Introduction
References
Acknowledgement
Biography
Contents
Pages 136 to 151
PREDICTING NON-STEADY SPEED DRIVING
I.D. Greenwood, R.C.M. Dunn and R.R. Raine
ABSTRACT
In order to quantify the effects of congestion on vehicle operating costs, it is necessary to model
not only the speed-flow effects but to also model the variation in speeds. This paper presents a
review of such a model developed to date that will enable the prediction of the costs of
congestion. The paper also presents an overview of future research aimed at refining the current
model form.
Other analyses indicate that the true cost of congestion may be under-estimated by as much as
30 per cent for passenger cars when accounting solely for the speed-flow effects. Given the
limited annual expenditure on roads, it is important to have a model capable of simply, yet
accurately, quantifying the cost of congestion to ensure a fair distribution of funds is observed.
Start of Paper
Introduction
Contents
Start of Paper
Contents
INTRODUCTION
The modeling of congestion effects on traffic flows has traditionally being consigned to the
theory of increased flow results in lower speeds. While this is quite valid, it does not explain
the total effect of congestion on vehicle operations. In particular, the variations in vehicle
speeds – stop/go waves – which occur as traffic volumes increase, are repeatedly left out of the
costing of congestion.
Greenwood and Bennett (1995a and 1995b) presented a model that illustrated that excluding the
non-steady portion – that of greater variation in speeds – could lead to an under-prediction of
vehicle operation costs by as much as 30 per cent for passenger cars. Similar work indicated
that owing to the large inertial mass of heavy vehicles an increase in fuel consumption of up to
200 per cent for these vehicles could be expected in heavily congested conditions.
The work undertaken and presented in this paper is targeted at accurately costing mid-block
congestion that occurs in uninterrupted conditions, and results in a series of stop/go waves.
Interrupted flow such as that occurring at signalised intersections, where drivers select
deliberate changes in mean speed, are not the focus of the research work.
Since this work in 1995, further work to refine the congestion model has been undertaken. To
date this has involved refining of the fuel efficiency model to better represent actual engine
efficiencies and operating characteristics. Work currently progressing includes the use of a
metered vehicle that will record high accuracy data on following distances and traffic flows and
speeds, with the aim of determining the effect of these parameters on vehicle driver patterns.
BACKGROUND INFORMATION
As part of the Highway Technical Relationships Study Team (HTRS) within the International
Study of Highway Development and Management Tools (ISOHDM) the first author was
responsible for developing the congestion model for inclusion into HDM-4 (Greenwood and
Bennett, 1995a and 1995b, NDLI, 1995). The model developed utilised the concept of
acceleration noise, defined as the standard deviation of accelerations, to define the magnitude of
the non-steady state portion of driving.
The data collected as part of the HDM-4 study in Malaysia (NDLI, 1995) enabled a model to be
developed. This model related acceleration noise to the volume to capacity ratio of the road
section (Greenwood and Bennett, 1995a and 1995b). One of the main inputs into the model
developed, is the volume to capacity ratio, yet in the measurements undertaken in Malaysia, this
could only be subjectively measured.
The new model being developed will enable the influence of following distance and volumes to
be better modelled, with the final result being the development of a comprehensive congestion
model. This project forms a component of a PhD research programme.
MODELING APPROACH
Overview
The method of analysing the cost of congestion is as illustrated in Figure 1. Descriptively the
process is as follows:
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obtain or calculate the various input parameters
determine the operating costs based on steady-state conditions (zero acceleration) and the
additional costs of the random accelerations
output both the steady-state and congested vehicle operating costs.
Each of these three distinct steps is described in more detail below.
It is noted that the primary use of the resultant model is for the costing of congestion within
treatment selection algorithms and project economic analyses. As noted previously within this
paper, it is not the intention to develop a model that is capable of modeling detailed interrupted
traffic flow situations such as occurs at signalised intersections. Rather, the model is aimed at
uninterrupted mid-block congestion that result in stop/go waves propagating through the traffic
stream.
Basic Inputs
Figure 1 indicates that the basic input parameters into the model can be separated into three
broad groups:
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environmental factors
traffic factors
vehicle factors
Environmental factors include such items as road gradient, pavement roughness, surface texture,
lateral clearances and side friction etc. These factors are independent of the vehicles using the
road and are common to all vehicles.
The second set of factors is those pertaining to the general traffic flow. These include such
items as the speed-flow model of the road, headway distributions, vehicle mix and vehicle size.
These items form a general description of the traffic stream as it operates under the current
environmental factors.
Thirdly, there are the individual vehicle factors. These include items such as vehicle power,
mass, engine efficiency, emission controls etc. It is the vehicle factors that enable the
performance of individual vehicles within the vehicle stream described by the traffic factors to
be determined.
Modeling Theory
It is the basic premise of the congestion modeling undertaken to date, that the cost of congestion
can be calculated as a two part cost. These costs are:
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the steady-state or deterministic portion (zero accelerations)
the variable or probabilistic portion (non-zero accelerations)
The former of these two items wherein average speeds are used, is what is commonly calculated
when evaluating the cost of congestion. It is the second component – that which models the
stop/go waves – which is being refined within this research.
Outputs
Outputs from the congestion model being created are:
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steady-state fuel consumption and vehicle emission results
additional fuel consumption and vehicle emissions owing to congestion
Previous work (NDLI, 1995) has provided an initial assessment of the additional fuel
consumption expected from modeling the non-steady component of congestion. Figure 2 taken
from this study clearly indicates a significant increase (in excess of 30 per cent) in fuel
consumption when operating under heavily congestion conditions. The evaluation technique
utilised to arise at this figure is described in the following sections.
CURRENT MODELS
In order to describe congestion effects, two parameters are utilised within the NDLI (1995)
model. Firstly, the average speed is deemed to represent the overall effect of the volume to
capacity ratio. Secondly, the term acceleration noise is used to describe the magnitude of the
random speed fluctuations around the average speed.
Greenwood and Bennett (1995) defined acceleration noise as the standard deviation of
accelerations. An analysis of accelerations recorded at 1 second intervals on motorways in
Malaysia indicate that in heavily congested conditions (volume to capacity ratio approaching
1.00) acceleration noise values of around 0.6m/s² were typical.
The proposed equation in HDM-4 (NDLI, 1995) for predicting acceleration noise as a function
of traffic volume is given below. The equation indicates that there are two components to
acceleration noise. Firstly, there is the natural noise that is related to environmental factors and
secondly there is the traffic induced acceleration noise.
σa = σat 2 + σan 2
where σa
σat
σan
is the total acceleration noise on the section (m/s²)
is the traffic induced acceleration noise (m/s²)
is the natural acceleration noise (m/s²)
The natural noise is considered to be a function of the following (Greenwood and Bennett,
1996):
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driver inability to maintain a perfectly steady speed
road alignment
presence of roadside stalls and other side friction
influence of slow moving transport
road roughness
Greenwood and Bennett (1995a and 1996) define the traffic induced acceleration noise as
illustrated below. This function is essentially a form of a s-curve as illustrated within Figure 2
and was arrived at through a regression analysis of a combination of actual and theoretical data.
σat = σat max
where σatmax
1.04
1+ e
(a0 + a1. RELFLOW )
is the maximum traffic acceleration noise (m/s²)
a0, a1
RELFLOW
are variables related to the form of the speed-flow equation
is the relative traffic flow on the section = volume/capacity ratio
The variables a0 and a1 are related to the speed-flow function as illustrated below.
definitions of the various flow variables refer to Figure 3.
 Qo 
a0 = 4.2 + 23.5 

 Qult 
2
 Qo 
a1 = − 7.3 − 24.1

 Qult 
where Qo
Qult
For
2
is the flow at which vehicle interactions begin to reduce speeds
is the ultimate capacity of the road section
ACCELERATION NOISE RESULTS TO DATE
Data collected in Malaysia for the HDM-4 study, on both high standard motorways and lower
standard roads indicate that the typical value for the maximum total acceleration noise is around
0.6 m/s². This value was recorded over various driver and vehicle combinations and initial data
collection in New Zealand indicates that this value is indeed transferable across international
borders. Values for the natural noise are typically around the 0.1 m/s² mark.
It is postulated that the acceleration noise level should be a function of the power to weight ratio
of the vehicle, as the ability to accelerate and decelerate is also limited by this ratio. To date no
tests have been performed to specifically address this issue, although limited test results in the
HDM-4 study (Greenwood and Bennett, 1995a and 1996) suggest that this may be the case.
The accelerations recorded have to date been found to not follow a strictly Normal Distribution.
The deceleration tail of the distribution is in general longer than the acceleration tail. As most
vehicles have a better breaking ability than they do acceleration ability, this finding is not
unexpected. However, to date it has been considered that the variation between the collected
data and a true normal distribution are sufficiently low to allow the data to be assumed to be
normal.
THE SIMULATION PROGRAM
A simulation program has been written in Visual Basic 5.0 to simulate a number of vehicles
(typically 1,000) driving along a section of road. Every second an acceleration value is
randomly selected based on the current predicted acceleration noise level. The speed of the
vehicle and the acceleration are then used to predict the fuel consumed during the second. The
initial speed of the vehicle is randomly generated based on a mean speed and a coefficient of
variation in speeds.
After the simulated vehicle has travelled a sufficient distance (typically 1 km) the current
vehicle speed is compared to the initial speed of the vehicle. The simulation is continued until
these two speeds are equal. The total fuel consumed within the simulation run is then compared
to that which would have occurred if the vehicle had travelled the same distance at a steady
speed equal to its initial value.
The ratio of the congested to steady-state fuel consumption is termed the fuel consumption ratio
or DFUEL. Figure 4 illustrates the variation in the fuel consumption ratio with differing mean
speeds and acceleration noise levels for a passenger car.
Work has commenced to add the prediction of vehicle emissions into the model and produce
results in a similar manner to that of the fuel consumption. It is considered that fuel
consumption and vehicle emissions are the components of vehicle operating costs most effected
by congestion and therefore the effort to date has concentrated on these two components.
Fuel consumption forms a major component of vehicle operating costs within congested
conditions and is therefore important in the economic evaluation of various project options.
Vehicle emissions form an important component of the environmental impact of road projects.
With the introduction of costing Carbon Dioxide within the Transfund New Zealand Project
Evaluation Manual (Transfund, 1994) vehicle emissions can also have an impact on the
economic evaluation of projects.
RECOMMENDED CHANGES TO THE FUEL CONSUMPTION
MODEL
As noted within the Introduction, models that better predict the operating characteristics of
vehicles have been adopted for this project. The basic fuel consumption model adopted for this
project is that recommended by Greenwood and Bennett (1995b) and NDLI (1995). This fuel
consumption model was primarily an adaptation of the ARFCOM model developed in Australia
during the 1980's (Biggs, 1988).
During the testing of vehicle fuel economy, several significant issues have arisen with respect to
the validity of parts of the previous model to modern vehicle fleets. In particular the form of the
engine efficiency equation and the minimum fuel consumption have major impacts on fuel
consumption under congested conditions.
The fuel consumption model adopted as the basis for this project includes a relationship that
implies that engine efficiency decreases (fuel consumption increases per unit of power required)
at higher power outputs. A review of the engine operating performance of several engines
indicates that engine efficiency is in fact a u-shaped relationship with engine power, with an
optimal efficiency around mid-power range. During stop-start conditions, such as are present
during congestion, the effect of the use of the greatly simplified model is considered to be
significant.
The data available to date indicates that it is necessary to provide both power and engine speed
into the engine efficiency equation to yield the correct result. The modification of the engine
efficiency equation is to be included within the next version of the simulation program. It is
anticipated that this could result in an even higher impact of congestion on fuel consumption.
Another significant change from the adopted model is that of a minimum fuel consumption for
the engine. Older style carburetted engines did not have the ability to completely shut off fuel
supply to the engine, therefore fuel was consumed even when coasting down a steep grade or
decelerating hard. To account for this, the adopted model of Greenwood and Bennett (1995b),
and NDLI (1995) stated that the minimum fuel consumption equals the idle fuel consumption.
Modern carburetted engines and fuel-injected engines can in fact run for short periods of time
with zero fuel consumption. Such occasions often occur during the initial stages of a
deceleration cycle or while travelling down steep grades. As the model being developed from
this project is aimed at predicting congestion effects, the use of a model not capable of
accurately portraying vehicle operations is unsuitable. As with the engine efficiency model, a
different fuel consumption model under negative power is also being developed as part of this
project.
CURRENT DATA COLLECTION
The next stage of this project – currently underway – is the collection of high quality data on the
Auckland Motorway system. The overall data collection components are illustrated in
Figure 5. A vehicle is being equipped with sensors to enable the following items to be recorded
and summarised at 1 second intervals:
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fuel consumption
engine speed
vehicle speed/distance
distance to the vehicle in front
In addition, data provided by Transit New Zealand will enable traffic flows and speeds to be
related to the driving conditions. The Transit New Zealand data is obtained through a series of
detector loops installed into the pavement at numerous motorway interchanges. The average
spacing between the interchanges on the proposed test section (Aucklands Southern Motorway)
is 3 km. These loops and associated data collection/processing units, summarise average speeds
and vehicle flows per lane in 3 minute intervals.
In addition to storing all the data onto computer, a video mounted within the vehicle will
provide a record of the actual traffic flows encountered. All data collected from the various
sensors will be overlaid onto the videotape in real time. The video will then be digitised onto
CD to enable a quick reference to any item of significance.
The method of collecting the fuel consumption data is through the collecting of the electric
pulses of the fuel injectors. By knowing both the average pulse width and the number of pulses
per second, an accurate estimation of the fuel consumption can be made. The number of pulses
also enables the engine speed to be estimated.
The vehicle speed and distance travelled each second is measured through the use of a sensor
attached to the rear wheel of the vehicle. As the test vehicle is front wheel drive, the rear wheel
does not exhibit the same level of skidding as the front wheel does. The sensor manufactured
for this project records 360 pulses per wheel revolution. This equates to an accuracy of around
5 mm.
As was noted earlier, the typical natural acceleration noise level is around 0.1 m/s². The
definition of acceleration noise level is the standard deviation of accelerations. As the distance
travelled is recorded every 1 second, the discrete distance measurements also translate into
discrete vehicle speeds and accelerations. By recording distance to the nearest 0.05m (5 mm)
accelerations as small as 0.05 m/s² can be recorded.
Readily available commercial odometer sensors only transmit 1 pulse around every 0.4 m,
which yield minimum non-zero accelerations of 0.4 m/s². Thus the acceleration distribution
being measured is around 25 per cent of the accuracy of the meter. The currently utilised
odometer sensor is considered to yield an optimum balance between the nominal accuracy and
the errors in the equipment.
The distance to the vehicle in front is considered to play an important role in determining driver
characteristics, especially acceleration habits. As part of the data collection exercise, a laser
based speed gun (similar to that employed by the police) will be mounted within the vehicle.
This device measures distances every 0.3 seconds, with the most recent result recorded along
with all the other information every second.
Statistical tests to determine what, if any, variable pertaining to the gap will be made. If the
distance to the vehicle in front is found to have a significant effect on the prediction of
acceleration noise, then an attempt at predicting this value from mean traffic speeds and flows
will be undertaken.
CONCLUSIONS
Data collected to date indicate that modeling congestion purely through the use of a speed-flow
relationship may be under-estimating the true cost by as much as 30 per cent for cars and 200
per cent for heavy vehicles. A combination of mean speed and acceleration noise is proposed as
a better description of congestion effects.
Acceleration noise is considered to be a combination of two primary components, one related to
traffic levels, the other to environmental conditions. Current prediction of the traffic related
component is based exclusively on the form of the speed-flow relationship and current traffic
volumes.
Future work is aimed at refining the prediction of acceleration noise through the use of high
quality data being collected on the Auckland motorway system. This data collection exercise
includes for vehicle speed, fuel consumption, the distance to the vehicle in front and general
mean vehicle speeds and flows.
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REFERENCES
Biggs, D.C. (1988). ARFCOM - Models for Estimating Light to Heavy Vehicle Fuel
Consumption. Research Report ARR 152, Australian Road Research Road Board, Nunawading.
Greenwood, I.D. and Bennett, C.R. (1995a). The Effects of Traffic Congestion on Fuel
Consumption. Asian Development Bank Regional Technical Assistance Project RETA:5549
Greenwood, I.D. and Bennett, C.R. (1995b). HDM-4 Fuel Consumption Modelling. Asian
Development Bank Regional Technical Assistance Project RETA:5549
Greenwood, I.D. and Bennett, C.R. (1996). Effects of Congestion on Fuel Consumption.
ARRB Road and Transport Research Journal. pp 18-32, Vol 5, No2 June 1996.
NDLI (1995). Modelling Road User Effects in HDM-4. Report to the Asian Development
Bank. N.D. Lea International, Vancouver.
Transfund (1994). The Project Evaluation Manual. Transfund New Zealand, Wellington, New
Zealand.
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ACKNOWLEDGMENTS
The authors wish to acknowledge the assistance of their respective organisations – Opus
International Consultants and The University of Auckland – in preparing this paper. The views
expressed within this paper are those of the authors and do not necessarily form the views of
their respective organisations.
The authors also wish to acknowledge the contribution of data to the next stage of the work by
Transit New Zealand. Transit New Zealand support of this project does not infer that the results
will formulate future policy.
Acknowledgment is also given to the various individuals within the University of Auckland
(Energy and Fuels Research Unit and Gary Carr), Highway and Traffic Consultants Limited (Dr
Christopher Bennett) and Chevron Engineering (Evan Fray) for the supply or manufacture of
the various items of data collection equipment used.
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AUTHOR BIOGRAPHIES
Mr Ian Greenwood completed his B.E (Civil) with first class honours in 1992, prior to taking
up a position as an Assistant Engineer with Opus International Consultants. He has been
involved in numerous research projects in the road and transport fields. In 1995 he was
seconded to N.D. Lea International in Malaysia for 9 months to take up the position of
Researcher Traffic for the HDM-4 Technical Relationships Study. Following this he spent 3
months at the University of Birmingham as an Honorary Research Associate, where he was
involved with implementation of his previous research.
He has spent time in Canada and
Australia while working on Pavement Management Systems. He is currently completing his
PhD (Civil Engineering) at the University of Auckland.
Mr Roger Dunn’s professional career began with 10 years in the Ministry of Works and
Development NZ engaged on various aspects of roading - he then joined Freeman Fox Wilbur
Smith & Associates (UK and France) on traffic planning and new town developments. In 1972
he returned to NZ to The University of Auckland. Current and recent projects have included the
Highway Technical Relationships Study for HDM-4 (for Asian Development Bank in
Malaysia), a Study on the Access Frequency and Accidents on Rural State Highways (for
Transit New Zealand) and applications of ITS (Intelligent Transport Systems). He is a member
of two international committees on the standardisation of traffic information and control
systems.
Dr Robert Raine undertook an apprenticeship at the British Aircraft Corporation before
completing his PhD on modelling of diesel engine emissions at the University of Southampton.
He was appointed to the University of Auckland in 1977 with main interests in thermodynamics
and internal combustion engines. Since then he has undertaken sabbatical leave at UMIST,
Oxford and Calgary Universities and has also taken research leave in Switzerland, Thailand and
China. At Auckland, in addition to lecturing, he has been Director of the Energy and Fuels
Research Unit with responsibility for the installation of engine and vehicle emissions analysis
equipment. The Research Unit has consulted extensively to government departments and
commercial organisations on the performance and emissions of vehicles and was closely
involved in technical aspects of the New Zealand natural gas vehicle programme.
Basic Inputs
Modelling Theory
Outputs
Environmental
Factors:
-grade
-surface texture
-roughness
-lateral clearances
Deterministic or steady state
component based on
average speed and zero
acceleration.
Steady-state:
-fuel
-emissions
Traffic Factors:
-speed-flow
-headway
-vehicle mix
-vehicle lengths
Vehicle Factors:
-power
-tyre type
-mass
-engine efficiency
-catalytic
converter
Probabilistic or variable
component based on
acceleration noise and
simulation
Congested:
-fuel
-emissions
Figure 1: Modelling Theory
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1.0
0.9
Qo/Qult=0.0
Qo/Qult=0.1
Total Acceleration Noise in m/s/s .
0.8
Qo/Qult=0.2
Qo/Qult=0.3
0.7
Qo/Qult=0.4
Qo/Qult=0.5
0.6
natural noise
0.5
0.4
0.3
0.2
0.1
0.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Relative Traffic Flow (Q/Qult)
Figure 2: Ratio of Congested to Steady State Fuel Consumption for a Passenger Car
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1.0
S1
Speed (km/h)
S2
S3
Snom
Sult
Qo
Qnom
Flow (PCSE/h)
Notes:
S1, S2, S3
PCSE
Q0
Qnom
Qult
=
=
=
=
=
the free speed of different vehicle types
passenger car space equivalents
flow at which speeds reduce below the free speed
flow at which all vehicles travel at the same mean speed
the ultimate capacity of the road
Figure 3: Generic Speed-Flow Model Used Within The Model
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Qult
1.6
0.2 m/s/s
0.4 m/s/s
1.5
Fuel Consumption Ratio .
0.6 m/s/s
0.8 m/s/s
1.4
1.3
1.2
1.1
1.0
0
10
20
30
40
50
Speed in km/h
60
70
80
90
Figure 4: Fuel Consumption Ratio versus Mean Speed and Acceleration Noise for a
Passenger Car
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100
Video mounted on
vehicle to keep
visual record. All
data overlaid onto
video.
Distance sensor
attached to nondriving wheel
±5mm
Fuel sensor
attached to
injector pulse wire
yielding average
pulse width and
number of pulses
Laser mounted on
vehicle measuring
distance to vehicle
in front
Loops embeded in
pavement yielding
flows and speeds
by lane at 3
minute intervals
Figure 5: Data Collection Equipment
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