Accident Prediction Models
Title
for Traffic Signals
Presented by:
Dr Shane Turner
Beca Infrastructure Ltd, New Zealand
Blair Turner
ARRB Group, Victoria, Australia
Professor Graham Wood
Macquarie University, NSW, Australia
Abstract
A significant proportion of urban crashes occur at traffic signals.
Many of the black-spots in both Australia and New Zealand
cities occur at high volume and/or high speed traffic signals.
Major intersections often have long cycle times and complex
phasing arrangements, which can confuse and frustrate drivers
and pedestrians. Right turning phases are often introduced at
traffic signals to reduce right-turn-against crashes, but this in turn
increases cycle lengths and overall delays. Some traffic signals
have unusual layouts, such as highly staggered right turn bays,
which may cause safety problems. Crash prediction models
have been produced, in several separate research projects for
traffic signals, examining the impact of traffic volumes, speed
limit, signal phasing, number of pedestrians and cyclists and
intersection layout on various crash types. These crash prediction
models have enabled a better understanding of the impact of
these factors on safety and also allow the safety impact to be
quantified. This paper summarises the outcomes of each of the
separate studies and key findings of the research.
Introduction
The majority of the higher volume intersections in our urban
areas have signalised control. Traffic signals are often introduced
at high volume priority controlled intersections and roundabouts
to address capacity and safety problems. However many of the
black-spots in our urban areas, particularly larger centres, are at
traffic signals, because of the high exposure levels. A significant
proportion of crashes occurred at traffic signals in NSW (22%),
Victoria (17%) and Queensland (14%). This compares with 8%
of crashes in New Zealand. Table 1 shows the number of injury
crashes of each type in each State and within New Zealand, as
well as the percent of fatal crashes at signals compared to all fatal
crashes.
Table 1: Average Crashes per year at Traffic Signals (over period
2001 to 2005)
Country/State
Fatal
Serious
Minor
New South Wales*
35 (8%)
4390
Victoria
20 (6%)
800
2100
Queensland*
11 (3%)
679
1246
New Zealand
9 (2%)
117
659
*based on 2005 data only
Considerable research has been undertaken internationally on the
safety of traffic signals (Hall, 1986, Hauer et al., 1989, Taylor et
al., 1996, Wang et al., 2003, Lyon et al., 2005 and Wong, 2007).
The study by Hall (1986) was one of the first to utilise generalised
linear modelling and a Poison error structure. The study draws
on a sample size of 177 intersections throughout England, with
around 30 in London. It considered eight different crash types,
including right angle, single vehicle and pedestrian versus motorvehicle crashes. A number of variables were considered including
traffic and pedestrian volumes, geometric features (approach
width, number of lanes and sight distance), signal timings
(inter-green time and cycle length), and the presence of antiskid surfacing. Hauer (1989) also used generalised linear models,
but this time with a negative binomial error structure. Flow-only
models were produced for the 15 major crash types for a sample
of 145 intersections in Toronto. Wong et al. (2007) produced
crash prediction models for the major crash types at 262 traffic
signals in Hong Kong. This study also used generalised linear
models with a negative binomial error structure. Key significant
predictor variables included; traffic volume, degree of approach
curvature, surround road environment, presence of tram stops,
pedestrian volumes, proportion of commercial vehicles and
average lane width. Wong’s paper also contains a literature
review of recent research on crash prediction models at traffic
signals.
A number of crash prediction modelling studies have been
undertaken of traffic signals in New Zealand, by Turner, and
these are outlined in the following section. These studies have
Page 1
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Accident Prediction Models for Traffic Signals
become more detailed over time and the impact of a number
of key variables, including, traffic flow, speed limit, number of
pedestrian and cyclists, signal phasing and intersection layout, on
the safety of traffic signals has been investigated.
Of particular interest is the effect that speed limit and signal
phasing have on safety. Several Australian states use traffic signals
in high speed limit urban environments, including 70 and 80
km/h zones. It could be expected that given the higher speeds in
such environments that the severity outcomes at such locations
would be higher if a crash were to occur. Information from
Victoria (again using information from 2001 to 2005) show that
half of all fatal crashes at traffic signals occurred where the speed
limits were 70 km/h or above (almost 10 fatal crashes per year),
while over a quarter of serious injury crashes (264 per year) occur
at such locations. The situation is similar in NSW, with almost
30% of fatal signal crashes in 2005 occurring at higher speed
intersections (70 km/h or above). Although numbers are less in
Queensland, 27% of fatal crashes (three of their 11 fatal signal
crashes in 2005) occurred in 70 km/h areas.
Traffic signals are not commonly used on high speed/rural roads
in New Zealand. Where signals have been used the general
experience has been that more severe crashes, be they fatal
or serious crashes have been more prevalent. With a strong
emphasis on reducing road trauma in New Zealand (and Australia)
the use of traffic signals in high speed environments has to be
questioned. But with traffic volumes growing and the increasing
costs and effects (eg severance) of alternative grade separation
options, particularly in urban areas, the use of traffic signals
in such environments is often considered. The most desirable
alternatives are standard or signalised roundabouts, but these are
not always an option, due to construction constraints and their
ability to handle high traffic volumes. They are also a major pinch
point for cyclists (and to a lesser extent pedestrians), and large
roundabouts have a poor safety record for cyclists.
Crash models, like those contained in this paper, can provide
useful future information for traffic engineers and decision
makers that are attempting to trade-off costs of more expensive
options and the safety consequences of installing traffic signals in
high speed areas.
One would expect that signal phasing, high degrees of saturation
and cycle length would impact on the safety of signalised
intersections. However, there is limited research available
internationally on the effect of these factors and traffic signal
technicians/engineers ideally require such information to address
safety issues. In the current environment the selection of safety
improvement options is often by trial and error. While further
research is required in this area, this paper does report on
research into the factors effecting right-turn against crashes at
traffic signals, including the provision of right turn phasing, in
combination with intersection layout factors.
This paper traces the development of crash models in New
Zealand for traffic signals and the key findings that are likely to
be of interest to traffic/transport engineers. The paper concludes
with a discussion on key areas of future research.
Signalised Intersection Crash Prediction Models
The first generalised linear models in New Zealand for crashes
at traffic signals were developed by Turner (1995) in the early
1990s, based on crash data from the mid to late 1980s. The
modelling methods used were based on generalised linear
modelling methods developed by Maycock and Hall (1984)
and Hauer et al. (1989). Specialised macros were developed in
Minitab to produce these models. The use of macros has enabled
the modelling methods to be easily modified over the last 15
years so that other features, such as goodness-of-fit statistics,
confidence interval routines and covariate analysis methods could
be added. This compares to proprietary software products which
are fairly inflexible. These initial models were flow-only, where the
independent variable was the conflicting flow movements and
the dependant variable was crashes.
Following on from his PhD work Turner (2000) produced a series
of flow-only crash prediction models for the most common urban
and rural mid-block and intersection types, including traffic
signals. Crash models were developed for three traffic signal
types; cross-road signals with all legs two-way, cross-road signals
where one road was two-way and the other was one-way, and
signalised T-junctions (with all legs two-way). A strict selection
criteria was developed to produce sample intersections that were
as consistent as possible in terms of layout variables. Several of
these models were incorporated into Appendix 6 of the New
Zealand Project Evaluation Manual (Transfund, 1997) (now the
Economic Evaluation Manual), when it was updated in 2001.
Building on this previous research, Turner and Roozenburg
(2004) added non-flow variables to the ‘right-turn-against’ crash
prediction models at 4-arm traffic signals. The objective of this
research was to consider a number of non-flow variables, and
determine whether these are also key predictors for accident
occurrence. The outcome was a more refined crash prediction
model for this accident type. Of particular interest was the impact
of right-turn phasing on accident occurrence. The key non-flow
variables examined were: intersection geometry and layout (eg
number of through lanes, right turn bay offset and intersection
depth); right-turn signal phasing (eg filtered turns); and forward
visibility to opposing traffic.
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Accident Prediction Models for Traffic Signals
Prior to 2004 no accident prediction models had been developed
in New Zealand for the non-motorised modes of travel (walking
or cycling). Internationally only a small number of studies
have considered these ‘active modes’. Turner et al. (2005)
developed models for pedestrian and cyclists accidents involving
motor-vehicles at intersections and mid-blocks. These models
investigated a small number of non-flow variables in addition to
motor vehicle, pedestrian and cycle traffic volumes.
This paper provides a summary of all the models that have been
developed by Turner and colleagues for traffic signals. All the
models presented are the preferred model forms for the given
predictor variables in each study. The fit of these models to the
data have been tested using the scaled deviance goodness-offit test and pass this test. Details on the goodness-of-fit testing
procedures and of the results of the testing for each model can
be found in the research papers and technical reports specified in
the reference list.
Table 2 shows that the major difference resulting from the
increased speed limit is an increase in rear-end crashes and a
large reduction in pedestrian crashes. The reduction in pedestrian
crashes is likely a result of many low speed limit intersections
being in commercial shopping areas, whereas high speed signals
are typical on the urban-rural fringe or on multilane roads with
little pedestrian activity.
Cycle crashes are included within the four major crash types.
Of particularly interest is the high number of cyclists involved in
right-turn-against (28%) and crossing (28%) crashes at low speed
traffic signals (Turner et al, 2005).
The major crash types at signalised T-junctions are shown in
Table 3.
Table 3 – Major Crash Types at 3-arm Traffic Signals (source: New
Zealand Crash database, CAS)
Crash Type
Low Speed
Traffic Signal
2001 to 2005
High Speed
Traffic Signals
2001 to 2005
Major Crash Types
Right Turn-Against e.g.
34%
30%
The major crash types at 4–arm traffic signals in New Zealand are
shown in Table 2 for both low speed (50 to 70 km/hr) and high
speed (80 km/h plus on at least one of the cross roads) traffic
signals.
Crossing e.g.
17%
10%
Rear End e.g.
21%
30%
Loss-of-Control e.g.
11%
12%
Pedestrian
16%
0%
Other
1%
18%
Urban Traffic Signals - Flow-only Models
Table 2 – Major Crash Types at 4-arm Traffic Signals (source: New
Zealand Crash database, CAS)
Crash Type
Low Speed
Traffic Signal
2001 to 2005
Signalised High
Speed Traffic
Signals
Right Turn-Against e.g.
30%
33%
Crossing e.g.
29%
26%
Rear End e.g.
10%
22%
Table 3 also shows that rear-end accidents are more prevalent at
high speed T-junctions, but the effect is not as significant as at
cross-roads. Again the percentage of pedestrian crashes is a lot
higher at low speed signals.
Crash Model Types
Loss-of-Control e.g.
6%
5%
Pedestrians
17%
2%
Other
8%
12%
There are three main flow-only model types that have been used
internationally. In Type 1 models (Lau and May 1988, Hughes,
1991 and Transfund NZ, 1997) the total number of crashes is
related to the sum of the traffic volumes entering the intersection.
Logic however suggests that crashes cannot occur when there is
zero traffic volume on at least one of the roads, and so this model
form is no longer in common use.
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Accident Prediction Models for Traffic Signals
In Type 2 models the total number of crashes is related to the
product of the traffic volumes on the approach roads. In Type 3
models (Maycock and Hall, 1984, Hauer et al., 1989, Turner, 1995
and Maher and Summersgill, 1996) the conflicting flow crash
types are related to the product of the conflicting traffic volumes.
Type 3 models enable the prediction of each crash type and
follow the logic that crashes involving two conflicting manoeuvres
cannot occur when there is zero traffic volume for one or both
conflicting movements. For these reasons most researchers
prefer Type 3 models. Type 2 models are less popular than Type
3 models, but are seen as a practical alternative to the conflicting
movement models when road safety engineers do not have
access to conflicting volume data at intersections. The New
Zealand Economic Evaluation Manual, EEM, (Land Transport NZ,
2006) contains both Type 2 and 3 models for this reason.
The Type 2 models in the EEM do in many cases break the crashes
down into the common crash types. A more detailed description
of the model types is given in Turner and Nicholson (1998).
The majority of the flow-only models presented in this paper,
and developed by Turner since 1995 are conflicting movement
models (Type 3 models), given their more direct link to causal
factors compared with the other model types. Details on the
latest modelling methods used by Turner are provided in Turner et
al. (2006a).
The four major all-vehicle crash types at cross-roads, and the
corresponding models are shown in Table 4.
Table 4: Signalised cross-road accident prediction models
Accident
Type
NZ Accident
Codes
Equation (accidents per approach)
Crossing
(No Turns)
HA
A = 1.57 × 10 -4 ×q20.36 × q110.38
Right Turn
Against
LB
A = 9.57 × 10 -5 ×q20.49 × q70.42
Rear-end
FA to FE
A = 1.66 × 10 -6 × Qe1.07
Loss-of –
control
C&D
A = 2.96 × 10 -6 × Qe0.95
Others
Rest of codes
A = 1.26 ×10 - × Qe0.46
Crash Prediction Models for T-junctions
The latest flow-only T-junctions models in New Zealand were
also developed by Turner (2000), from a sample set of 30
intersections. The six conflicting flow movements used in the
various models are shown in Figure 2.
Figure 2: Conflicting and approach flow types (T-junction)
Cross-road Crash Prediction Models
The latest Type 3 crash prediction models in New Zealand for all
major crashes types at cross-roads traffic signals were developed
in the late 1990s (Turner, 2000), based on a sample set of 109
intersections (or 436 approaches). Figure 1 shows the conflicting
movements that were used in the models for each approach ( Qe
is the total traffic volume on each approach). For each of the four
approaches the three turning movements on the approach of
interest are q1 to q3. So there are for example four combinations
of q2 and q11 at each intersection.
Figure 1: Conflicting and approach flow types (Cross-roads)
The four major all-vehicle crash types and models at T-junctions
are shown in Table 5.
Table 5: Signalised T-junction accident prediction models
Accident
Type
NZ Accident Equation (accidents per approach)
Codes
Right Turn
Against
LB
A = 1.08 × 10 -1 × q5-0.38 × q30.56
Rear-end
FA to FD
A = 7.66 × 10 -8 × Qe1.45
Crossing
(Vehicle
Turning)
JA
A = 2.67 × 10 -2 × q5-0.30 × q10.49
Loss-of –
control
C&D
A = 1.91 × 10 -3 × Qe0.17
Others
All other
codes
A = 1.69 × 10 -2 × Qe0.15
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Accident Prediction Models for Traffic Signals
The large negative parameters in the ‘LB’ and ‘JA’ models
indicate that intersections with higher flows have fewer crashes.
This is an unexpected result. It is speculated that at high traffic
flows the installation of right turn bays and exclusive right turn
phases reduces crash occurrence. Further research is required to
investigate this issue. Ideally the sample size should be increased
from 30 up towards 100 or more intersections.
major impact on crash occurrence at T-junction traffic signals.
It is possible that signal phasing and layout are more important
factors.
Pedestrian & Cycle Crashes
Turner et al. (2005) developed crash prediction models for
pedestrians and cyclists. Prior to this research, crash prediction
models in New Zealand had only been developed using motor
vehicle volumes and for total crashes of each type. ie without
consideration of the road user types involved in a crash.
Pedestrian and cycle crashes are fairly common at most low speed
urban traffic signals. It might be expected that the likelihood of
such crashes would depend on the volumes of these road users
travelling through the intersection, and so these flows are likely
to be important for pedestrian and cycle crash prediction models.
The cycle and pedestrian flows in the sample set vary from very
low (close to zero) up to relatively high volumes. For example,
the cycle volumes at traffic signals, per approach, vary from 20 to
around 350 cyclists per day, with the majority of flows in the 100
to 250 flow range.
Product of Link Models at Cross Roads and T-junctions
Type 2 models were also produced for signalised cross-roads
and T-junctions by Turner (2000). These models (Equation 1 and
2) are useful when conflicting flow data is not available at an
intersection, as may be the case when only automatic tube counts
are available for the approaches to an intersection. In both cases
the model is used to calculate the total number of crashes per
year.
Equation 1
AT = 3.69 × 10 -3 × Qminor0.14 ×Qmajor0.46
Equation 2
Two model types were developed for cycle versus motor-vehicle
crashes at signalised cross-roads. The first, a ‘same direction’
model predicts crashes on a single approach between cyclists
either colliding with a stationary vehicle or moving motor-vehicle,
travelling in the same direction. The second model is for rightturn-against crashes where a cyclist is travelling straight through
the intersection and collides with a motor vehicle turning right.
Table 6 and 7 present these two models and the proportion
of cycle crashes that they represent at signalised cross-roads.
Cycle movements are coded in a similar manner to motor-vehicle
movements. Entering flows, for example Ce, are the sum of all
cycle entering flows, for example c1 + c2 + c3. Figure 3 shows the
movements graphically.
AT = 1.73 × 10 -1 × Qstem0.12 × Qmajor0.04
Where,
Qmajor is the highest of the two-way link volumes for crossroads or the main road flow for T-junctions
Qminor is the lowest of the two-way link volumes for crossroads, and
Qstem is the stem flow for T-junctions.
It is interesting to note the relatively high coefficient at the
front of Equation 2 and the low values of the two traffic flow
exponents. This indicates that traffic flow does not have a
Table 6: Signalised cross-road cycle crash prediction equations
Crash Type
Crash Codes
Equation (crashes per approach)
Proportion of Cycle Crashes
Same Direction
A, E, F, G
A = b0 × Qe × Ce
35%
Right Turn Against - Motor
vehicle turning
LB
A = b0 × q7b1 ×c2b2
b1
b2
21%
Table 7: Signalised cross-roads – cycle crash prediction model parameters
Crash Type
b0
b1
b2
Error Structure
Same Direction
7.49 × 10 -4
0.29
0.09
Poisson
Right Turn Against - Motor
vehicle turning
4.41 × 10
0.34
0.20
Negative Binomial
-4
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Accident Prediction Models for Traffic Signals
Figure 3: Cycle model variables
Figure 4: Pedestrian model variables
The small value of the exponent of cycle flows (b2) in Table 7
indicates a ‘safety in numbers’ effect where the crash rate per
cyclist decreases substantially as the number of cyclists increases.
Two models were developed for predicting pedestrian crashes
at signalised cross-roads. The majority of all crashes involving
pedestrians, not just those at signalised cross-roads, occur where
vehicles are travelling straight along the road and the pedestrian
is crossing. These crashes represent 50% of pedestrian crashes
at signalised cross-roads. The second major type of pedestrian
crashes at signalised cross-roads is where right turning vehicles
collide with pedestrians crossing the side road. Table 8 and 9
present these two models. Pedestrian movements differ from
motor-vehicle and cycle movements. For cross-roads, four
movements are used, one for pedestrians crossing each approach.
Figure 4 shows the movements used graphically.
Table 8: Signalised cross-road pedestrian crash prediction
equations
Crash Type
Crash
Codes
Equation (accidents
per approach)
Proportion
of Ped.
Crashes
Crossing – vehicle
intersecting
NA, NB
A = b0 × Qb1 × Pb2 50%
Crossing – vehicle
turning right
ND, NF
A = b0 × q4b1 × p1b2 36%
Table 9: Signalised cross-roads – pedestrian crash prediction
model parameters
Crash Type
b0
b1
b2
Error
Structure
Crossing – vehicle
intersecting
7.28 × 10 -6
0.63
0.40
Negative
Binomial
Crossing – vehicle
turning right
5.43 × 10 -5
0.43
0.51
Negative
Binomial
Unlike the cycle models, the ‘safety in numbers effect’ is not
as pronounced, with exponents of flow being similar to those
observed for motor vehicle flows.
High Speed Traffic Signals
Crash prediction models were developed from high speed traffic
signals by Turner et al (2006b) using signalised intersections in
Melbourne, Victoria and throughout New Zealand.
There is a lot of variety in the layout and approach speed limits at
high speed traffic signals. In this study only sites with at least two
legs with a speed limit of 80 km/h or higher were selected. Sideroads typically had a speed limit of 50 km/h in New Zealand and
60 km/h in Melbourne. In some cases both intersecting roads had
high speed limits. Both 3 and 4-arm intersections were included
in the sample set.
Table 10 shows the number of sites in New Zealand and
Melbourne that met the selection criteria and where suitable data
was available. As the number of signalised seagull intersections
was small these were not analysed further in this study.
Table 10 Numbers of High Speed Signalised Intersections in Study
New Zealand
Melbourne
Total
Crossroads
4
24
28
T-Junctions
8
7
15
Seagull
3
0
3
The typical mean-annual numbers of reported injury crashes for
high-speed signalised T-junctions can be calculated using the crash
prediction models in Table 11. Table 11 includes a column for the
variable ϕVIC, which is a multiplication factor for sites in Melbourne,
Victoria (Vic). This variable indicates that for most crash types the
number of crashes at similar high-speed traffic signals in Victoria
would be higher than in New Zealand. It is unclear why the crash
risk in Victoria is higher than New Zealand. It could be due to
differences in reporting rates (the models provided are for reported
injury crashes) or due to different speed limits in the two countries,
different road environments (most of the high speed traffic signals
in Victoria are in the middle of the urban areas, whereas most New
Zealand sites are on the urban-rural boundary). It may be due to
different road layout standards or different driver behaviour. A larger
sample set and more detail on the various contributing factors, eg
speed limits would be needed to understand the differences.
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Accident Prediction Models for Traffic Signals
Table 11: High-speed Signalised T-junction crash prediction models
Crash Type
Equation (crashes per approach)
Right-turn-against
ARATT1 = 8.29 × 10 ×q3
-2
0.26
×q5
0.29
Major
-0.15
× ϕVIC
Error Structure
Sig. Model
2.85
Negative Binomial
Yes
0.89
Poisson
Yes
Rear-end (Major Road)
ARATT2 = 2.28 × 10 -2 × Q
Crossing (Vehicle turning)
ARATT3 = 3.18 × 10 -2 ×q10.12 × ϕVIC
1.67
Poisson
Yes
Loss-of-control (Major Road)
ARATT4 = 5.77 × 10 × Q
× ϕVIC
1.06
Poisson
Yes
Other (Major Road)
ARATT5 = 1.82 × 10 -3 × Q
× ϕVIC
2.81
Poisson
No
Other (Minor Road)
ARATT6 = 1.40 × 10 -3 × Q
× ϕVIC
5.04
Negative Binomial
Yes
-3
× ϕVIC
ϕVIC
0.32
Major
0.37
Major
0.41
Minor
The modelling shows that the sign on the straight through volume (q5) for the right-turn-against crash type is negative. This indicates
that an intersection is safer with respect to this crash type when the through movement is high. It is unclear why this should be so. It is
possible that it may be associated with the phasing of the signals, as these crashes occur when vehicles are ‘running the lights’, as the
right turn phase is fully controlled (ie no filtering allowed). A very similar result was observed for this crash type at lower-speed urban
signalised T-junctions.
The modelling process was repeated for crashes at high-speed signalised crossroad intersections. Table 12 presents the models and
multiplication factors for the signals located in Victoria, Australia. Again, the variables for intersections located in Victoria indicate that
the numbers of crashes for similar traffic volumes are higher than in New Zealand. However, these models may not be particularly
applicable to New Zealand, as unlike for signalised T-junctions, only a small number of New Zealand signalised crossroads were included
in the sample set.
Table 12: High-speed signalised crossroad crash prediction models
ϕVIC
Error Structure
Sig. Model
3.95
Poisson
Yes
ARAXT2 = 2.17 × 10 -2 × q20.20 × ϕVIC
1.43
Negative Binomial
Yes
Rear-end
ARAXT3 = 4.16 × 10 -7 × Qe1.18 × ϕVIC
9.91
Negative Binomial
Yes
Loss of Control
ARAXT4 = 5.75 × 10 × Qe
× ϕVIC
1.15
Negative Binomial
Yes
Others
ARAXT5 = 1.04 × 10 -2 × Qe0.14 × ϕVIC
4.44
Negative Binomial
Yes
Crash Type
Equation (crashes per approach)
Crossing
ARAXT1 = 6.82 × 10 × q2
Right-turn-against *
-5
-5
0.31
0.70
×q
0.35
11
× ϕVIC
* the right running volume q7, was not found to be a key variable for this model. A model was produced that included q7, but the exponent on this
variable was close to zero. This may be the result of a relatively small sample size.
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Accident Prediction Models for Traffic Signals
Non-Flow Variables – Signal Phasing & Layout
The study (Turner 2004) on the affects of signal phasing has to
date focused on the provision of right turning signal phasing at
traffic signals as there is much debate within New Zealand on the
safety merit of installing such phasing. Extra phasing adds to the
cycle length and lost time at most traffic signals, which in turn
can increase delays for vehicles travelling straight through the
intersection, which is often the predominant traffic movement.
An increase in the cycle time also leads to more driver frustration,
as drivers on average have to wait longer to proceed through
the intersection. This in turn may lead to an increased safety risk
as drivers may be more likely to run a red or amber signal when
cycle times are longer. Given this uncertainty around the safety
impacts of right turn phasing on ‘right-turn against’ crashes this
crash type was investigated.
The two movements of specific interest for this project were the
through movement for each approach (of which there are four for
most signalised cross-roads) (q2) and the opposing right turn (q7)
as shown in Figure 5.
Figure 5 – Conflicting flow movements for right-turn-against
crashes
Data Collection
Data for this project was provided by three city councils in New
Zealand; Christchurch, Hamilton and Palmerston North. Each
of the councils provided traffic volumes, signal phasing and
intersection geometry and layout information.
A total of 455 approaches were selected for inclusion in the
sample set for analysis and the development of crash prediction
models. Table 13 shows the number of intersection approaches
from each city in the sample set.
Table 13 - Regional Distribution of Traffic Signal Approaches
City
Number of Approaches
Christchurch
309
Palmerston North
71
Hamilton
75
Predictor Variables
The data collected from each council is detailed below.
a) Traffic volumes
Traffic counts provided by councils were generally of one or two
hours in duration and collected over two or three time periods,
typically the morning and afternoon/evening peaks and an interpeak period. All traffic counts were disaggregated by approach
and by movement ie left, through and right for each approach.
Hourly factors were applied to the raw traffic counts to calculate
an AADT for each straight and turning movement. The procedure
to determine the AADT involved summing the raw traffic count of
each movement and dividing that by the sum of the appropriate
hourly factors (see Turner, 1995 for details).
b) Signal phasing
Signal phasing for right turn movements was separated into three
categories; filtered, partially controlled and full controlled signal
phasing. For many intersections there are two or more phase
types for the four combinations of through and opposing right
turn movements.
‘Filter Control’ (Phase 1) is no green signal phase (arrow) for
traffic turning right. A red phase (arrow) may appear at certain
times throughout the signal cycle for various reasons eg large
opposing through movements, crossing pedestrians.
‘Partial Control’ (Phase 2) is a green phase (arrow) being
displayed for right turners for part of the green phase allocated
to each approach. Right turning traffic may filter turn at other
times throughout the green phase, on the full green aspect.
‘Partial Control’ is associated with a lead or lag right turn phase
(arrow). No differentiation is made between lead and lag right
turn movements, as this information is not readily available for a
number of intersections. ‘Partial Control’ also includes approaches
where a green phase (arrow) for the right turn movement may
only be displayed at certain times of the day or on demand.
Generally such phases are applied when the right turning traffic
volume is high.
‘Full Control’ (Phase 3) is a green phase (arrow) or red phase
(arrow) being displayed for the right turning movement at all
times of the day. Right turning traffic may not filter turn at other
times throughout the signal cycle.
A breakdown of approaches by signal phase type and number of
opposing lanes is displayed in Table 14.
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Accident Prediction Models for Traffic Signals
Table 14: Phase Type and Number Opposing Lanes
Non-Flow Variable
Number of Approaches
Phase 1
330
Phase 2
97
Phase 3
28
One Opposing Lane
292
Two or more Opposing Lanes
163
There are insufficient Phase 3 approaches in the sample set to
produce results specifically for this type of signal phasing. The
Phase 3 approaches were therefore combined with the Phase 2
approaches to assess the overall effect of right turn phases on
accident occurrence.
c) Intersection geometry and layout
Intersection geometry and layout information was obtained from
as-built drawings provided by each council. In Christchurch City
the as-built drawings record the date the intersection was last
upgraded, and hence those that were significantly upgraded in
the period 1998 to 2002 could be removed from the sample. For
the other two councils the date of upgrades was less clear, so
each council was contacted to identify sites that were upgraded
during this period. The following information was collected at
each intersection by approach.
ƒƒ Lane Information - The type (permitted movement), number
and width of each lane. Of particular interest was the number
of straight through lanes opposing each right turn. As the
more lanes generally the greater the distance right turners
have to travel to get to the safety of the side-road.
ƒƒ Right Turn Lane Offset - The lateral distance between a
prolongation of the right edge of the right turn lane and a
prolongation of the left edge of the opposing right turn lane.
d) Visibility
The visibility of right turning drivers is often restricted by vehicles
turning right from the opposing direction. In this study the
visibility was measured from the limit line of the right turn lane
to the centre of the rightmost opposing through lane (ie furthest
from the kerb-line), as illustrated in Figure 6. The driver’s position
in the right turn lane was assumed to be 1/3 of the width of the
right turn lane from the right hand edge of that lane.
In cases where the rightmost through lane was a shared through
and right turn lane it was assumed that this lane is occupied by
a right turning vehicle and through vehicles pass on a lane to
the left, if that lane can be used for through movements. In the
majority of cases the right turn lane was exclusive and hence
it was not possible, due to the small sample size, to assess the
safety of the shared lanes. Approaches with no opposing right
turn lane (shared or exclusive) and those without a through lane
when a vehicle is turning from a shared right and through lane,
were removed from the sample set.
Three methods were used to calculate visibility for right turning
vehicles were:
1. Mathematical – where the visibility was calculated
using trigonometry. This method could be used when
opposing approaches are straight and close to parallel
in alignment. A manual check from plans of 10% of all
intersections was completed for quality control purposes.
2. Manual – where the visibility was measured directly from
aerial photographs or other intersection geometry and
layout plans. This method was used when opposing legs
had a curved alignment or were not parallel.
3. Field – where the visibility was measured in the field. This
method was used where the visibility was restricted by
vertical geometry.
ƒƒ Intersection Depth - The distance between limit lines
measured parallel with the road alignment.
Figure 6: Illustration of visibility measurement
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Accident Prediction Models for Traffic Signals
Accident data
b3
is a model parameter. It is applied as the power of C
Accident data for this project was sourced from the Land
Transport NZ’s CAS database, for the five-year period 1998 to
2002. All right turn against (Type LB) injury accidents in this
period were assigned to the leg of the intersection on which the
right turning vehicle originated.
φ
is a multiplicative model parameter for a discrete nonflow variable, which can take on one of two values.
Crash Model Equations
In previous research into crash prediction models in New Zealand
the models for right-turn-against accidents only included the two
conflicting traffic volumes, straight through and right turn. The
form of this conflicting flow only model is:
Equation 3
AT = b0 × q2b1 × q7b2
Where:
b o
is a model constant
q2
is a the daily through traffic flow opposing right turning
traffic
b1
is a model parameter. It is applied as the power of q2
q7
is a the daily right turning traffic flow
b2
is a model parameter. It is applied as the power of q7
The flow-only model form was modified to allow non-flow
variables to be added. The form of the extended crash prediction
model is as follows:
In Equation 4 the φ enters in the format “exp (b x V)”, where V is
the coded value (always chosen as “+1” and “-1”). The discrete
model parameter then has the un-logged model value of “exp (b4
x code value)”.
Three new variables were found to be important features;
visibility, number of opposing lanes and signal phasing type.
Other variables, such as opposing right turning flow and
intersection depth were also investigated but were not significant.
Visibility and intersection depth are continuous variables, and
can be added as ‘c’ variables in Equation 4. Variables such as the
number of opposing lanes or signal phasing are discrete variables
and are added as multiplicative parameters (φ) in Equation 4.
With the current model forms the continuous variable only applies
over a particular range. An example of a continuous variable is
the visibility in each direction at an intersection. This value can be
a large number, but is generally not measured once it exceeds a
particular threshold, around 400 to 500 m, as visibility above this
level is not expected to improve safety. If a value of visibility of say
1 km is entered into the equation then the crash prediction will be
very low, and not realistic. In this case the visibility measurement
is outside the range over which visibility measurements are
normally taken. In the event that actual visibility data was
recorded and long visibility lengths were collected then a better
model form would involve introducing this continuous variable as
‘exp (b3 × C1)’, rather than ‘c1b3‘.
This study did not consider the correlation between the various
variables. Correlation between variables can distort model
parameters.
Equation 4
AT = b0 × q2b1 × q7b2 × c1b3 ×φ
Where:
Crash Prediction Models
a) Flow-only models
AT
is the predicted mean number of crashes over a given
period,
b0
is a model constant,
q2
is a the daily through traffic flow opposing right turning
traffic,
b1
is a model parameter. It is applied as the power of q2,
q7
is a the daily right turning traffic flow,
b2
is a model parameter. It is applied as the power of q7,
c
is a continuous non-flow or non-conflicting flow variable
– such as visibility (V) or intersection depth (I), both
measured in metres
To allow comparison with previous studies a flow-only model was
produce containing only the two flows (daily through and right
turn flows). The model has the following multiplicative form:
AT = 8.09 × 10 -6 × q20.733 × q70.431 (crashes/year)
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Accident Prediction Models for Traffic Signals
Figure 7: Predicted mean number of accidents for different flow combinations
Figure 7 shows how the predicted number of crashes is more
dependent on the volume of conflicting through traffic ( q2 )
than the volume of right turning vehicles ( q7 ). This differs from
the results in Table 4, which are models that were produced
some years earlier. In Table 4 the exponent on both the through
traffic (q2 ) and the right turning vehicles (q7 ) are similar, and
close to that for q7 in the above model, while the constant value
is a magnitude of 10 higher. It is unclear why this change has
occurred, but may be a result of other factors, such as signal
phasing options. This matter needs to be explored further.
b) Visibility Models
Initially the flow-only models were extended to include one
additional non-flow variable. The first such variable was visibility.
The model form is:
AT = 1.29 × 10 -5 × q20.729 × q7439 × V -0.111
The resulting model was as follows.
AT = 5.97 × 10 -5 × q20.664 × q70.446 × (V − VR + 100)-0.329
where
V
is the visibility in metres
VR
is the recommended visibility from AUSTROADS (in
metres).
The resulting model has a smaller log-likelihood than that of
including visibility only (Table 15). Again it indicates that the more
visibility the driver has the lower the accident rate.
c) Opposing through lane models
where
V
make this possible a value of 100 metres was added to the
visibility. The value of 100 ensures that all the visibility values are
positive. Higher values, such as 1,000 or 10,000, would result in
the term being less sensitive to changes in visibility, which is not
desirable.
is the visibility in metres
The negative exponent of visibility indicates that the number of
accidents would decrease as the visibility increases.
Although this model does predict a change in the number of
accidents with varying visibility, an initial data analysis indicated
that there was a stronger relationship between the number
of crashes and the difference between the observed and
recommended visibility (as specified in the Austroads guides
to Traffic Engineering). To investigate this further a model was
developed using the difference in visibility from the recommended
visibility in Austroads. However because of the way generalised
linear models are fitted, all the values have to be positive. To
The second non-flow variable to be included in the crash
prediction model is that of number of opposing through lanes.
For this analysis a discrete variable was used for one opposing
lane or more than one opposing lane. The resulting model is as
follows:
AT = 1.47 × 10 -4 × q20.435 × q70.389 × φL
where
φ L
= 0.714 for a single opposing through lane
= 1.401 for multiple opposing through lanes.
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Accident Prediction Models for Traffic Signals
The above factors for φL indicate that where the opposing
through and right turning traffic volumes are held constant, then
the predicted crash rate for an intersection with two or more
opposing through lanes would be nearly twice that for the same
flows as a single opposing lane.
d) Signal phasing models
Another non-flow variable that was investigated was that of the
signal phasing with the model depending on whether the right
turn was a filter turn or a fully or partially protected turn (green
arrow). The resulting model is:
AT = 6.68 × 10 -6 × q20.735 × q70.457 × φP
where
φP
= 1.048 for a fully filtered turn
= 0.954 for fully or partially protected turns.
The two above φP factors indicate that the predicted number of
crashes is higher, but only just for approaches with a fully filtered
turn, than for approaches where there is at least a partially
protected signal phase. The model indicates that a site with a fully
filtered turn on average would have an accident rate 10% higher
than one with a partially or fully protected turn.
The closer the log-likelihood is to zero the more important the
predictor variable. A large drop in the log-likelihood indicates that
the variable explains a significant amount of the variability in the
accident data. Table 15 indicates that the number of opposing
through lanes has the greatest effect in reducing the loglikelihood and should be added to the model. The variable that
appears to have the next best drop in log-likelihood is the visibility
difference from recommended. Combining these two non-flow
variables into a model produces the following model:
AT = 3.94 × 10 -4 × q20.411 × q70.399 × (V − VR + 100)-0.190 × φL
where
V
is the visibility in metres
VR
is the recommended visibility from AUSTROADS (in
metres)
φ L
= 0.726 for a single opposing through lane
= 1.378 for multiple opposing through lanes.
f) Separate signal phasing models
The model for approaches with filtered turns only is as follows:
AT = 2.01 × 10 -5 × q20.516 × q70.586 × φL
where
e) Multiple non-flow variables
The value of the log-likelihood can be use to assess how
important each of the non-flow variables are to the model fit.
Table 15 shows the respective log-likelihood for each of the
models, when only one additional variable is added to the flowonly model.
Table 15: Log-likelihood comparison – Models developed using
entire dataset
Model
Log-likelihood
Conflicting flow only model
-384.75
Including:
Visibility
-384.58
Difference in visibility from
recommended
-383.61
Number of opposing through lanes
-378.87
Signal phasing
-384.63
Opposing right turning flow
-383.86
Intersection depth
-383.84
φ L
= 0.718 for a single opposing through lane
= 1.392 for multiple opposing through lanes.
The resulting model indicates that crossing one lane of through
traffic, without right turn signal phasing, is safer than crossing
multiple lanes.
The model where approaches are either fully or partially protected
is as follows:
AT = 2.88 × 10 -3 × q20.223 × q70.221 × φL
where;
φ L
= 0.659 for a single opposing through lane
= 1.518 for multiple opposing through lanes.
The number of opposing lanes is more important for approaches
with fully or partially protected right turn phases than for filtered
turns. Fully or partially protected signal phases do not appear to
be effective when there are multiple opposing lanes.
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Accident Prediction Models for Traffic Signals
Future Research
Crash prediction modelling in New Zealand is getting to a stage
at which the effects of a number of non-flow variables, such as
visibility, signal phasing and intersection layout on crash rates
can be quantified. Traffic engineers and planners can use such
research to justify or reject safety improvement projects at traffic
signals.
There are a number of areas where further research would be
beneficial to traffic engineers and planners. Key areas for future
research include:
1. An analysis of signal phasing programs, lost time and cycle
times at traffic signals on major crash types, including red
light running and rear-end crashes, along with the right-turnagainst crashes. There is a lot of support for such research
from traffic signal technicians and engineers.
2. The impact of green time allocation and level-of-service (or
level of delay) for various approaches and movements on
major crash types.
3. The impact of operating speed and speed limit, both on
the main road and side-roads, on crash occurrence. The
effectiveness of treatments, such as high friction surfaces on
intersection approaches and extensions to all-red periods, in
response to vehicles caught in the amber dilemma zone on
intersection safety at high speed locations.
4. An analysis of gap acceptance and crash data to determine
the traffic volumes levels at which priority controlled
intersections and roundabouts need to be upgraded to traffic
signals.
5. Research on model transferability methods. How can models
developed in one country or state be transferred to another,
eg between New Zealand and Victoria. Refer to Turner et al.
2007 for a discussion on this topic.
Conclusions
A number of crash prediction models have been developed for
traffic signals over the last 15 years in New Zealand. Such models
have a number of applications and allow traffic engineers, along
with the results of ‘before and after’ studies to quantify and/or
justify safety improvement works at traffic signals. A selection
of the models produced so far are summarised in this paper.
References are provided to the various reports and papers where
a large number of other models are presented. Appendix A6 of
the New Zealand Economic Evaluation Manual also has a number
of models for traffic signals and other intersection and link types.
The key findings to date from research on traffic signals are as
follows:
1. Overall traffic volumes were not found to be strong predictor
variables at signalised T-junction. The research indicates
for some crash types that intersections with higher traffic
volumes were actually safer than intersections with lower
volumes. It is likely that other factors, such as the provision
of right turn phasing and right turn lanes/bays are more
important factors at such intersection as they reduced the
crash risk at higher volume intersections.
2. The cycle-versus-vehicle crash models show a strong safetyin-number effect for cyclists at traffic signals. This finding
indicates that strategies to concentrate cyclists on particular
road corridors is safe than a more disperse approach to
providing for cyclists. Ideally cyclists are concentrated
on routes with low traffic volumes and speeds or where
interaction with motorists is minimised.
3. The high speed crash models indicate that Victorian traffic
signals are less safe than New Zealand traffic signals. This
may be due to many of the Victorian intersections being
in built up urban areas and typically higher speed limits on
arterial and collector road in Australia.
4. As the number of opposing through lanes increases the
number of right turn against crashes increases. Partially or
fully controlled right turning phases are effective in reducing
right turn against crashes. Right turn signal phasing is
more effective for single opposing lanes than two or more
opposing lanes. This may be due to the safety disbenefit
that results from increased cycle time at larger multi-lane
intersections.
5. That the inter-visibility between right turners and opposing
through traffic, when a vehicle is in the opposing right
turn lane, is an important factor in right turn against crash
occurrence.
The crash prediction models presented in this paper (and the
more detailed technical reports that are available on each study)
can be used to compare the safety performance of traffic signals
in different speed environments, with different mixes of road
users (motor vehicles, cyclists and pedestrians), for different crash
types and for different signal phasing and layouts.
There are a number of areas were further research would be
beneficial to traffic engineers, as outlined above. The findings to
date indicate the usefulness of such research going forward.
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Accident Prediction Models for Traffic Signals
References
Hall, R. D 1986, “Accidents at 4-arm single carriageway urban
traffic signals”, Transport and Road Research Laboratory
Contractor Report CR65, UK.
Hauer, E, Ng J.C & Lovell J 1989, “Estimation of safety of
signalised intersections”, Transportation Research Record 1185, p.
48-61, USA.
Hughes, B. P 1991, “Accident Predictions at Traffic Signals”, Main
Roads Department, Perth, Australia.
Land Transport NZ 2006, “New Zealand Economic Evaluation
Manual”, Land Transport NZ, NZ.
Lau. M.Y.K and May A.D 1988, “Injury accident prediction models
for signalised intersections” Transportation Research Record 1172,
pp 58-67.
Lyon, C, Haq, A, Persaud, B and Kadama, S.T 2005, “Safety
performance functions for signalised intersections in large urban
areas – development and application to evaluate left-turn priority
treatment, Transportation Research Record, 1908, p 165 to 171,
USA .
Turner, S.A, Wood, G.R & Roozenburg, A 2006a, “Accident
Prediction Models for Roundabouts”, 22nd ARRB Conference,
Canberra, Australia.
Turner, S.A, Wood, G.R and Roozenburg, A.P 2006b, “Accident
Prediction Models for High Speed Intersections (Both Rural and
Urban)”, 22nd ARRB Conference, Canberra, Australia.
Turner, S.A, Persaud, B, Lyon, C, Roozenburg, A and Chou,
M 2007, “International Crash Experience Comparisons Using
Prediction Models”, 86Th Annual Transportation Research Board
Meeting, Washington DC, United States of America.
Wang, Y, Ieda, H and Mannering, F 2003, “Estimating rear-end
accident probabilities at signalised intersections: occurrencemechanism approach”, Journal of Transportation Engineering,
ASCE, 129,4 p 377-384, USA .
Wong, S.C, Sze, N.N and Li, Y.C 2007, “Contributing Factors to
Traffic Crashes at Signalized Intersections in Hong Kong”, 86th
Annual Transportation Research Board Meeting, Washington DC,
United States of America.
Maher, M.J & Summersgill. I 1996, “A comprehensive
methodology for the fitting of predictive accident models”, AAP
28 Vol 3, pp281-296.
Maycock, G & Hall, R.D 1984, “Accidents at four-arm
roundabouts”, Transport and Road Research Laboratory Report
LR1120, UK.
Taylor, M.C, Hall, R.D & Chatterjeek, K 1996, “Accidents at 3-arm
traffic signals on urban single-carriageway roads”, TRL Report
135, Transport Research Laboratory, Wokingham RG 40 3GA, UK.
Transfund NZ 1997, “New Zealand Project Evaluation Manual (has
been superseded)” Land Transport NZ, (Appendix A6 updated in
2001).
Turner, S.A 1995, “Estimating Accidents in a Road Network”, PhD
Thesis, Dept of Civil Engineering, University of Canterbury.
Turner, S.A & Nicholson, A.J 1998, “Intersection Accident
Estimation: The role of intersection location and non-collision
flows”, AAP Vol 30 No 4. pp 505-517.
Turner, S.A 2000. “Accident Prediction Models”. Transfund New
Zealand Research Report No. 192, Transfund NZ, Wellington, New
Zealand.
Turner, S.A & Roozenburg, A.P 2004, “Accident Prediction
Models at Signalised Intersections: Right-Turn-Against Accidents,
Influence of Non-Flow Variables, Unpublished Road Safety Trust
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Accident Prediction Models for Traffic Signals
Shane Turner
Shane is a Technical Director in the consulting firm Beca
Infrastructure Ltd. He is based in the Christchurch office where he
leads a team of ten transport professionals. He is also the national
transport research manager for Beca. Shane completed his BE
(Hons) from the University of Auckland in 1990 and his PhD,
specialising in the development of accident prediction models,
at the University of Canterbury in 1995. He was appointed an
Adjunct Senior Fellow at the University of Canterbury in 2006,
where he teaches in the Master of Transport course. Shane is
also a member of the TRB Committee on Safety Data, Analysis
and Evaluation (2008 to 2011). Shane has extensive experience,
through leading many road safety research projects, in safety
related research, particularly the development of crash prediction
models. He is the author of over 20 road safety publications.
Graham Wood
Graham’s current role is Professor of Statistics in the Department
of Statistics, Macquarie University, Sydney. Graham has worked
at the University of Canterbury, Central Queensland University
and Massey University, prior to moving to Sydney. He is the
author of 80 internationally refereed papers in mathematics
and statistics, about 40 other miscellaneous publications and
has co-authored two books. Graham has been involved with
the fitting and development of accident prediction models
in New Zealand for the past fifteen years, leading recently to
the publication of three papers in the area. Graham’s current
research interests are in mathematical and statistical modeling,
particularly in optimisation, traffic accident prediction modeling
and bioinformatics.
Blair Turner
Blair joined ARRB Group Ltd at the end of 2004, and has a
number of years experience in road safety, both in Australasia
and Europe. He initially worked for the New Zealand Government
(LTSA) before moving to the UK to continue his career. He has
been involved in a wide range of road safety research projects,
road safety audits and investigation of crash locations, and
production of road safety reviews (including a review of the UK
Road Safety Strategy). Before moving to Australia, Blair also spent
time at the UK Home Office where he further developed his
research skills. He is currently a Senior Research Scientist at ARRB
Group, and responsible for research on road safety engineering
risk assessment.
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