Statistical modelling and inference for traffic networks : a thesis submitted for the degree of Doctor of Philosophy
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2012
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Massey University
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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.
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Keywords
Traffic flow, Traffic systems, Traffic networks, Traffic network modelling