Modelling Traffic Networks

1
Modelling Traffic Networks
Osvaldo Anacleto-Junior (o.anacleto-junior_at_open.ac
.uk) Supervisor Dr. Catriona Queen
Statistics Group, The Open University
PROBLEM
FLOW DIAGRAM EXAMPLE
It is helpful to draw a flow diagram to
define the dependence structure between the
vehicle counts time series. To do this, it is
important to consider how the traffic flows into
the network and also to assume that drivers will
behave rationally and will follow the most direct
route through the network. A flow diagram for
the London network based on its layout is given
below
Congestion on roads is a worldwide
problem causing environmental, health and
economic problems. On-line traffic data can be
used as part of a traffic management system to
monitor traffic flows and reduce congestion by
taking actions, such as imposing variable speed
limits or diverting traffic onto alternative
routes. Reliable short-term forecasting and
monitoring models of traffic flows are crucial
for the success of any traffic management system.
Traffic data can be represented
through a set of time series of vehicle counts,
and each time series describes a sequence of
counts from a specific site over time. It is not
unlikely to have a causal dependence structure
between these time series, due to the traffic
flow directions of a network. Apart from that,
external events, like traffic accidents and
roadworks, can heavily affect traffic flows,
leading to sudden changes in the data being
analysed.
PROJECT SUMMARY
DIRECTED ACYCLIC GRAPH (DAG)
This project will use what are known as
graphical dynamic models to forecast and monitor
traffic flows. These models represent the flows
in the network by a graph. This graph is not only
a useful pictorial representation of the network,
but it also ensures that model computation is
always simple, even for very complex road
networks. A basic graphical dynamic model has
been shown to be extremely promising for
short-term forecasting in two UK networks.

A DAG is a type of graphic representation
language to display variables and relationships
among them. A DAG for the sites 167, 168, 170A
and 170B is given below.
DATA DESCRIPTIONS

• London
• (M25 / A2 / A296 Junction)
• 17 data sites
• 21 weeks of data
• Hourly counts

Yt(i) is a parent of Yt (j) if there is an arc
leading from Yt(i) to Yt(j). E.g., Yt(167) is a
parent of Yt(168).
THE MODEL
It will be used in this project the
Linear Multiregression Dynamic Model (LMDM). This
model represents time series by a DAG, and
describe each time series as a separate
univariate model, considering its parents as
linear regressors. The plot below shows
that it is reasonable to assume a linear
relationship between parent and child depending
on the time of the day. .

• 32 data sites
• Over a year's worth of data
• Minute data

Manchester M60 / M62 / M602 Junction
Within this approach, model computations
are fast and relatively straightforward, no
matter how complex is the network. Apart from
that, the model provides an easy way to handle
changes in the network (since its graphical
structure) and also to include information
related to external events which can affect the
behaviour of the time series.
Number of vehicles over time in a week at site
167 of the London Network
RESEARCH TOPICS

• There are many interesting problems associated
  with using these models for modelling traffic
  networks. For example
• The model has so far been used to forecast
  hourly traffic flows. Will the same model be
  useful for data collected in smaller time
  intervals? The smaller the time interval, the
  more there is congestion can the model be
  adapted to cope with this?
• Any change in traffic flows is often associated
  with an incident, such as a road traffic
  accident. Can a monitor be developed which can
  detect any unexpected changes in traffic flow?
  And can a monitor detect when a road is reaching
  capacity, so that congestion is likely to occur?
• On-line traffic flow data often exhibit errors
  there may be a physical problem with a detector,
  for example, or there may be a communication
  problem between the detector and the data
  processing centre. How might such data errors be
  detected? And how might we forecast the true
  traffic flow when data errors are present?
  

The Open University, Milton Keynes
Department of Mathematics and Statistics, Walton
Hall, Milton Keynes, MK7 6AA, United Kingdom