Intersections Control and Safety
143
Traffic conflicts at roundabouts:
risk analysis under car-following conditions
G. Guido, A. Vitale & V. Gallelli
Department of Town and Country Planning, University of Calabria, Italy
Abstract
Roundabouts have had a remarkable spread since the 80s of the twentieth
century, especially in Europe. Compared to the conventional intersection’s
layout, traffic control systems based on roundabouts are suitable for improving
road safety and urban design. Nevertheless, much research has addressed
investigating safety issues related to the traffic conflicts of interesting
roundabouts’ traffic flows. The focus of this paper is on the analysis of safety
levels at roundabouts as regards the rear-end vehicles’ interactions in carfollowing conditions. Levels of safety are evaluated on the basis of a traffic
conflict technique applied to vehicles’ trajectories obtained experimentally from
a frame-by-frame analysis of video-taped traffic data. In order to estimate traffic
conflicts, reactions of following vehicles were observed at a roundabout case
study, and then were compared to the estimated ones obtained from a carfollowing model, based on a properly calibrated stimulus-response function.
Keywords: driver behaviour, roundabout, car-following, road safety.
1 Introduction
Intersections can be considered as the most sensible part of the road network due
to the fact that intersection accidents constitute a significant portion of total
crashes [1]. In many countries in the world, in order to increase road safety and
capacity at the same time, many intersections have recently been converted into
roundabouts. Roundabouts, indeed, eliminate or change the dynamics of conflict
types, reducing crash severity and drivers’ speeds [2]. Therefore, more studies
and research in this sector could provide additional information on the safety on
roundabouts, and, consequently, suggest helpful solutions for planners and
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
doi:10.2495/978-1-84564-764-3/013
144 Intersections Control and Safety
designers in identifying existing deficiencies and in refining their design
concepts.
This paper presents a risk analysis at a roundabout with particular attention to
rear-end interactions among vehicles. With the help of a video image processing
technique and a frame-by-frame analysis, more than 500 trajectories were
observed at a roundabout case study, determining the instantaneous speed and
acceleration of vehicles. This trajectories’ sample allows the authors to calibrate
a car-following model able to replicate rear-end interactions of the traffic stream.
For each couple of vehicles (lead and following vehicle) a risk analysis was
performed using traffic conflict technique [3–6]. In particular, for each couple of
lead and following vehicles Deceleration Rate to Avoid the Crash (DRAC) was
determined, identifying potential conflict scenarios. Finally, the authors compare
the conflict scenarios derived from the direct observation of vehicles’
manoeuvres with those obtained applying a properly calibrated car-following
model.
2 State of the art of car-following models
In car-following theory, the following vehicle (fv) decelerates or accelerates as a
response of the stimulus induced by leading vehicle (lv). The different models
vary according to the definition of the stimulus that, generally, may include the
velocity and the acceleration of the lv, the relative velocity and spacing between
lv and fv. Chandler et al. [7] formulated a first car-following model in which the
stimulus is specified as the relative velocity between lv and fv. The functional
form of the model is:
a n t     Vnfront t   n 
(1)
where,
n = perception time of driver n;
an(t) [response] = acceleration applied by driver n at time t;
Vnfront(t-n) [stimulus] = speed difference between user n and the preceding
vehicles in the same lane at time t-n;
[sensitivity] = constant.
On the basis of this first formulation, Gazis et al. [8], in 1959, suggested a
model taking into account the relative spacing between two successive vehicles:
a n t  

X n t   n 
 Vnfront t   n 
(2)
where,
Xn (t-n) is the relative spacing between lv and fv at time t-n.
In 1960, Edie [9] modified the model considering that the velocity of vehicle
itself influences driver behaviour. In consequence, the model can be more
generally expressed as:
a n t   
Vn t   n 

X n t   n 

 Vn front t   n 
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
(3)
Intersections Control and Safety
145
where,
Vn(t) speed of the driver n at time t-n.
Many calibrations of the model were carried out from 1959 [10,11], using
various approaches and on different scales (microscopic and macroscopic).
Therefore, the formulations defined by Chandler et al. [7] and by Gazis et
al. [8] can be considered special cases derived from the above-mentioned model.
The recent developments in sensor technologies led to the definition of more
general models and different combinations of and [12–14].
In 1996, Subramanian [15] proposed a formulation based on the GMN model,
in which a random term appears associated with the n-th user at time t. This term
is normal distributed while perception and reaction time  is considered as a
random variable truncated lognormal distributed:
a n t   
Vn t   n 

X n t   n 

 Vnfront t   n    n t 
(4)
In 1999, Ahmed [16] formulated a new expression of the GMN model,
considering the effect of flow’s density (Kn(t-n)) in the sensitivity function and
suggesting a non-linear relationship between acceleration and the stimulus
function (Vnfront(t-n)).
a n t   
Vn t   n 

X n t   n 

 K n t   n   Vnfront t   n 


(5)
in which ((0;1)) is a parameter that describes the n-th user’s perception of the
congestion level.
Besides the above-described models, based on the stimulus-response function,
there are other types of car-following models, some of them based on the
concept of braking distance [17–19], as well as models based on linear relations
[20–23], psychophysical models [24–27], models based on fuzzy logic [28–31],
and other models based on ITS systems [32–34].
3 Analysis of traffic conflicts under car-following conditions:
case study
Traffic flow was analysed at a roundabout placed near the motorway turnoff of
Cosenza, a medium-sized town in southern Italy, in order to calibrate the GMN
car-following model revised by Subramanian [15], and evaluate the potential
conflict scenarios for rear-end vehicles’ interactions.
3.1 Data collection
The test area is close to the Cosenza North motorway
important node in the local road network because of
neighbourhood, of the Arcavacata University campus,
regional university complex. Considerable traffic flows
turnoff, which is an
the presence, in the
the most important
use this roundabout,
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
146 Intersections Control and Safety
because it is located along the only corridor that connects both the railway
station and the highway with the university campus.
The geometric features of the intersection have been obtained by preliminary
surveys: this is a single-lane roundabout (the inscribed circle diameter varies
between 68 and 80 meters) with four entries.
Afterwards the roundabout was video-taped by a camera during the afternoon
peak hour, between 1:00 pm and 2:00 pm.
This survey allowed us to obtain the O/D matrix during the peak hour, to
individuate the busiest entries of the roundabout and to evaluate the traffic flow
in the circulatory roadway (Figure 1).
Figure 1:
Traffic flows (veh/h) during peak hour.
The car-following conditions occur for distances of less than 75 metres in
accordance with the theory of Aycin and Benekohal [35]; indeed, for distances
greater than this critical value, user behaviour is not influenced by preceding
vehicles in the same lane.
The roundabout monitored was divided into further trunks in order to
determine the most important parameters for the definition of the car-following
model. The aim of this discretization is to carry out the instantaneous dynamic
features of each vehicle.
The following data were extracted from the recording stage: Vn(t), speed of
the user n (fv) at instant t; Vn(t-n), speed of the user n (fv) at instant t-n;
Vn-1(t-n), speed of the user’s predecessor (lv) at instant t-n.
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
Intersections Control and Safety
147
In order to determine the perception and reaction time () of the users, it was
used an experimental relationship suggested by Italian rules [36], in which:
 n  2.8  0.01  Vn t 
(6)
The determination of the reaction (acceleration or deceleration) applied by the nth user at instant t was carried out using the following equation:
a n t  
Vn t   Vn t   n 
n
(7)
3.2 Data analysis and calibration of the model
The analysis of the trajectories recorded through the video-taping stage
suggested that a higher percentage of the manoeuvres were carried out in
deceleration conditions, hence the authors calibrated a general deceleration
model in car-following conditions.
A statistical analysis was carried out to determine the correlation among the
observed parameters useful to describe the car-following model.
The deceleration applied by the n-th user at instant t proved to vary linearly
both with velocity Vn and with Vn, whereas the relationship between the same
parameter (an) and the distance headway Xn is better characterized by an
exponential function (Equations (8), (9) and (10)).
a n t   2.004  0.062  Vn t 
(8)
a n t   0.026  0.065  Vn t 
(9)
a n t   1.436  exp  0.041  X t 
(10)
The parameters of the model (α, β, γ) were estimated through the Nonlinear
Least Square Analysis, whose numerical solution was provided by the damped
least-squares (DLS) method, or Levenberg-Marquardt algorithm. The general
expression of the model assumes the following shape:
a n t   0.001
Vn t   n 
2.498
X n t   n 
0.481
 Vnfront t   n    n t 
(11)
The calibration of the model shows that parameters   and have order of
magnitude corresponding to that obtained by other studies [12, 15, 16, 37].
Differences in the estimation can be ascribed to different calibration and testing
contexts. Indeed, almost all the car-following models are calibrated on straight
stretches of road, in which drivers’ behaviour is different from that observed at
roundabouts.
Random terms of the model (n(t)) are normally distributed with a mean equal
to -0.047 (m/s2) and standard deviation equal to 0.237 (m/s2). Further
information about the model and the estimated parameters are described in
Guido and Vitale [38].
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
148 Intersections Control and Safety
3.3 Risk analysis
In order to estimate traffic conflicts, reactions of following vehicles’ were
observed in specified sections of the roundabout and then were compared to the
estimated ones obtained from the model.
These reactions, expressed in terms of deceleration rate, were analyzed on the
basis of the expected values of Deceleration Rate to Avoid the Crash (DRAC).
DRAC was defined in terms of the speed differential between following vehicle
and lead vehicle divided by their closing time [39], and for rear-end interactions
this can be expressed as:
DRACn t  
Vn t   Vn 1 t 2
X n t   Ln 1
(12)
DRAC values were classified according to Hydén [40] to identify braking
levels and verify if the observed and the estimated reactions were properly
applied by users.
Therefore, six conflict levels were established depending on DRAC values:
1) DRAC equal to 0 m/s2 – evasive action not necessary; 2) DRAC ranging from
0 to 1 m/s2 – adaptation necessary; 3) DRAC ranging from 1 to 2 m/s2 – reaction
necessary; 4) DRAC ranging from 2 to 4 m/s2 – considerable reaction necessary;
5) DRAC ranging from 4 to 6 m/s2 – heavy reaction necessary; 6) DRAC greater
than 6 m/s2 – emergency reaction necessary. No conflict is expected for the first
two levels.
Table 1 shows the number and the percentage of vehicles that applied
observed and estimated reactions according to the expected levels of DRAC.
Table 1:
Number and percentage of vehicles according DRAC and
observed/estimated reactions.
Level of
conflict
DRAC
(m/s2)
# veh.1
%
veh.2
# obs.
veh.3
% obs.
veh.4
# est.
veh.5
% est.
veh.6
1







2







































1
Number of vehicles having DRAC according to conflict levels.
2
Percentage of vehicles having DRAC according to conflict levels.
3
Number of observed vehicles applying deceleration according to conflict levels.
4
Percentage of observed vehicles applying deceleration according to conflict levels (column
five/column three).
5
Number of estimated vehicles applying deceleration according to conflict levels.
6
Percentage of estimated vehicles applying deceleration according to conflict levels (column
seven/column three).
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
Intersections Control and Safety
149
A first observation concerns the high percentage of observed vehicles
(94.31%) that are not in traffic conflicts according to DRAC classification above
described; however, 93.21% of vehicles should adapt their condition to the
leader vehicles’ behavior.
The difference found between the observed and the estimated number of
vehicles having deceleration ranging from 0 to 1 m/s2 is justified considering the
fact that the lower limit of this level of conflict is equal to 0 m/s2, and many
observed reactions (accelerations and decelerations) are close to this value.
Therefore, the model provided reactions with more occurrences of deceleration
compared to those observed, even if the average reactions’ values are close to the
real ones.
It should also be emphasized that model replicates well the expected reactions
based on the DRAC values. Indeed, for the second level of conflict (DRAC
ranging from 0 to 1 m/s2), the model forecasts reactions of following vehicles in
terms of deceleration with a percentage equal to 71.46%, while only 22.44% of
observed users react applying deceleration, although a necessary adaptation is
expected [40].
Concerning the levels of conflict 3, 4, 5 and 6, there are no appreciable
differences between the observed values and the estimated ones.
4 Conclusions
The analysis of safety at a roundabout intersection was performed on the basis of
traffic conflict technique. Rear-end vehicles’ interactions were evaluated from a
frame-by-frame analysis of a video-taped sample of trajectories. This analysis
allowed the authors to calibrate a car-following model able to replicate rear-end
interactions of the traffic flow. The calibrated behavioural model provided
estimates of the users’ reaction to a stimulus produced by the preceding vehicles
in the traffic stream.
Furthermore, following and lead vehicles’ pairs were identified from the
observed trajectories to assess conflict levels according to Deceleration Rate to
Avoid the Crash, a surrogate safety performance measure based on the
differential speeds and spacing associated with each vehicle’s pair.
In car-following conditions, potential conflict scenarios occur when the
following vehicle reacts with a deceleration lower than a threshold corresponding
to a certain value of DRAC. However, the authors classified the levels of conflict
on the basis of DRAC [40], and established whether drivers should have applied
a suitable reaction. Conflict scenarios derived from the direct observation of
vehicles’ reactions were compared with those obtained applying the carfollowing model.
From the analysis it emerged that 94.31% of observed vehicles were not in
traffic conflicts according to DRAC classification, and no reaction was expected,
but 93.21% of vehicles should have adapted their condition to the leader
vehicles’ behavior being in second level of conflict.
For DRAC ranging from 0 to 1 m/s2 the model forecasts that vehicles adapt
their movement with more occurrences of deceleration compared to those
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
150 Intersections Control and Safety
observed; however, since no conflict is expected, observed drivers apply their
adaptations with safety margin. Regarding the levels of conflict requiring
reactions (levels 3 to 6), there are no appreciable differences between the
observed number of vehicles reacting and the estimated ones.
Future developments of the research could be addressed to the transferability
of the car-following model and to the analysis of different roundabout’s
configurations in order to better investigate safety issues and, consequently,
suggest helpful solutions for planners and designers.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
Neuman, T.R., Pfefer, R., Slack, K.L., Hardy, K.K., Harwood, D.W.,
Potts, I.B., Torbic, D.J. and Kohlman Rabbani, E.R., NCHRP Report 500:
Guidance for Implementation of the AASHTO Strategic Highway Safety
Plan, vol. 5: A Guide for Addressing Unsignalized Intersection
Collisions. Transportation Research Board, Washington, DC, 2003.
FHWA, Roundabouts: An Informational Guide. Publication FHWA-RD00-067, Washington, DC, 2000.
Guido G., Saccomanno F.F., Vitale A. and Cunto F., Comparing Safety at
Signalized Intersections and Roundabouts Using Simulated Rear-End
Conflicts, Transportation Research Record, Journal of the Transportation
Research Board, Vol. 2078, pp. 90–95, 2008.
Guido G., Saccomanno F.F., Vitale A., Astarita V. and Festa D.C.,
Comparing safety performance measures obtained from video capture
data, Journal of Transportation Engineering, ASCE, Vol. 137, N° 7,
pp. 481–492, 2011.
Guido G., Astarita V., Giofrè V. and Vitale A., Safety performance
measures: a comparison between microsimulation and observational data,
Procedia – Social and Behavioral Science, 20, pp. 217–225, 2011.
Praticò F. G., Vaiana R. and Gallelli V., Transport and traffic
management by micro simulation models: operational use and
performance of roundabouts, Urban Transport 2012, WIT Press, ISBN:
978-1-84564-580-9. DOI: 10.2495/UT120331, A Coruña, Spain, 2012.
Chandler R., Herman R., and Montroll E., Traffic dynamics; studies in car
following, Operations Research 6, 165+, 1958.
Gazis D., Herman R. and Potts B., Car-following theory of steady state
traffic flow, Operations Research 9, 449+, 1959.
Edie L. C., Car following and steady state theory for non-congested
traffic. Operations Research, 9(1), pp. 66–76, 1961.
Herman R., Montroll E. W., Potts B. and Rothery R. W., Traffic
dynamics: analysis of stability in car following, Operations Research, 7,
pp. 86–106, 1959.
Montroll E.W., Acceleration and clustering tendency of vehicular traffic,
in Proceedings of the Symposium on Theory of Traffic Flow, Research
Laboratories, General Motors, pp. 147–157, New York: Elsevier, 1959.
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
Intersections Control and Safety
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
151
May A. and Keller H., Non integer car following models, Highway
Research Record 199, 1967.
Heyes M. P., Ashworth R., Further research on car following models,
Transportation Research 6, pp. 287–291, 1972.
Ceder A., May A. D., Further evaluation of single and two regime traffic
flow models, Transportation Research Record, 567, pp. 1–30, 1976.
Subramanian H., Estimation of car-following models, Master's thesis,
MIT, Department of Civil and Environmental Engineering, Cambridge,
Massachusetts, 1996.
Ahmed K. I., Modeling driver’s acceleration and lane changing
behaviour, Doctoral thesis in Transportation Systems and Decision
Sciences, MIT, Department of Civil and Environmental Engineering,
Cambridge, Massachusetts, 1999.
Gipps P. G., A behavioural car-following model for computer simulation,
Transportation Research B 15B, pp. 105–111, 1981.
McDonald M., Brackstone M. and Jeffery D., Simulation of lane usage
characteristics on 3 lane motorways, in Proceedings of the 27th ISATA
Conference, Aachen, Germany, 1994.
Kumamoto H., Nishi K., Tenmoku K. and Shimoura H., Rule based
cognitive animation simulator for current lane and lane change drivers, in
Proceedings of the Second World Congress on ATT, pp. 1746–1752,
Yokohama, Japan, 1995.
Helly, W., Simulation of Bottlenecks in Single Lane Traffic Flow, in
Proceedings of the Symposium on Theory of Traffic Flow., Research
Laboratories, General Motors, pp. 207–238, New York: Elsevier, 1959.
Hanken A. and Rockwell T.H., A model of car following derived
empirically by piece-wise regression analysis, in Proceedings of the 3rd
International Symposium on the Theory of Traffic Flow, pp. 40–41, New
York: Elsevier, 1967.
Bekey G. A, Burnham G. O. and Seo J., Control theoretic models of
human drivers in car following, Human Factors, 19 (4), pp. 399–413,
1977.
Xing, J., A parameter identification of a car following model, in
Proceedings of the Second World Congress on ATT, Yokohama, pp.
1739–1745, 1995.
Michaels R. M., Perceptual factors in car following, in Proceedings of the
Second International Symposium on the Theory of Road Traffic Flow, pp.
44–59, Paris: OECD, 1963.
Evans L. and Rothery R., Perceptual thresholds in car following: a recent
comparison, Transportation Science, 11 (1), 60–72., 1977.
Wiedemann R. and Reiter U., Microscopic traffic simulation: the
simulation system MISSION, background and actual state, CEC Project
ICARUS (V1052), Final Report, vol. 2, Appendix A, Brussels: CEC,
1992.
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)
152 Intersections Control and Safety
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
Cameron D., Proceedings of the 28th ISATA Conference, Advanced
Transportation Systems Symposium, pp.475–484, Stuttgart, Germany,
1995.
Kikuchi C. and Chakroborty P., Car following model based on a fuzzy
inference system, Transportation Research Record, 1365, pp. 82–91,
1992.
Rekersbrink A., Mikroskopische verkehrssimulation mit hilfe der fuzzy
logic, Strass enverkehrstechnik, 2/95, 68–74, 1995.
Brackstone M., McDonald M. and Wu J., Development of a fuzzy logic
based microscopic motorway simulation model, in Proceedings of the
IEEE Conference on Intelligent Transportation Systems (ITSC97),
Boston, USA, 1997.
Mar J., Lin F., Lin H. and Hsu L., The car following collision prevention
controller based on the fuzzy basis function network, Fuzzy Sets and
Systems 139, pp. 167–183, 2003.
Daganzo C.F., in Traffic Flow, Cellular Automata = Kinematic Waves,
Research Report, UCB-ITS-RR-2004-5, ISSN 0192 4095, 2004.
Zhao X. and Gao, Z., A control method for congested traffic induced by
bottlenecks in the coupled map car-following model, Physica A:
Statistical Mechanics and its Applications, Volume 366, Issue 2, pp. 513–
522, 2006.
Ge H.X., Dai S.Q. and Dong, L.Y., An extended car-following model
based on intelligent transportation system application, Physica A:
Statistical Mechanics and its Applications, Volume 365, Issue 2, pp. 543–
548, 2006.
Aycin M. F. and Benekohal R., A linear acceleration car following model
development and validation, Transportation Research Board, 77th Annual
Meeting, 1998.
Ministero delle Infrastrutture e dei Trasporti, Norme funzionali e
geometriche per la costruzione delle strade, D.M. 05/11/2001, Roma,
Italy, 2001.
Ozaki H., Reaction and anticipation in the car following behavior,
Proceedings of the thirteenth international symposium on traffic and
transportation theory, pp. 349–366, Berkeley, CA, USA, 1993.
Guido G. and Vitale A., Analysis of users behaviour a roundabout under
car-following conditions, WIT Transactions on the Built Environment,
Urban Transport XII: Urban Transport and the Environment in the 21st
Century, Vol. 89, WIT Press, 2006, Southampton, UK, pp. 317–326
(ISSN 1743-3509; ISBN 1-84564-179-5; DOI 10.2495/UT060321).
Almquist S., Hydén C. and Risser R., Use of speed limiters in cars for
increased safety and a better environment, Transportation Research
Record: Journal of the Transportation Research Board, No. 1318 (1991),
Transportation Research Board of the National Academies, Washington,
D.C., pp. 34–39.
Hydén C., Traffic safety work with video-processing, Technical report,
Transportation Department, University Kaiserslautern, 1996.
WIT Transactions on State of the Art in Science and Engineering, Vol 66, © 2013 WIT Press
www.witpress.com, ISSN 1755-8336 (on-line)