisions can be computed by considering the distribution of travel time and associated risks. More specifically, the routing decision process is modeled in a way that explicitly considers the dependence between the travel times of different links and the risks associated with the volatility of travel time. Furthermore, the computation of this volatility allows for the development of the travel time derivative, which is a financial derivative based on travel time. It serves as a value or congestion pricing scheme based not only on 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 part one (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 the data from fundamental traffic conditions, a scenario-based GCMM is studied. A distribution of the path scenario representing path traffic status is first defined; then, the dependent structure between constructing links in the path is modeled as a Gaussian copula for each path scenario and the scenario-wise path travel time distribution is 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. Different estimation methods are employed based on whether or not the path scenarios are observable: An explicit two-step maximum likelihood method is used for the GCMM based on observable path scenarios; for GCMM based on unobservable path scenarios, extended Expectation Maximum algorithms are designed to estimate the model parameters, which introduces innovative copula-based machine learning methods. In part two (Chapter 5), travel time derivatives are introduced as financial derivatives based on road travel times—a non-tradable underlying asset. This is proposed as a more fundamental approach to value pricing. The chapter addresses (a) the motivation for introducing such derivatives (that is, the demand for hedging), (b) the potential market, and (c) the product design and pricing schemes. Pricing schemes are designed based on the travel time data captured by real time sensors, which are modeled as Ornstein-Uhlenbeck processes and more generally, continuous time auto regression moving average (CARMA) models. The risk neutral pricing principle is used to generate the derivative price, with reasonably designed procedures to identify the market value of risk.

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