Statistical modelling and inference for traffic networks : a thesis submitted for the degree of Doctor of Philosophy

Abstract

There are two facets that are important in providing reliable forecasts from observed traffi c data. The first is that the model used should describe and represent as many characteristics of the system as possible. The second is that the estimates of the model parameters need to be accurate. We begin with improved methods of statistical inference for various types of models and using various types of data; and then move onto the development of new models that describe the day-to-day dynamics of traffic systems. Calibration of transport models for traffic systems gives rise to a variety of statistical inference problems, such as estimation of travel demand parameters. Once the ways in which vehicles move through the network are known, statistical inference becomes straightforward, however, at present, the data available are predominantly vehicle counts from a set of links in the network. The fundamental problem is that these vehicle counts do not uniquely determine the route ows, as there are a large number of possible route ows that could have led to a given set of observed link counts. A solution to this problem is to simulate the latent route ows conditional on the observed link counts in a Markov Chain Monte Carlo sampling algorithm. This is challenging because the set of feasible route ows will typically be far too large to enumerate in practice, meaning that we must simulate from a set that we cannot fully specify. An innovative piece of work here was the extension of an existing sampling methodology that works only for linear networks to be applicable for tree networks. In simulation studies where we use the sample to estimate average route ows, we show that our method provides more reliable estimates than generalised least squares methods. This is to be expected given that our method exploits information available via second order properties of the link counts. We provide another demonstration of how this generalised sampler can be applied whenever the need to sample from the set of latent route ows is pivotal for making statistical inference. We use the sampler to estimate travel demand parameters for day-to-day dynamic process models, an important class of model where the data has been collected on successive days and hence allows for inference using the evolution of the traffic flows over time. A new type of data, route flows from tracked vehicles, is becoming increasingly available through emerging technologies. Our contribution was to develop a statistical likelihood model that incorporates this routing information into currently used link-count data only models. We derive some tractable normal approximations thereof and perform likelihood-based inference for these normal models under the assumption that the probability of vehicle tracking is known. In our analysis we find that the likelihood shows irregular behaviour due to boundary effects, and provide conditions under which such behaviour will be observed. For regular cases we outline connections with existing generalised least squares methods. The theoretical analysis are complemented by simulation studies where we consider the tracking probability to be unknown and the effects on the accuracy in estimation of origin-destination matrices under estimated and/or misspecified models for this parameter. Real link flow count data observed on a sequence of days can exhibit considerable day-to-day variability. A better understanding of such variability has increasing policy-relevance in the context of network reliability assessment and the design of intelligent transport systems. Conventional day-to-day dynamic traffic assignment models are limited in terms of the extent to which non-stationary changes in traffic flows can be represented. In this thesis we introduce and develop an advanced class of models by replacing a subset of the fixed parameters in currently used traffic models with random processes. These resulting models are analogous to Cox process models. They are conditionally non-stationary given any realisation of the parameter processes. Numerical examples demonstrate that this new class of doubly stochastic day-to-day traffic assignment models is able to reproduce features such as the heteroscedasticity of traffic flows observed in real-life settings.