Appendix A Description, Calibration, and Validation of the CA
Model
INTRODUCTION OF CA MODELS
Microscopic simulation is found to be an effective method to estimate road safety, as it can take into
account many factors such as traffic volume, signal control and driver behavior (Huang et al. 2013). A
software package called Surrogate Safety Assessment Model (SSAM) developed by Federal Highway
Administration (FHWA) has been used to estimate conflicts by identifying critical safety indicators,
such as Time-to-Collision (TTC) through trajectory files generated by PTV VISSIM, which is a
commercial microscopic simulation package (Gettman et al. 2008). However, SSAM relies on
VISSIM simulation that does not currently allow for estimation of the effect of RLC so far. A more
flexible and generalized simulation tool is needed. An improved Cellular Automata (CA) is thus
developed in this study.
In the model, position and velocity of each vehicle are represented in discrete values and are updated
by user-defined transition rules. A classic one-dimensional model was developed by Nagel and
Schreckenberg in 1995, known as Nagel-Schreckenberg (NaSch) model. For city road networks, the
most popular model is Biham-Middleton-Levine (BML) model developed as a two-dimensional
system (Biham et al. 1992) which allows change of trajectory. Based on flexible transition rules, it is
becoming easier to use CA models to simulate microscopic traffic behavior accurately while
leveraging on parallel CA computation (Clarridge and Salomaa, 2010; Luo et al., 2013). Moreover,
compared to existing commercial simulation packages, CA models are more flexible to model
microscopic vehicle movements as well as geometric layouts (Chai and Wong 2013b; Kerner et al.
2011).
However, CA models are mostly applied in estimating road capacity and traffic performances, such as
travel time and space-time relationship. A previous study conducted by the authors successfully
modified conventional CA models for safety assessment (Chai and Wong, 2014). In that study, vehicle
conflicts with different severity grades were generated through simulating vehicle movements. The
CA approach, which has been validated and compared to other analytical and simulation methods, is
found to be able to assess safety performance instead of relying upon accident counts.
DEVELOPMENT OF IMPROVED CA MODEL
For the improved CA model, simulation accuracy was increased through choosing a smaller cell size
to simulate heterogeneous traffic flow with three vehicle types. In consideration of typical lane width
and vehicle sizes, in this study, each cell was selected as a square space of 0.9m width and 0.9m
length. Lane width was taken to be 3.6m, and each lane contains four rows of cells. Car, heavyvehicles and motorcycle were simulated as a mixed traffic flow to approximate real traffic flow
composition in Singapore. According to the actual sizes of different vehicle types, a car occupies 2 ×5
cells, a heavy vehicle occupies 3×13 cells, and a motorcycle occupies 1×3 cells. Moreover, a leading
cell for each vehicle was defined (shown as the black cells in Figure A1) to define the position of each
vehicle.
In the improved CA model, forwarding rules for vehicle movements were modified from a multi-lane
NaSch model (Spyropoulou 2007). In NaSch model, a vehicle movement in one time step has four
basic considerations: acceleration, deceleration, random deceleration, and update velocity and position.
The acceleration or deceleration rate of the subject vehicle due to neighboring traffic conditions and
signal phase was first determined; velocity and position at the beginning of next time step were then
updated.
In Singapore, vehicles are driven on the left hand side of the road and lane-changing is allowed along
approach and departure areas subject to enough gaps in current and target lanes. Moreover, for cars
and heavy vehicles, lateral drift within the same lane may occur due to the intent of lane-changing or
giving way to following motorcycles.
In this study, front and alongside gaps were observed for over 300 vehicles in stand-still queues at 3
approaches, at Approaches No. 3, 5 and 6 shown in Table A1. Minimum gap in front of cars and
heavy vehicles was around 2.5m. Therefore, frontal gap tolerance (minimum gap accepted in
simulation) was set as 3 cells (2.7m) for cars and heavy vehicles. Alongside gap tolerance was set for
different situations based on observed traffic flow. A minimum alongside gap of 1 cell was set
between two vehicles or two motorcycles. In South East Asian countries, some motorcycles ride or
queue between two vehicles. Therefore, alongside gap tolerance was not set between a motorcycle and
a longer vehicle. An illustration is shown in Figure A2 where circumscribing gray area represents cells
which cannot be occupied due to the gap tolerance rule.
In the improved CA model, the stopping probability of first vehicle at onset of amber was calculated
according to a regression model. Computer algorithm made a decision according to the stopping
probability and checks whether there is enough distance to stop. If there was not enough distance to
stop fully, the vehicle would proceed to cross the stop-line. If the decision was to stop, the following
vehicle(s) would also stop. If not, the same procedure would apply to the following vehicle until a
vehicle stops.
MODEL CALIBRATION BASED ON FIELD OBSERVATIONS
The observations were conducted at 10 approaches (5 with RLCs, 5 at intersections without RLCs)
located at ten (4-way) cross-intersections in Singapore, as summarized in Table A1. The selected
intersection approaches vary in traffic volume, speed limit, road width and crash occurrence to
achieve generalized traffic movement characteristics. To reduce the “spillover” effect, selected nonRLC sites were located at least two intersections away from any RLC intersections. Approaches No.
1-6 were used to calibrate model parameters, and Approaches No. 7-10 were used for model
validation. Through automatic vehicle classification and tracking technologies (Chai and Wong
2013a), vehicles’ velocity, position, front gap, as well as vehicle type were recorded at peak and offpeak periods for each studied intersection approach. The observations of each approach were made
during 3 weekdays (MON, TUE, and WED) at 10:00-11:00 am as off-peak hour and 6:00-7:00 pm for
peak hour. A total number of 34,384 vehicles were collected from Approaches No. 1-6.
A sensitivity analysis based on Elementary Effect (EE) method was conducted to test which modeling
parameters will affect simulation outputs significantly (Morris, 1991). EE method has been
successfully applied in sensitivity analysis of simulation models with large numbers of inputs (Ge and
Menendez 2012). Traffic characteristics that were tested include average stand-still front gap,
maximum velocity of different vehicle types, initial velocity, average acceleration/deceleration rates,
and maximum acceleration/deceleration rates. Other parameters in the CA model, such as random
deceleration ratio, were also tested.
For the EE test, different ranges for tested parameters were first selected according to previous studies,
as shown in Table A2. For each simulation run, one input parameter (𝑋𝑖 ) is changed by a certain
interval (Δ, pegged at 10%-step in this study) while the other input parameters were kept the same. 𝑚
number of input parameters were generated to achieve an unbiased sampling. Trajectories (moving
directions) of input parameters were generated according to Quasi-Optimized approach developed by
Ge and Menendez (2012). For each trajectory, two combinations of input parameters 𝑃1 and 𝑃2 were
simulated to compute simulation results in the average travel time of vehicles, as 𝑌(𝑃1 ) and 𝑌(𝑃2 ).
According to the definition of EE, elementary effect of each parameter along a trajectory was
computed as 𝐸𝐸(𝑋𝑖 ) = [𝑌(𝑃2 ) − 𝑌(𝑃1 )]/∆. For each input parameter, Total Sensitivity Index (TSI)
was computed (𝑇𝑆𝐼 (𝑋𝑖 ) = ̅̅̅̅̅̅̅̅̅
𝐸𝐸(𝑋𝑖 )／𝑋̅𝑖) and summarized in Table A2. The TSI values represents the
percent change of simulation results related to change (at 10%-step in this study) of the input
parameters. A TSI value of 0.1 (or higher) is equivalent to 1% (or larger) change in the simulation
results. In Table A2, most of the parameters were found to be sensitive (pegged at TSI >0.1) except
for initial velocity. The most sensitive parameters were maximum velocity and maximum acceleration
and deceleration rates. Random deceleration ratio in NaSch model was calibrated as 0.2 through
comparing simulation results with field observations. Other sensitive parameters were calibrated
according to field observations as described in the following.
1) Maximum velocity
Velocity profiles are computed for each tracked vehicle (sample size = 34, 384) during both peak and
off-peak periods at the approaches. Table A3 shows observed average and 95th percentile vehicle
velocities along intersection approach lanes (within 150m to the stop-line). Both average and 95th
percentile velocities were found to be larger in off-peak period. Moreover, average velocity along
approaches with RLCs installed was found to be significantly lower for all vehicle types at 5%
significant level (for 1-sided test).
2) Acceleration and deceleration rates
According to vehicle’s capability, the maximum acceleration and deceleration rates of cars are 7m/s2
and ̶ 9m/s2 (Bae et al. 2001). For heavy vehicles, the maximum acceleration and deceleration rates
were 3 m/s2and ̶ 5 m/s2 (Woodrow and Poplin 2002). For motorcycles, maximum acceleration and
deceleration rates are  5m/s2 (Limebeer et al. 2001). In Singapore’s local conditions, an 85th
percentile maximum deceleration rate of ̶ 4.5m/s2 was observed in a mixed traffic flow (Koh and
Wong 2007). Therefore, in the CA model, maximum acceleration and deceleration rates are defined as
shown in Table A4.
Multiple acceleration and deceleration rates (from 0.1 to maximum) were computed at each time step
according to current velocity and front gap. Regression equations from observation study are
calibrated with a minimum R2= 0.892 (as shown in Table A5). Front gap and moving velocity were
used for calibration. 𝜑𝑎 and 𝜑𝑑 were acceleration and deceleration rates, v (km/h) was the moving
velocity,
g (m) was front gap and 𝑑(m) was distance to stop-line in the equations.
3) Stopping propensity
Drivers approaching a signalized intersection at the onset of amber have to decide whether to stop or
cross the stop-line. According to maximum deceleration rate calibrated in Table A4, some vehicles
will not be able to fully stop before the stop-line. A regression model of the probability to stop at
amber onset has been calibrated for the first vehicles before stop-line at all 10 studied approaches. If
the first vehicle decides to stop, following vehicles will also stop. However, if the first vehicle decides
to cross the stop-line, the following vehicle will become the first vehicle. Stopping propensity of the
following vehicle will thus be calculated independently. The variables include whether there is a RLC
(A, correlation coefficient r= 0.48), distance to stop-line (B, r=− 0.75) at amber onset, velocity (C, r=
0.83), and whether it is peak hour (D, r= 0.37). According to the correlation analysis, RLC is a
significant factor that affects the stopping propensity of individual vehicle. The stopping propensity
for different vehicle types was modeled by Eqns. (1-3):
𝑝𝑠 (𝑐𝑎𝑟) = [1 + exp{−(−1.02 − 1.32𝐴 + 0.129𝐵 − 0.54𝐶 − 0.03𝐷)}]−1
(1)
−1
𝑝𝑠 (h𝑒𝑎𝑣𝑦 𝑣𝑒h𝑖𝑐𝑙𝑒) = [1 + exp{−(−2.61 − 0.85𝐴 + 0.17𝐵 − 0.31𝐶 − 0.01𝐷)}] (2)
𝑝𝑠 (𝑚𝑜𝑡𝑜𝑟𝑐𝑦𝑐𝑙𝑒) = [1 + exp{−(2.59 − 0.52𝐴 + 0.08𝐵 − 0.72𝐶 − 0.01𝐷)}]−1
(3)
MODEL VALIDATIONS
The performance of the CA model was evaluated by a comparison of simulated vehicle trajectories
against field data obtained by automatic vehicle detection and tracking at another four studied
approaches (No. 7-10) for both peak and off-peak hours. In order to generate the same initial headway,
observed arrival distribution and initial vehicle density were used to generate vehicles in the
simulation.
Figure A3 shows examples of comparison between trajectories (longitudinal distance) from CA model
and field data in Lane 2, during peak hours at studied Approach No.7. Table A6 summarizes Mean
Percentage Error (MPE) and Root Mean Square Error (RMSE) of studied approaches. These relatively
small and acceptable errors (around 5%) in comparison between the simulation and field data
presented evidence that the CA model can well describe traffic dynamics at the microscopic level.
Appendix B Supporting Tables and Figures
Table A1 Selected intersection approaches for field observation
Studied
approach
Road Name
Junction
with
Installation
of RLC
Speed
limit
(km/h)
1
International
Rd
Bukit
Panjang Rd
Clementi Rd
Jln Boon Lay
Y
Bangkit
Road
West Coast
Rd
Woodlands
Ave 5
Sengkang
East Way
Jurong East
Ave 1
Tampines
Ave 8
Jurong West
St 92
Marine
Parade
Central
Jurong West
Ave 4
2
3
4
5
6
7
8
9
10
Woodlands
Ave 2
Sengkang
East Road
Jurong Town
Hall Rd
Tampines
Ave 5
Jurong West
St 91
Marine
Parade Rd
Jln Bahar
No. of
lanes
60
Traffic
volume
during
peak hour
(pcu/h)
1450
Y
60
1320
5
Y
60
1010
4
N
70
1270
5
N
60
1330
5
N
60
1460
6
Y
60
740
3
N
50
480
2
Y
60
960
4
N
60
1510
5
5
Table A2 Results of sensitivity analysis
Parameter
Average stand-still front gap
Maximum velocity (Car)
Maximum velocity (Heavy vehicle)
Maximum velocity (Motorcycle)
Initial velocity
Average acceleration rate (Car)
Average acceleration rate (Heavy vehicle)
Average acceleration rate (Motorcycle)
Average deceleration rate (Car)
Average deceleration rate (Heavy vehicle)
Average deceleration rates (Motorcycle)
Maximum acceleration rate (Car)
Maximum acceleration rate (Heavy vehicle)
Maximum acceleration rate (Motorcycle)
Maximum deceleration rate (Car)
Maximum deceleration rate (Heavy vehicle)
Maximum deceleration rate (Motorcycle)
Random deceleration ratio
Range
1-10m
20-60 km/h
20-60 km/h
20-60 km/h
20-60 km/h
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.1-6 m/s2
0.05-0.3
TSI
0.28
1.45
1.02
0.91
0.02
0.46
0.55
0.21
0.32
0.15
0.16
0.64
0.58
0.34
0.72
1.10
0.58
0.86
Table A3 Observed average and 95th percentile vehicle velocities at intersection approaches
Average velocity
(km/h)
95th % velocity
(km/h)
Car
RLC
Peak
13.5
Off-peak 18.2
Peak
52.8
Off-peak 53.1
Heavy vehicle
No RLC RLC No RLC
15.8
12.2 13.5
20.6
13.5 14.0
57.0
45.0 48.7
58.1
45.2 48.7
Motorcycle
RLC No RLC
14.3 16.5
17.2 18.3
49.5 52.9
52.0 53.1
Table A4 Maximum acceleration and deceleration rates
Car
Heavy vehicle
Motorcycle
Maximum acceleration rate
4 cells/s2 ( 3.6 m/s2)
3 cells/s2 ( 2.7 m/s2)
4 cells/s2 ( 3.6 m/s2)
Maximum deceleration rates
̶ 5 cells/s2 ( ̶ 4.5 m/s2)
̶ 3 cells/s2 ( ̶ 2.7m/s2)
̶ 5 cells/s2 ( ̶ 4.5 m/s2)
Table A5 Linear regression models to determine acceleration and deceleration
Vehicle
type
Car
Peak
Offpeak
Heavy
vehicle
Peak
Offpeak
Motorcycle
Peak
Offpeak
RLC
No
RLC
RLC
No
RLC
RLC
No
RLC
RLC
No
RLC
RLC
No
RLC
RLC
No
RLC
Acceleration rate (m/s2)
Deceleration rate (m/s2)
1) 𝜑𝑎 = −0.03𝑣 + 0.27𝑔 − 0.99
1) 𝜑𝑑 = −(0.30𝑣 − 0.17𝑔 − 2.51)
2) 𝜑𝑎 = −0.03𝑣 + 0.36𝑔 − 1.70
2) 𝜑𝑑 = −(0.18𝑣 − 0.32𝑔 − 2.70)
1) 𝜑𝑎 = −0.03𝑣 + 0.12𝑔＋1.07
1) 𝜑𝑑 = −(0.22𝑣 − 0.21𝑔 − 1.90)
2) 𝜑𝑎 = −0.03𝑣 + 0.21𝑔 − 1.54
2) 𝜑𝑑 = −(0.16𝑣 − 0.41𝑔 − 2.64
1) 𝜑𝑎 = −0.03𝑣 + 0.30𝑔 − 1.21
1) 𝜑𝑑 = −(0.36𝑣 − 0.30𝑔 − 2.04)
2) 𝜑𝑎 = −0.04𝑣 + 0.37𝑔 − 1.81
2) 𝜑𝑑 = −(0.22𝑣 − 0.4𝑔 − 1.77)
1) 𝜑𝑎 = −0.03𝑣 + 0.15𝑔＋0.56
1) 𝜑𝑑 = −(0.39𝑣 − 0.23𝑔 − 2.23)
2) 𝜑𝑎 = −0.03𝑣 + 0.32𝑔 − 2.14
2) 𝜑𝑑 = −(0.23𝑣 − 0.25𝑔 − 2.85)
1) 𝜑𝑎 = −0.02𝑣 + 0.34𝑔 − 0.51
1) 𝜑𝑑 = −(0.21𝑣 − 0.25𝑔 − 1.35)
2) 𝜑𝑎 = −0.02𝑣 + 0.27𝑔 − 0.64
2) 𝜑𝑑 = −(0.12𝑣 − 0.27𝑔 − 2.05)
1) 𝜑𝑎 = −0.02𝑣 + 0.22𝑔＋0.02
1) 𝜑𝑑 = −(0.17𝑣 − 0.17𝑔 − 0.88)
2) 𝜑𝑎 = −0.02𝑣 + 0.5𝑔 − 1.58
2) 𝜑𝑑 = −(0.16𝑣 − 0.35𝑔 + 0.07)
1) 𝜑𝑎 = −0.02𝑣 + 0.37𝑔 − 0.67
1) 𝜑𝑑 = −(0.24𝑣 − 0.41𝑔 − 1.49)
2) 𝜑𝑎 = −0.02𝑣 + 0.32𝑔 − 0.77
2) 𝜑𝑑 = −(0.25𝑣 − 0.46𝑔 − 0.83)
1) 𝜑𝑎 = −0.02𝑣 + 0.24𝑔 + 2.00
1) 𝜑𝑑 = −(0.19𝑣 − 0.30𝑔 − 1.36)
2) 𝜑𝑎 = −0.02𝑣 + 0.3𝑔 − 0.38
2) 𝜑𝑑 = −(0.25𝑣 − 0.32𝑔 − 0.98)
1) 𝜑𝑎 = −0.02𝑣 + 0.14𝑔 + 2.51
1) 𝜑𝑑 = −(0.39𝑣 − 0.17𝑔 − 0.61)
2) 𝜑𝑎 = −0.01𝑣 + 0.15𝑔 + 1.61
2) 𝜑𝑑 = −(0.12𝑣 − 0.3𝑔 − 0.46)
1) 𝜑𝑎 = −0.01𝑣 + 0.10𝑔 + 2.10
1) 𝜑𝑑 = −(0.41𝑣 − 0.10𝑔 − 0.51)
2) 𝜑𝑎 = −0.02𝑣 + 0.25𝑔 + 2.04
2) 𝜑𝑑 = −(0.38𝑣 − 0.22𝑔 − 1.47)
1) 𝜑𝑎 = −0.01𝑣 + 0.15𝑔 + 2.03
1) 𝜑𝑑 = −(0.31𝑣 − 0.15𝑔 − 0.07)
2) 𝜑𝑎 = −0.01𝑣 + 0.21g + 2.46
2) 𝜑𝑑 = −(0.42𝑣 − 0.38𝑔 − 0.02)
1) 𝜑𝑎 = −0.02𝑣 + 0.23𝑔 + 3.51
1) 𝜑𝑑 = −(0.42𝑣 − 0.25𝑔 − 0.35)
2) 𝜑𝑎 = −0.01𝑣 + 0.21𝑔 + 2.39
2) 𝜑𝑑 = −(0.40𝑣 − 0.28𝑔 − 2.18)
1) acceleration/ deceleration rates during green signal phase
2) acceleration/ deceleration rates during amber/ red signal phase
Table A6 Deviations of observed and simulated velocity
Studied
approach
Studied
period
Approach 7
RLC
Approach 8
No RLC
Approach 9
RLC
Approach 10
No RLC
Peak
Off-Peak
Peak
Off-Peak
Peak
Off-Peak
Peak
Off-Peak
Car
RMSE
(km/h)
2.11
2.15
0.49
0.70
3.28
3.10
3.40
2.35
MPE
(%)
1.92
̶ 2.43
1.14
1.63
2.60
− 2.89
3.05
̶ 2.94
Heavy vehicle
RMSE
MPE
(km/h)
(%)
4.23
̶ 3.05
3.27
̶ 4.93
3.09
4.17
2.45
− 3.68
3.05
1.41
3.75
− 4.29
4.54
̶ 4.45
4.06
3.04
Motorcycle
RMSE
MPE
(km/h)
(%)
2.92
̶ 5.93
2.28
̶ 4.81
3.49
3.98
0.91
2.87
1.95
2.54
2.71
− 3.47
2.17
3.28
5.03
3.95
Table B1 Comparison of average safety indicators between CA simulation and field data
Rear-end
Average TTC (s)
Obs1 Sim2 Error
1.00 0.96 4.00%
Average PET (s)
Obs1 Sim2
Error
1.69 1.75 −2.46%
Lane-changing
1.30
0.97
3.00%
2.03
2.08
−3.55%
Right-angle
0.52
0.50
3.85%
1.04
0.98
5.77%
Right-turn-against 0.45
Obs : Observed average safety indicator
Sim2: Simulated average safety indicator
0.47
̶ 4.44% 1.39
1.46
−5.04%
Conflict types
1
Table B2 Simulation scenarios
Scenario
Scenario (1)
Scenario (2)
Scenario (3)
Scenario (4)
Installation of RLC
Yes
Yes
No
No
Traffic condition
Peak (270 pcu/h/lane)
Off-peak (90 pcu/h/lane)
Peak (270 pcu/h/lane)
Off-peak (90 pcu/h/lane)
Table B3 Simulated red-running violations
Scenario
Scenario (1)
Scenario (2)
Scenario (3)
Scenario (4)
Traffic condition
No. of red-running violations
Peak (1300 pcu/h/approach)
13
Off-peak (580 pcu/h/ approach)
9
Peak (1300 pcu/h/ approach)
29
Off-peak (580 pcu/h/ approach)
21
Figure A1 Mixed traffic flow representation of CA model
Figure A2 Gap tolerance for heavy vehicles
Figure A3 Comparison of longitudinal distance of vehicles between CA model and field data (Lane 2,
approach 5, peak hour)
C: car; H: heavy vehicle; M: motorcycle
Figure B1 Geometric layouts and signal phases of case intersections
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