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.