ACCIDENT PREDICTION MODELS FOR
Dr Shane Turner, Beca Infrastructure Ltd, New Zealand
Professor Graham Wood, Macquarie University, NSW, Australia
Aaron Roozenburg, Beca Infrastructure Ltd, New Zealand
The management of speed is considered an important safety issue at roundabouts. The
approach speed and negotiating speed through roundabouts depends on both the geometric
design of the roundabout and sight distance. In New Zealand and in the Australian States the
design standards (based on Austroads) recommend long approach sight distance and provision
of relatively high design speeds. This is in contrast to European roundabouts where visibility is
normally restricted and the geometric design encourages slow approach and negotiation
speeds. The ‘flow-only’ models developed in Turner (2000) have been extended to include sight
distance, intersection layout and observed speed variables. Models have been produced for the
major motor-vehicles only, pedestrian versus motor-vehicles and cyclists versus motor-vehicle
accident types. ‘Flow-only’ models have also been produced for roundabouts on roads with
high speed limits. The models have then been used to assess whether a move towards the
European design philosophy, of lower speed and reduced sight distance, is likely to produce
lower accident rates for all modes, particularly in areas that have high concentrations of
pedestrians and cyclists.
Safety deficiencies in existing and proposed roundabouts have received considerable attention
from safety auditors over the last 10 years or more. The reoccurrence of common deficiencies
in the design of new roundabouts in New Zealand has lead to the publication of the guide “The
Ins and Outs of Roundabouts”, which was published by Transfund NZ (2000). This guide
provides a list of problems that have been encountered in 50 safety audit reports. Visibility and
geometric design features, particularly inadequate deflection and marking, feature as problems
in many of the safety audit reports. While not specifically mentioned in this report, approach
and negotiating speed do have the potential to exacerbate any sight distance, geometric and
other deficiencies present at a roundabout. As far as we are aware the effect on safety of speed
at roundabouts, in combination with other deficiencies, has not previously been investigated
using accident prediction modelling methods in New Zealand. The models enable the combined
impact of speed and each of the other key variables on accident risk to be quantified. Safety
auditors and other transport professionals can use the models to assess the impact on safety of
a particular deficiency and prioritise for treatment.
Roundabouts, particularly large and 2-lane roundabouts, have a poor safety record with respect
to cyclists. This is illustrated in the proportion of injury accidents involving cyclists at
roundabouts (25%), compared with traffic signals (7%) and priority junctions (16%). Many cycle
advocates have strong opinions on this matter and strongly oppose the use of roundabouts,
particularly larger roundabouts on cycle routes. There are two reasons given for this increased
accident risk to cyclists; 1) as roundabouts become larger, with more lanes, and often higher
speeds, they become more complex to negotiate by motor-vehicle drivers, and motorists are
more likely to not see the cyclist, due to their relatively small size and 2) as motor-vehicle
speeds increase, the relative speed between cyclists and motor-vehicles increases and there is
more potential that drivers will overtake cyclists in an unsafe manner or that cyclists will
misjudge the gap/space required for various manoeuvres. So it is expected that reduced
vehicle speeds and complexity (single lane circulating) should improve safety for cyclists.
The research presented in this paper focuses on the relationship between accidents, speed,
traffic volume and sight distance for various approach and circulating movements at
roundabouts. The ‘flow-only models developed by Turner (2000) have been extended to include
observed speed, sight distance and intersection layout variables in various forms. Given the
different impact vehicle speed is expected to have on the ‘active’ modes (walking and cycling),
separate models have been developed for the major accident type for each mode.
The research team had access to an existing sample set of roundabouts that was collected in
two previous studies, by Turner (2000) and Turner et al. (2006b). The majority of the sites in the
more recent study were in Christchurch, and were single lane, 4-arm intersections. A number of
additional sites were added from Auckland and New Plymouth to increase the sample size and
enable other roundabout types to be added.
Site Selection Criteria
A roundabout is made up of a series of give-way controlled T-junctions, where the through (or
circulating) route is one-way. Roundabouts can be large or small and can have one or more
circulating and entry lanes. There is significant variety in the roundabouts found in New
Zealand due to different design practices through many decades.
The most common roundabout in New Zealand has four-arms with one circulating lane.
Previous studies on roundabouts by Turner (2000) and Turner et al. (2006b) concentrated on
this common roundabout type. Even within this roundabout type there is a lot of variety in terms
of central island diameter, approach design and overall roundabout shape.
The research steering group and research team were of the view that a broader sample of
roundabouts should be included in this study, so that the effects of speed, visibility and layout
could be better assessed. Hence the sample set for this study includes 3, 4 and 5 arm
roundabouts, with different distances between arms. The sample includes both single and dual
entering and circulating lanes, although there are considerably more roundabouts with single
entering and circulating lanes.
While a wide variety of roundabout types were included in the sample set, sites that had been
constructed within the last five years or had undergone significant modification during this period
Experience in other studies of this type indicates that a sample set of at least 100 sites is
necessary to developed accident prediction models for the major accident types. A large
sample size is particularly important in this study, where there is a variety of intersection types, a
lot of non-flow variables and when looking at accidents involving less common modes, such as
cyclists and pedestrians.
In total a sample set of 104 roundabouts were selected in Auckland, Christchurch and
Palmerston North. Table 1 shows a breakdown of the sites by location and roundabout type.
Table 1: Roundabout Locations and Types
Single Lane Circulating
Two Lane Circulating
There is no database that lists all the roundabouts in New Zealand. So it was not possible to
use a formal sampling procedure to select a sample of sites that meet the criteria. The sites
were instead selected so that a variety of different layouts and sizes were included in the
sample from around the country.
A smaller sample set of 17 high-speed roundabouts was also selected from around the country.
This included sites in Christchurch, Auckland, Hamilton and Tauranga. A high-speed
roundabout must have one road that has a speed limit of 80km/h or more. Given the limited
number of sites that meet these criteria, all high-speed roundabouts for which data was readily
available were included in the sample set.
PREDICTOR VARIABLES & DATA COLLECTION
A list of key roundabout variables was specified following the outcomes of a workshop with
experts in roundabout design, a review of overseas studies on roundabouts and a review of the
publication ‘Ins and Outs of Roundabouts’ (Transfund 2000). This process identified the
following variables: sight distance, approach and negotiation speed, traffic and cyclist volume,
deflection, approach and exit curve design, approach and circulating road width. The following
sections describe the data that was collected.
Traffic Volume Data
The flow variables used in the urban roundabout intersection models are versions of those
defined in Turner (1995), where each movement is numbered in a clockwise direction starting at
the northern-most approach. Approaches are also numbered using the same technique and are
numbered in a clockwise direction (see Figure 1).
Individual movements are denoted as a lower case character for the user type (e.g. qi). Totals of
various movements are denoted with an upper case character (e.g. Qi). Models are developed
for each approach and are defined using the totals of various movements. These are:
Qe Entering volume for each approach.
Qc Circulating flow perpendicular to the entering flow.
Qa Approach flow (the sum of the entering and exiting flow for each approach).
Three one-hour manual turning volume counts were collected at each site, in the morning,
evening and at mid-day. Weekly, daily and hourly correction factors from the “Guide to
Estimation and Monitoring of Traffic Counting and Traffic Growth” (TDG, 2001) were used to
estimate the AADT. The hourly factors were calculated from flow profiles for the different road
For the analysis of high-speed roundabouts, approach volumes (Qa) have been used. The
volumes for the high-speed intersections have been estimated from the link volumes collected
through tube counting programmes.
Pedestrian and Cyclist Volume Data
Manual pedestrian and cyclist movement counts were collected at each site, in the morning,
evening and at mid-day. Like motor-vehicle counts, seasonal, daily and hourly correction factors
were used to estimate annual averaged daily volumes. These factors were calculated from
continuous counts collected for a previous study (Turner et al., 2006b).
Cyclist flow variables used in the urban roundabout intersection models are defined in an
identical process to motor vehicle movements, numbered in a clockwise direction at
intersections, starting at the northern-most approach. Individual cyclist movements are denoted
as a lower case character for the user type (e.g. ci) and totals of various movements are
denoted with an upper case character (e.g. Ci).
Pedestrian flow variables used in the models are defined as the number of pedestrians crossing
each approach in either direction. The total crossing volume for each approach is denoted as
an upper case P.
Visibility and Speed
Speeds measured in this study are the free speeds of vehicles travelling through the
roundabouts and not of vehicles turning left, right or having to give way. The visibility and speed
variables used in the models are shown in Table 2. Diagrams of vehicle speeds and the
measurement of visibility variable can be found in Figure 2 and Figure 3 respectively.
Table 2: Visibility and Speed Variables
visibility from the limit line to vehicles turning right or traveling through the
roundabout from the approach to the right;
visibility from 10 metres back from the limit line to vehicles turning right or
traveling through the roundabout from the approach to the right;
visibility from 40 metres back from the limit line to vehicles turning right or
traveling through the roundabout from the approach to the right;
free mean speed of entering vehicles traveling through the roundabout at the
free mean speed of circulating vehicles traveling through the roundabout as they
pass the approach being modeled;
standard deviation of free speeds of entering vehicles at the limit line;
standard deviation of free speeds of circulating vehicles as they pass the
approach being modeled;
Data on the layout of each roundabout were collected on site. From this data, variables were
developed to represent different situations; these variables were not of the continuous type such
as vehicle flows and mean speeds and were incorporated into the accident prediction models as
covariates. The covariates are represented by multiplicative factors that are used to adjust the
prediction if the feature is present. The covariates used in the modelling process and their
definitions are shown in Table 3.
Table 3: Intersection Layout Covariates
Multiple entering lanes
Multiple circulating lanes
Intersections with three arms
Downhill gradient on approach to intersection
Accident data for roundabouts nationally was extracted from the Ministry of Transport’s Crash
Analysis System (CAS) for the period 1January 2001 to 31 December 2005. During this period
there were 1202 reported injury accidents at urban roundabouts, including 7 fatal and 154
serious accidents. This compares to 365 reported injury accidents, including 2 fatal and 44
serious accidents at the 104 urban roundabouts included in the sample set.
Figure 4 shows the proportion of reported injury accidents at roundabouts nationally involving
single motor-vehicles only, multiple motor-vehicles only, cyclists, and pedestrians. This shows
that 67% (around ⅔) of accidents involve motor vehicles only and 25% involve a cyclist.
Figure 5 shows the proportion of major injury accident types occurring nationally; this has not
been categorised by vehicle type. However, the most common cycle accident type is entering
versus circulating (82% of cycle accidents), 74% of which occur with the cyclist circulating and a
motor vehicle entering.
Based on this analysis, the accident type groups to be modelled were determined. All accident
types were grouped by road user involvement and proportion of accident type. The accident
groups are as follows:
Entering-vs-Circulating (Motor-vehicle only)
Rear-end (Motor-vehicle only)
Loss-of-control (Motor-vehicle only)
Other (Motor-vehicle only)
Entering-vs-Circulating (Cyclist circulating)
Using the process outlined in the accompanying conference paper (Turner et al, 2006a),
accident prediction models were developed for the main accident types at roundabouts for each
mode. A number of models were developed that incorporated flow and non-flow variables. The
Bayesian Information Criterion (BIC) and a goodness-of-fit measure for these models were then
calculated, in order to determine the ‘preferred model’ for each accident type. The preferred
model includes all conflicting flows, fits the accident data well and contains a parsimonious set
This section outlines the interpretation of model parameters and how these relate predictor
variables to accidents. Caution should always be exercised when interpreting relationships as
in some multiple predictor variable models two or more variables can be highly correlated. If
this occurs then the exponents can be difficult to interpret. The modelling process described in
the accompanying paper (Turner et al. 2006a), however, often means that variables in the
‘preferred’ model are not highly correlated. This is because the method acknowledges that
adding a variable correlated to those already in an existing model does not improve the fit of the
model compared to the addition of important non-correlated variables. Hence, interpretation of
model parameters can be straightforward for the preferred models (those presented in this
A typical model describes the relationship between the mean number of accidents and
predictors such as traffic volumes and non-flow variables. For two continuous variables (such
as flows or speeds) the model usually takes the form of a power function:
21 210 bb xxbA
where A is the annual mean number of accidents, x1 and x2 are average daily flows of vehicles
or non-flow variables, and b1, b2 and b3 are model parameters.
In this model form the parameter b0 acts as a constant multiplicative value. If the number of
reported injury accidents is not dependent on the values of the two-predictor variables (x1 and
x2), then the model parameters b1 and b2 are zero. In this situation the value of b0 is equal to
the mean number of accidents. The value of the parameters b1 and b2 indicate the relationship
that a particular predictor variable has (over its flow range) with accident occurrence. There are
five types of relationship for this model form, as presented in Figure 6 and discussed in Table 4.
Table 4: Relationship between predictor variable and accident rate
Value of Exponent
Relationship with accident rate
bi > 1
For increasing values of the variable, the number of accidents will
increase, at an increasing rate
bi = 1
For increasing values of the variable, the number of accidents will
increase, at a constant (or linear) rate
0 < bi < 1
For increasing values of the variable, the number of accidents will
increase, at a decreasing rate
bi = 0
There will be no change in the number of accidents with increasing
values of the variable
bi < 0
For increasing values of the variable, the number of accidents will
Generally, accident prediction models of this form have exponents between bi = 0 and bi = 1,
with most flow variables having an exponent close to 0.5, i.e. the square root of flow. In some
situations, however, parameters have a value outside this range.
In the case of models including a covariate (here, discrete variables with a small number of
alternatives) a multiplier for different values of the variable is produced, and it is easy to interpret
the relationship. This factor indicates how much higher (or lower) the number of accidents is if
the feature is present. A factor of 1 indicates no effect on accident occurrence.
It is important to note that these relationships apply only to models of the above form (power
function models). Other model forms are tested in the modelling process (for example
polynomials, Hoerl’s function and combination power and exponential functions). The
interpretation of these is often more complex and to examine the relationship between predictor
variables and accidents the model should always be plotted.
The typical mean-annual numbers of reported injury accidents for urban roundabouts can be
calculated using turning movement counts, non-flow data and the accident prediction models in
Table 5. The total number of accidents can be predicted by summing the individual predictions
for each accident group on each approach.
The flow variables used in these models are for daily average flows and are shown graphically
in Figure 1. Table 2, Figure 2 and Figure 3 define the visibility and speed variables.
Table 5: Urban roundabout accident prediction models
Equation (accidents per approach)
eUMAR eQA 42.2
31036.6 VQA aUMAR
UPAR ePA 67.0
21007.2 aaUCAR CQA
*k is the gamma distribution shape parameter for the negative binomial (NB) distribution.
**GOF (Goodness Of Fit statistic) indicates the fit of the model to the data. A value of less than
0.05 indicates a poor fit whereas a high value indicates a very good fit.
Unlike previous models developed by the study team, two of the seven preferred models had
model forms that deviated from the traditional ‘power function’ form. The data for these accident
types (pedestrian versus motor-vehicle and rear-end motor-vehicle) exhibit relationships
between the flow variables and accidents that are not adequately described by a ‘power
function’. To investigate what model forms may be appropriate the Hauer and Bamfo (1997)
integrate-differentiate (ID) method was followed. This lead to the trial of a combination of
exponential and power functions (as in the pedestrian model) and Hoerl’s function (as in the
rear-end model). An interesting property of these models is that they do not indicate that for
zero motor vehicle flows that the number of accidents is zero (although it does indicate that zero
pedestrian flows results in zero pedestrian accidents); this is a result of the more flexible model
The reason why these exponential and combination model types fit better than power functions
for these accident types is that at low volumes there are very few accidents. This persists until
the flow increases to a point where far more accidents begin to occur. A power function is not
suitable for representing this type of relationship. Figure 7 illustrates this through a graph of
Hauer and Bamfo’s “Empirical integral function”; this represents the integral of the function
relating accidents to entering flow. The low increase in accidents until approximately 5000 vpd
means that a power function is not suitable. Even when using Hoerl’s function to predict rear-
end accidents, care must be exercised at very low flows due to the ‘zero accidents, zero flow’
All of the preferred models for motor-vehicle and pedestrians accidents include non-flow
variables. For the motor-vehicle entering versus cycle circulating accidents, the non-flow
variable is the mean speed of circulating vehicles (Sc). The exponent on this variable indicates
that as circulating speeds increase so does the number of accidents. This relationship implies
that the European approach to the design of roundabouts has safety benefits by reducing
vehicle speeds. For example, the model suggests that if mean circulating speeds of 26 km/hr
were reduced by 20% then the resulting reduction in accidents of this type would be 38%.
Examination of the correlation matrix indicates that the speed of circulating vehicles is
correlated to the flow of circulating vehicles. This may be a result of roundabouts at higher
volumes being designed for faster speeds, for capacity reasons. There is therefore a clear
The ‘loss-of-control’ model was the only preferred model to include a visibility variable. In
developing models for other accident types the only other model where it featured as a stronger
predictor variable than speed was for ‘other cyclist’ accidents. The exponents of the visibility
variables were consistent, however, taking positive values ranging from 0.08 to 0.8 for most
accident types except both ‘other’ accident types (other cyclist, and other motor-vehicle) where
they were generally in the range -0.3 to -0.4. The reason for most accident types showing an
increase in accidents with increased visibility is likely to be the result of associated speed
increases. It is unclear why this would be different for ‘other’ accidents.
For the ‘other motor-vehicle’ and ‘all accident’ models the preferred models included the
covariate for number of entering lanes. Both these models indicate that the accident rate is
higher if the roundabout has multiple entry lanes for a given traffic flow. No matter which
accident type was being modelled, every time this variable was included the covariate was
always greater than 1.0. This strong result indicates the reduced safety of multi-lane
roundabouts when compared to single lane roundabouts.
The models developed can be compared with those of previous studies, as illustrated here by
comparing models developed for ‘entering-versus-circulating’ accidents developed in Turner
(2000) and Turner et al. (2006b). To allow for this comparison, the ‘flow only’ models developed
for this study are shown in Table 6 along with the model for cyclist circulating accidents from
Turner et al. (2006b) and the model for accidents involving all wheeled road users (cyclists and
motor-vehicles) in Turner (2000).
A comparison between the preferred models in Table 5 and the flow-only models in Table 6
illustrate the effect of the correlation between circulating flow and mean circulating speed in the
models for motor-vehicle only accidents. This can be observed by the lower exponent for the
circulating flow in the preferred model when compared to the flow-only model.
Table 6 shows that the relationships between the flow variables and motor-vehicle accidents are
similar for the current study and the Turner (2000) study. The higher coefficient for the earlier
study is likely to be the result of a downward trend in accidents in New Zealand and the
inclusion of cyclist accidents. It is interesting that the models for cyclist accidents have similar
exponents on the circulating flow variable to the models for motor-vehicle only accidents. This
indicates that similar relationships between flows and accidents may exist for both road user
Table 6: Entering-versus-circulating accident prediction models
Equation (accidents per approach)
Motor Vehicle Only
Accidents (Flow Only
11049.2 ceUMAR QQA
Motor Vehicle and
11014.1 ceUWXR QQA
Accidents (Flow Only
11051.1 ceUCAR CQA
Turner et al.
11040.2 ceUCXR CQA
Effect of Higher Speed Limits
Using the link data collected from the high speed roundabouts with speed limits greater than
70km/h, a covariate analysis of the effect of higher speed limits on accidents was carried out.
The following model was developed using a data set that contains approach flows, accidents on
each approach and the respective speed limit grouping:
The model is a good fit and has a negative binomial dispersion parameter (k) of 1.9. The
covariate for the higher speed sites indicates that at speed limits of 80 km/hr or greater there
are 35% more reported injury accidents than at a roundabout with an urban speed limit, for a
given traffic volume.
APPLICATIONS OF MODELS
There are a number of applications for accident prediction models, including the roundabout
accident prediction models presented above. The models can be used for performance
assessment of a current high and low speed roundabouts, by comparing the observed accident
rate with that predicted by the models, which is in effect a national or regional prediction of the
expected accident rate. Accident Prediction Models are used in New Zealand in economic
evaluation at new sites and at sites where there is a limited accident record, due to changes to
the site or low traffic volumes. These two applications will be covered in more detail below.
Accident prediction models are also used in New Zealand in the assessment of development
applications and for developing road safety strategies and policies. These applications are
discussed in the accompanying conference paper (Turner et al 2006a). Further applications of
the models are discussed in Turner et al. (2003).
Performance Assessment/Blackspot Identification
The majority of roading controlling authorities, including Transit NZ and Christchurch City
Council, have, or are in the process of developing, Safety Management Systems for their road
networks. These systems consist of a number of road safety processes that the road controlling
authority undertakes to identify, investigate, improve and monitor over their road network.
The majority of safety investigation programmes base the identification of accident trouble-
spots, and the monitoring of safety, on accident frequency. Given that higher volume sections of
the road network have a higher accident exposure, and therefore are more likely to have
accident clusters, most of the attention focuses on such sections. An enhancement to the
current investigation and monitoring systems would be to focus on accident risk and
consequences, which would also highlight high-risk sites, irrespective of the traffic volumes.
It is possible to incorporate accident risk and consequences within safety investigation
programmes using the following process:
Stage 1 – Calculate the expected number of accidents (estimator of the UTAR) at each
intersection, on each link and at each ‘other’ site (e.g. railway crossing or bridge) within the
study network using accident prediction models.
Stage 2 – Compare the observed number of accidents at each intersection, along each link and
at each ‘other’ site with the predicted accident rate.
Stage 3 – Identify and investigate those sites (as part of accident reduction studies and a safety
audit program) that have observed accident rates that are significantly higher than the accident
predictions. Make improvements to the sites and monitor them by comparing future accident
occurrence with model predictions.
Stage 4 – Identify and investigate those sites that have a high accident risk and/or high accident
consequences, irrespective of the traffic volumes. As funding allows, reduce the accident risk
and consequences at such sites through low cost accident remedial measures.
As engineers become more successful in addressing safety deficiencies at the black-spot and
black-route sites identified in Stage 3, the number of accident clusters will reduce and accidents
will become more spread out within road networks. This will lead to a greater focus on Stage 4
of the above process and on making small incremental steps towards reducing accident risk
over the entire road network.
The availability of accident prediction models enables road controlling authorities (RCAs) not
only to identify existing or potential accident trouble spots, but also to monitor accident risk over
their networks and compare the level of risk in their networks with other RCAs. The use of
APMs will improve the allocation of road safety improvement funding to areas with the most
need in the road network.
In New Zealand all substantial road safety improvement projects submitted for central
Government funding (through Land Transport NZ) must be accompanied by an economic
evaluation. There are three economic evaluation methods available in New Zealand for
assessing the safety benefits of road safety treatments. Two of the methods, Accident Rate
Analysis and Weighted Accident Procedure (WAP) utilise Accident Prediction Models. This
paper discusses the latter WAP method.
The WAP makes use of the following equation:
Aw = w * AT + (1-w) * AS
where w = k/(AT + k) for generalised linear models with a negative binomial distribution. As is
the site-specific accident rate, which is the annual average number of historical accidents in the
last five years. AT is the typical or national accident rate predicted using an accident prediction
model and ‘k’ is a parameter of the negative binomial distribution.
The better the accident prediction model, reflected in a high risk k, relative to AT, the more
weight is placed on the typical accident rate. Low k-values occur for site types where there is a
high variability in accident observations. In this case more weight is placed on the historical
The weighted accident rate procedure makes use of data from both sources and while taking
into account the expected accident risk at a site, also acknowledges that there are features of
sites that are unique and need to be considered when estimating the UTAR of the existing sites.
The UTAR of the upgraded site is calculated using one of two methods. If the change to the site
is fundamental (the pattern or severity of subsequent accidents at the site are expected to be
significantly different), then accident rate analysis is used for the economic evaluation, as the
accident history is no longer valid. In accident rate analysis a prediction model is used to
calculate the option accident rate (per year). In cases where the changes at a site are not
fundamental (similar types of accidents are expected) then a weighted procedure is used for the
option accident evaluation. The formula used for calculating the option accident rate is:
Aw (option) = AT (option) * (Aw (Do minimum)/AT (Do minimum))
More detail on this application can be found in Turner et al. (2005).
Changes in Form of Control
The accident prediction models can be used to evaluate the safety benefits (or disbenefits) of
converting an urban priority intersection to roundabout or traffic signal control. Furthermore,
models can be used to compare the changes in the major accident types.
For the traffic flows at the four-arm intersection illustrated in Figure 8, the annual number of
accidents of each type can be calculated for each form of control. This analysis used models
for motor-vehicle accidents at traffic signals and priority control from Turner (2000) and models
for pedestrian and cyclist accidents at traffic signals from Turner et al. (2006b).
The analysis shows that the predicted annual number of accidents for priority control is 1.51
acc/year, for signalised control 1.24 acc/year and for roundabout control 0.71 acc/year. Along
with the large changes in the total number of reported accidents there are also large changes in
the accident types and road user involvement. Table 7 illustrates the predicted numbers of
accidents by accident type and road user for the three control types. This shows that although a
roundabout is the safer form of control overall, with considerable safety benefits for motor-
vehicle users, it is likely to have a much higher number of injury accidents involving cyclists
compared to traffic signals.
Table 7: Predicted accidents for different forms of control
Crossing (No turns)
Right turn Against
Loss of control
Right Turn Against
Crossing (No turns)
Right turn Against
Loss of control
All road users
This paper presents a number of accident prediction models that have been developed for
roundabouts in urban and rural road networks. Models have been developed for the major
accident types for motor vehicles only, motor vehicles versus cyclists and pedestrians versus
motor vehicle classifications. The models include the principal flow variables and a number of
non-flow variables. Multiplicate factors have been produced to show the difference in accident
rate for low speed (70 km/hr and less) and high speed (80 km/hr and more) at roundabouts.
The model forms specified by Hauer and Bamfo (1997) have been used in addition to the
standard models used by the study team. The Hauer and Bamfo model forms allow greater
flexibility in the nature of the relationship modelled. Like all accident prediction models these
models should only be used over the flow ranges of the underlying dataset. However, further
care must be taken with these model forms as they can only be applied over a particular flow
range, because of peculiarities in the underlying accident relationships.
The preferred ‘non-flow’ models include a number of the variables that were collected in addition
to the flow variables, including visibility, speed and multiple entry lanes. While not in all
preferred models, there were strong relationships observed between visibility and number of
entry lanes with accident occurrence.
The models indicate that there would be benefits in a move to European design standards that
reduce both circulating and entry speeds. For example, the models indicate that reduction of
mean circulating free speeds of 26km/hr by 20% would result in a 38% accident reduction in
entering-versus circulating accidents. There are also benefits possible through reduction of
visibilities. Further work, however, is required to explain why the models indicate that ‘other’
motor-vehicle accidents may increase with reduced visibilities.
There are a number of applications of accident prediction models. Two applications of
roundabout accident prediction models have been outlined. The models can be used for
performance assessment sites and identification of high risk (but not necessarily high volume)
sites for crash reduction studies. This is an alternative to the picking of sites based on accident
frequency (Blackspot Identification). The models can also be used in economic evaluation. In
New Zealand the Weighted Accident (analysis) Procedure (WAP) makes use of the accident
history and accident prediction models. This is expected to lead to a better assessment of
accident benefits by acknowledging the stochastic nature of the historical accident rate at lower
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explanatory variables” Published in Proceedings of ICTCT 97 Conference, November 5-7 1997,
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Growth”, Transfund Research Report No. 205, Transfund New Zealand, Wellington, New
Transfund “Ins and Outs of Roundabouts: Safety Auditor’s Perspective”. Transfund New
Zealand, Wellington, New Zealand. (2000)
S. A. Turner, “Estimating Accidents in a Road Network”, PhD Thesis, Dept of Civil Engineering,
University of Canterbury. (1995)
S. A. Turner. “Accident Prediction Models”. Transfund New Zealand Research Report No. 192,
Transfund NZ, Wellington, New Zealand. (2000)
S. A. Turner, P. D. Durdin, I.Bone and M.Jackett, “New Zealand Accident Prediction Models and
Their Applications”. 21st ARRB /REAAA conference. (2003)
S. A. Turner, I. Melsom and P. D. Durdin, “Land Transport NZ’s Proactive Accident Analysis
Method: Weighted Accident Procedure” Unpublished Paper presented to 2005 ITE conference,
Melbourne, Australia (available form the author Shane.Turner@beca.com) (2005).
S. A. Turner, and A. Roozenburg, “Roundabout Crash Prediction Models”, Draft Land Transport
NZ Research Report, Land Transport NZ, Wellington NZ, (2006)
S. A. Turner, A. Roozenburg, T. Francis and G. Wood, “Prediction Models for Pedestrians and
Cyclists Accidents”, Towards Sustainable Land Transport Conference, Wellington, NZ. (2004).
S. A. Turner, A. Roozenburg, and T. Francis, “Predicting Accident Rates for Cyclists and
Pedestrians”, Land Transport NZ Research Report (to be published late 2006), Land Transport
NZ, Wellington NZ, (2006b)
S. A. Turner, G. R. Wood and A. P. Roozenburg, “Rural Intersection Accident Prediction Models”,
22nd ARRB Conference, Melbourne, Australia. (2006a)
G. R. Wood, “Generalised Linear Accident Models and Goodness-of-fit Testing”, Accident
Analysis and Prevention 34 (2002) pp. 417 – 427.
Shane is a Senior Associate in the consulting firm Beca Infrastructure Ltd. He is based in the
Christchurch office where he leads a team of seven 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 is a guest lecturer in the Master
of Transport course at the University of Canterbury. Shane has extensive experience, through
leading many road safety research projects, in safety related research, particularly the
development of accident prediction models.
Graham’s current role is Professor of Statistics and Head of Department 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.
Aaron Roozenburg is a transportation engineer in the Christchurch office of Beca Infrastructure
Ltd. After graduating with a Masters in Transportation Engineering from the University of
Canterbury in 2004, Aaron has worked as a consultant in the road safety, traffic engineering,
sustainable transport and research fields. Aaron has been involved in a number of accident
prediction modeling research projects including projects developing models for pedestrian and
cyclists at intersections and right-turn-against accidents at traffic signals. He is currently
involved in three studies; the accident benefits of installing cycle facilities, the safety impact of
visibility and speed on accidents at roundabouts and the development of a comprehensive
accident prediction model for rural link crashes.
Figure 1: Numbering convention for movements and approaches
Figure 2: Entering and circulating vehicle speeds
Figure 3: Measurement of V
Figure 4: Road user involvement in injury accidents at urban roundabouts
Figure 5: Injury accident types of reported crashes at urban roundabouts)
1 2 3 4 5
b = 1
b = 0.5
b = - 0.5
b = 1.5
b = 0
Figure 6: Relationship between accidents and predictor variable x for different values of
model exponents (b
05000 10000 15000 20000
Cumulative 'Bin Area' (F(Qe))
Figure 7: Empirical integral function for rear-end accidents
Figure 8: Example daily motor-vehicle, cyclist and pedestrian flows