PhD Thesis Full Version - Jezan Md Diah

CHAPTER FIVE
MODEL DEVELOPMENT AND VALIDATION

5.1 INTRODUCTION

Basically, the weaving section flow model consists of two main components,
the non-conflicting flow and the conflicting flow. Within these components the
parameters are non-conflicting movement (q11 and q22), conflicting movement (q12 and
q21) and time safe gap (Tisg). The non-conflicting movement is quite straight forward
(Qncf = q11 + q22), while as equation for conflicting movement is quite complicated and
needs to consider the available gap or time (ideal safe gap). Therefore, this chapter
discusses and interprets the descriptive statistics accrued from first an empirical data
analysis on conflicting flow (Qcf) and ideal safe gap (Tisg), and followed with model
development process of weaving flow model, Qwsf.

Firstly, raw data obtained from site were organized to make it compatible with
MINITAB, the statistical software used to assists in the research works. Data
preparation process had been explained in Chapter 3 (refer Figure 3.15) which
involves several stages including data verification process of the selected stable flow
traffic operation. Field data that were collected was stored in the master data file (as
shown in Appendix A); these data (variables) are considered as possible independent
variables and dependent variables. Descriptive statistics that had been considered are;
minimum, maximum, mean, median and standard deviation value. Correlation
analysis was performed to identify whether there is significant relationships between
the variables. Multiple regressions of data transformation analyses were carried-out to
justify the level of reliability of the developed weaving section flow model. Once, the
required model had been developed, the next stage is the validation process.

Based on Kutner et al. (2005), “model validation usually involves checking a
proposed model against independent data. The basic ways of validating a regression
model are:

i. Collection of new data to check the model and its predictive ability, or

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ii. Comparison of results with theoretical expectations, earlier empirical results
and simulation results, or

iii. Use of a holdout sample or data that were not being used in creating and
calibrating the model to check the model and its predictive ability”.

The collections of new data set are used in this study for validation of the
developed model. The deliberation and discussion in the following sections would
focus on the resolution that originate in validating regression equations of data
transformation at weaving section of conventional roundabout.

5.2 GENERAL STATISTIC PRINCIPLE

The descriptive statistics for non-conflicting flow, conflicting flow and ideal
safe gap in weaving section area of conventional roundabout were calculated and
plotted using MINITAB. These plots are shown in Appendix B. In most cases, all the
graphs seem to be normally distributed in bell-shape curve which relate to the
empirical rule (Mendenhall et al., 2006) with 95% confident level. Table 5.1 shows a
summary of the Descriptive Statistics carried-out using MINITAB, from the Master
Database. From Table 5.1, the values for skewness and kurtosis are relatively small
for all variables which confirmed that the data is approximately normal.

TABLE 5.1
Summary of the Overall Descriptive Statistics

Variable Number of Mean Standard Min Median Max Skewness Kurtosis
observation Deviation 318.0 1239.5 2606.0 0.46 -0.17
q11
(pcu/hr) 112 1265.7 521.0

q22 112 1703.9 442.7 763.0 1653.0 2734.0 0.20 -0.16
(pcu/hr)
112 149.1 86.72 45.0 120.0 360.0 0.59 -0.53
q12
(pcu/hr) 112 119.9 65.98 45.0 105.0 330.0 0.82 0.43

q21 112 2.504 0.566 1.440 2.498 3.600 0.14 -0.73
(pcu/hr)
112 3238.7 799.2 1672.0 3241.0 4739.0 -0.05 -0.99
Tisg
(second) 112 269.0 125.9 90.0 262.5 540.0 0.49 -0.72

Qwsf 112 2969.7 746.8 1462.0 2988.0 4514.0 -0.11 -0.92
(pcu/hr)

Qcf
(pcu/hr)

Qncf
(pcu/hr)

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5.3 EMPIRICAL DATA ANALYSIS ON CONFLICTING FLOW AND
IDEAL SAFE GAP
Figure 5.1, Figure 5.2 and Figure 5.3 illustrate the scatter plots between Qcf vs

q12, Qcf vs q21 and q12 vs q21. From Figure 5.1 and Figure 5.2, it is clear that in general,
once the conflicting flow of weaving section Qcf increase, the conflicting flow from
inner to outer lane q12 and the conflicting flow from outer to inner lane q21 are also
increased respectively. This trend is as expected as it follows the generally traffic flow
fundamental. In weaving area of conventional roundabout, individual conflicting
vehicles attempt to find gaps in the adjacent lane traffic stream. As exits are on the left
side of the roundabout in Malaysian condition, the weaving section lane in which exit
roundabout vehicles seek gaps is outer lane. Based on Figure 5.3, it is clear that
conflicting flow rate from outer to inner lane q21 is less affected than conflicting flow
from inner to outer lane q12.

FIGURE 5.1
Measured Conflicting Flow Qcf vs Lane q12

Qcf (pcu/hr)

0 q12 (pcu/hr)

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FIGURE 5.2
Measured Conflicting Flow Qcf vs Lane q21

Qcf (pcu/hr)

0 q21 (pcu/hr)

FIGURE 5.3
Measured Lane q12 vs Lane q21

q12 (pcu/hr)

0 q21 (pcu/hr)

Consideration of stable flow condition, by omitting abnormal situations such
as ‘forced movement’, the range of conflicting flow and ideal safe gap in stable flows
are shown in Figure 5.4 and Figure 5.5. As with ideal safe gap requirement, it seems
that a much higher flow from inner to outer lane q12 when compared to conflicting
flow from outer to inner lane q21 at weaving area of conventional roundabout (refer

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Table 5.1). This situation happened because most local drivers in outer lane may
prefer not to weave, thus traverse along the outer lane until the exit arm or still in the
outer lane. While the drivers who want to move to the exit arm which is in inner lane
are needs or forced to weave so that their vehicles are able to move to the exit arm.
The interactions are dynamic in the weaving section influence areas therefore any
weaving vehicles tend to move inner to outer or outer to inner lane as long as there is
gap to do so. Hence, the ideal safe gap is important to be included in the conflicting
flow equation because of the applicability of this parameter for weaving purposes at
the weaving section of conventional roundabout. Although the q12, q21 and Tisg
parameters are the proportion of the Qcf parameter the collinearity issue can be
checked in the equation residual error. “For prediction conflicting movement equation,
collinearity is not harmful if the residual error of the equation complies with the
regression assumption (El- Shaarawi and Piegorsch, 2002).”

FIGURE 5.4
Measured Lane q12 vs Ideal Safe Gap Tisg

q12 (pcu/hr)

Tisg (sec)
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FIGURE 5.5
Measured Lane q21 vs Ideal Safe Gap Tisg

q21 (pcu/hr)

Tisg (sec)
The scatter plot of Qcf with the Tisg is as shown in Figure 5.6. From the
quantitative point of view, the range of conflicting flow Qcf is between 100 pcu/hr –
550 pcu/hr and the range of ideal safe gap Tisg is 1.5 sec – 3.5 sec. Based on the ideal
range of conflicting flow and the ideal safe gap, this is an interesting process that
necessitates further investigation.

FIGURE 5.6
Measured Conflicting Flow Qcf vs Ideal Safe Gap Tisg

Qcf (pcu/hr)

Tisg (sec)
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5.4 EMPERICAL DATA ANALYSIS ON WEAVING SECTION FLOW

This section discusses scatter plot of the empirical data on weaving section
flow Qwsf. In Figure 5.7, Figure 5.8 and Figure 5.9 illustrate the scatter plot between
Qwsf vs Qncf, Qwsf vs Qcf and Qncf vs Qcf. From Figure 5.7, it shows that once the
weaving section flow Qwsf increase, the non-conflicting flow Qncf is also increased and
this trend follows rightfully the traffic flow fundamental. Although Qcf, Qncf and Tisg
parameters are the proportion of the Qwsf, collinearity issue can be checked in the
model residual error. “For prediction models, collinearity is not harmful if the residual
error of the model complies with the regression assumption (El- Shaarawi and
Piegorsch, 2002).”

FIGURE 5.7
Measured Weaving Section Flow Qwsf vs Non-Conflicting Flow Qncf

Qwsf (pcu/hr)

Qncf (pcu/hr)

Figure 5.8 and Figure 5.9 show the range of conflicting flow of between 50
pcu/hr to 550 pcu/hr for both the Qwsf with Qcf , and Qncf and Qcf in range almost
between 1400pcu/hr to 4800pcu/hr respectively. Based on these ranges, the trend of
Figure 5.8 (Qwsf vs Qcf) and Figure 5.9 (Qncf vs Qcf) are seems to be increasing when
the conflicting flow increased. Thus, the relationship between Qwsf, Qncf and Qcf
warrant further investigation with ideal safe gap Tisg, are presented and discussed in
the following paragraph.

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FIGURE 5.8
Measured Weaving Section Flow Qwsf vs Conflicting Flow Qcf

Qwsf (pcu/hr)

Qcf (pcu/hr)

FIGURE 5.9
Measured Non-Conflicting Flow Qncf vs Conflicting Flow Qcf

Qncf (pcu/hr)

Qcf (pcu/hr)
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As can be seen in Figure 5.10 and Figure 5.11, based on ideal safe gap, the
flow is much higher in non-conflicting flow as compared with the conflicting flow at
weaving area of conventional roundabout. This scenario occurs because drivers who
want to move to the exit arm while in the inner lane are required or forced to weave so
that their vehicles are able to move to the exit arm. While in some cases, there are also
drivers who are from the outer lane need to move to inner lane in the weaving area of
conventional roundabout. The range of the ideal safe gap is between 1.50 sec to 3.5
sec either in non-conflicting flow and conflicting flow respectively. Since it is well
known that the influence on available gap can cause ‘disruption’ to flow movement,
thus the ideal safe gap for this study can be as an appropriate measure to represent the
model in following section.

FIGURE 5.10
Measured Non-Conflicting Flow Qncf vs Ideal Safe Gap Tisg

Qncf (pcu/hr)

Tisg (sec)

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FIGURE 5.11
Measured Conflicting Flow Qncf vs Ideal Safe Gap Tisg

Qcf (pcu/hr)

Tisg (sec)
The scatter plot of Qwsf with the Tisg is as shown in Figure 5.12. From the
quantitative point of view, the range of conflicting flow Qwsf is between 1500 pcu/hr –
5000 pcu/hr and the range of ideal safe gap Tisg is 1.50 sec – 3.50 sec. Based on the
idea of weaving section flow and the ideal safe gap, this is an interesting process that
necessitates further investigation.

FIGURE 5.12
Measured Weaving Section Flow Qwsf vs Ideal Safe Gap Tisg

Qwsf (pcu/hr)

Tisg (sec)
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5.5 DEVELOPMENT OF WEAVING SECTION FLOW MODEL, Qwsf

Weaving section flow Qwsf (pcu/hr) is used as an indicator or measurement to
determine the level of service for conventional roundabout. Consequently, a model
which representing the weaving influence area at weaving section of conventional
roundabout was calibrated using multiple regression of data transformation analysis.
Hence, the following paragraphs discuss the statistical analysis and model calibration
process of developing the weaving section flow model.

5.5.1 Descriptive Statistic for Qwsf Data

Figure 5.13 shows a sample of the reduced data from frame by frame analysis.
The range of the reduced weaving section flow Qwsf data that was used in statistical
analysis is presented in Appendix C. From Figure 5.13, it shows that there are peak,
non-peak and peak based on traffic flow values. Thus, it can be deduced that at the
beginning and ending, the flows normally came from people who goes to work and
goes to their home respectively. Else, only few people went out during resting time of
their work which causes non-peak flow. Data screening needs to be carried out in
order to examine and identify possible errors in the data set before the reduced data
can be used for analysis (Norusis, 1994). Figure 5.14 shows the histogram plot for the
overall weaving section flow data in the weaving area of conventional roundabout and
it shows a normal distribution.

FIGURE 5.13
A Sample of Qwsf Reduced Data for 0.04s Frame by Frame Analysis

in Weaving Area for 1 Minutes Time Interval

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FIGURE 5.14
Histogram Plot for Measured Weaving Section Flow in Weaving Area

Qwsf

A descriptive statistics for Qwsf data is as shown in Table 5.2. Table 5.3 shows
the statistics of skewness and kurtosis for weaving section flow data. The data is
shown as approximately normal because the weaving section flow variable has small
values that are less than 1.0 for skewness and kurtosis.

TABLE 5.2
Descriptive Statistics for Qwsf Flow

Variable Total Mean Standard Min Median Max
Qwsf Count 3238.7 Deviation 1672.0 3241.0 4739.0
112
799.2

TABLE 5.3
The Statistics of Skewness and Kurtosis for Qwsf Flow

Variable Skewness Kurtosis
Qwsf -0.05 -0.99

In order to obtain the optimum combination set for the predictors to model the
weaving section flow in weaving area of conventional roundabout, the stepwise
regression of data transformation method was used. Basically, the stepwise regression
of data transformation (e.g. Step 1, 2, n...) will be stopped depend on its R-sq and P-
value. Normally, the equation is statistical acceptable as Nagar (2008) mentioned,

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there exists a strong relationship when the values of R-sq and P-value is more than
50% and less than 0.05 respectively. The variables considered for this case were non-
conflicting flow Qncf (pcu/hr), conflicting flow Qcf (pcu/hr) and ideal safe gap Tisg
(sec). Table 5.4 shows the output from MINITAB software for stepwise regression of
data transformation.

TABLE 5.4
Output Iteration or Data Transformation Analysis in Calibrating Qwsf Model

Step 1 2

Constant 2305.14 2699.76
T-Value 29.80 29.80
P-Value 0.000 0.000

Qncf3/2 . Qcf 0.00001977 0.00002828
T-Value 14.69 16.05
P-Value 0.000 0.000

Tisg . Qcf - -1.2174
T-Value - -6.39
P-Value - 0.000

R2 0.662 0.754
Adj. R2 0.659 0.750

The equations produced in step1 and step2 are as shown in equation 5.1 and
equation 5.2 respectively.

Step 1: Qwsf = 2305 + 0.000020 Qncf3/2. Qcf (5.1)
Step 2: Qwsf = 2700 + 0.000028 Qncf3/2. Qcf – 1.22 Tisg . Qcf (5.2)

By referring to Figure 3.15 in Chapter 3 (using eight steps analysis), the initial
process on justifying the data transformation stepwise search is made many times (see
in Appendix D) in order to represent the final model which later being validated
statistically through eight steps analysis. Finally, it was found that Qncf3/2. Qcf is the
best entered variable for the model, and the P-values are calculated for each potential
variable mentioned earlier.

In the beginning of the stepwise search for predicting Qwsf, the non-conflicting
flow Qncf and conflicting flow Qcf are entered in the model. The R2, R2(adj) and P-

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value are calculated for each potential variable. The P-value for this test statistics is
0.000 and hence Qncf3/2.Qcf is added to the model. At this stage, step 1 has been
completed. At the bottom of column 1, a number of variables-selection criteria,
including the value of R2 is 0.662 and R2(adj) is 0.659 are provided.

In step 2 processes, variable Tisg. cf is added to the model and the two variables
are fitted. The P-value for step 2 is 0.000 so that the Tisg.Qcf parameter was considered
in the model. The variable of Qncf3/2.Qcf and variable of Tisg.Qcf are now in the model
with R2 of 0.754. Finally, all regression of data transformation model containing Qncf,
Qcf and Tisg are fitted. These parameters with R2 is 0.754 provide the appropriate
combination set for the prediction of weaving section flow Qwsf.

The final deduced model is as shown in equation 5.3 and the details of the
model are as shown in Table 5.5.

Qwsf = 2700 + 0.000028 Qncf3/2 . Qcf - 1.22 Tisg . Qcf (5.3)

Table 5.5 shows that Qncf, Qcf and Tisg as data transformation of Qncf3/2 . Qcf
and Tisg. Qcf are very significant independent variable for predicting Qwsf where the P-
value is less than 0.05 means that the predictor is significant, and these parameters
have to be included in the model for estimating Qwsf. Generally, the coefficients and
the standard error have the same units. “The relative value of standard error to the
coefficient is important in determining the reliability of the test statistics in estimating
the population parameter” (Faria, 2003). Thus, it can be said that the test coefficient
can produce better results when the smaller values of the standard error is obtained.

TABLE 5.5
Data Transformation Analysis for Final Model Qwsf vs. Qncf, Qcf and Tisg

Predictor Coefficient Standard T-Value P-Value
Error

Constant 2699.76 90.60 29.80 0.000
Qncf3/2 . Qcf 0.00002828 0.00000176 16.05 0.000
-6.39 0.000
Tisg . Qcf -1.2174 0.1906

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The hypothesis test is as follows:

H0 : There is absolutely no relationship between the variables
(Qncf3/2 . Qcf and Tisg . Qcf) in the model or that the
correlation coefficient in the model is equal to zero.

H1 : There is absolutely relationship between the variables
(Qncf3/2 . Qcf and Tisg . Qcf) in the model or that the correlation
coefficient in the model is not equal to zero.

Analysis of variance consists of calculations that provide information about

levels of variability within a regression model and form a basis for tests of significant.

The analysis of variance portion of the MINITAB output is as shown in Table 5.6.

Based on the F test statistic conducted the P-value is less than 0.001, providing strong

evidence against the null hypothesis or H0 is rejected.

TABLE 5.6

Analysis of Variance for Final Model, Qwsf

DF SS MS F P

Regression 2 53472539 26736270 167.32 0.000
Residual Error -
114 17417325 159792 -

5.5.2 Scatter Plot of Residuals for Qwsf Model

It is important to investigate the residuals (Mendenhall et al., 2006), in order to
determine whether or not they appear to fit the assumption of a normal distribution
after the fitting regression plane for Qwsf model is examined. Figure 5.15 shows that
the residuals do not seem to turn out of the way from a random sample from a normal
distribution in any systematic manner. In this study, the Anderson-Darling Normality
test, Kolmogorov Smirnov test and Durbin Watson test were conducted in order to
make sure that the errors between the predicted and measured values is normally
distributed by the rule of regression and the results is as shown in Table 5.7. The
normal probability plot shows that the residuals were scattered closely to the line, as
shown in Figure 5.16 and Figure 5.17. While from Figure 5.18, it is clear that the
histogram plot of the residual is normally distributed. Thus, this normality can be

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deduced that a data set is well-modelled by a normal distribution. However, this visual
observation needs to be further analysed based on its P-value in the hypothesis test in
order to accept the significant of model Qwsf. This hypothesis was discussed in the
following paragraphs.

FIGURE 5.15
Residual vs. the Fitted Values for Final Model Qwsf

Residuals Versus the Fitted Values

(r(eRsepsopnosneseisisQQwswfs.f)m)
1000

500

Residual 0

-500

-1000 2500 3000 3500 4000 4500 5000 5500
2000

Fitted Value

FIGURE 5.16
Normal Probability Plot of Qwsf Residual based on Anderson-Darling Test

Probability Plot of Residuals

Normal

99.9 Mean -2.25344E-12

StDev 396.1
99 N 112

95 AD 0.277

90 P-Value 0.650

Percent 80
70
60
50
40
30
20

10
5

1

0.1 -1000 -500 0 500 1000 1500

Residual

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FIGURE 5.17
Normal Probability Plot of Qwsf Residual based on Kolmogorov Smirnov Test

Probability Plot of Residuals

Normal

99.9 Mean -2.25344E-12

StDev 396.1
99 N 112

95 KS 0.049

90 P-Value >0.150

Percent 80
70
60
50
40
30
20

10
5

1

0.1 -1000 -500 0 500 1000 1500

Residual

FIGURE 5.18
Histogram of the Residual for Final Model Qwsf

Histogram of Residuals
(r(ResepsopnosneseisisQQwswfs.fm) )

Frequency 14
12
10 -600 -300 0 300 600 900

8
6
4
2
0

-900

Residual

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The Anderson Darling Test and Kolmogorov Smirnov test due to the
hypothesis test can be stated as follows:

H0 : The residuals for Qwsf model is normal.

H1 : The residuals for Qwsf model is not normal.

If P-value is greater than α=0.05, H0 is not rejected. Since both test produced
P-value greater than α in Table 5.7, as the results the residuals are normal for model
Qwsf and hence there is no explanation to doubt the validity of the regression
assumptions. Test from Durbin Watson give the value of 1.563 which is between 0 – 4
show that the model Qwsf is valid.

TABLE 5.7
Normality Test Results for Qwsf Model

Normality Test P-Value

Anderson Darling Test 0.650

Kolmogorov Smirnov test > 0.150

Durbin Watson 1.563

5.6 COLLECTION OF NEW DATA AND METHOD TO CHECK MODEL
VALIDITY

“The best way to carry out model validation is through the collection of new
data set (Kutner et al., 2005).” The reason in collecting new data is to be able to
examine whether the regression model of data transformation (RMDT) developed
from the earlier data is appropriate for the new data set. Consequently, one can have
certainty about the relevant of the model to be used.

“There are variety methods for examining the validity of RMDT against new
data set. One validation method is to re-estimate the model form chosen earlier using a
new data set. The estimated regression coefficients and various characteristics of the
fitted model are then compared for consistency to those of the RMDT based on the
earlier data. If the results are consistent, they provide strong support that the chosen

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RMDT is applicable under broader circumstances than those related to the original
data (Kutner et al., 2005).”

5.7 DESCRIPTIVE STATISTICS OF THE VALIDATION DATA SET
FROM NEW FIELDWORK

A new fieldwork data set for validation purposes was based on the same
criteria used throughout this study and a detail of 73 set of the data is attached in
Appendix E. The descriptive statistics for the variables of the new fieldwork data used
in the validation process is shown in Table 5.8. All the variables that were used in the
validation database occur within the range of the database variables used in model
calibration data set earlier (refer Table 5.1).

TABLE 5.8
Descriptive Statistics Validation Dataset for New Fieldwork

Variable Total Count Mean Standard Minimum Median Maximum
73 1709.3 Deviation 1028.0 1769.0 2027.0
q11 1998.0
(pcu/hr) 255.3 360.0
288.0
q22 73 1091.6 333.3 488.0 1049.0 4329.0
(pcu/hr) 516.0
73 199.8 91.2 45.0 195.0 3936.0
q12 3.200
(pcu/hr) 73 100.73 55.9 45.0 60.0

q21 73 3101.1 507.6 2145.0 3122.0
(pcu/hr)
73 300.5 109.3 105.0 285.0
Qwsf
(pcu/hr) 73 2800.6 478.9 1938.0 2757.0

Qcf 73 2.383 0.380 1.510 2.352
(pcu/hr)

Qncf
(pcu/hr)

Tisg
(second)

5.7.1 THE GOODNESS OF FIT FOR MODEL Qwsf

The goodness of fit from the new empirical data calibrated in this research
against weaving section flow model is illustrated in Figure 5.19. (Note: Qwsf observed
will be denoted as Qwsf.f and the model Qwsf predicted using equation 5.3 will be
denoted as Qwsf.m). Referring to Figure 5.19, it seems that in general the observed

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Qwsf.f against Qwsf.m model is correlating well with each other with R-Square of 82.3%.
However, this visual observation needs to be further analysed based on its P-value in
the Paired t-Test in order to accept the significant of model Qwsf.m.

FIGURE 5.19
Predicted Flow Qwsf.m from Eq. 5.3 versus Observed Flow

Qwsf.f from New Fieldwork Validation Database

Qwsf.m (pcu/hr)

R2 = 0.823

Qwsf.f (pcu/hr)

Paired t-Test is used to compare between weaving section flow Qwsf.m predictor
with Qwsf.f observed. Referring to Table 5.9 and Figure 5.20, the p-value is 0.912
which is greater than 0.05 the level of significance, therefore the null hypothesis is not
rejected at the 5% significance level between Qwsf.m and Qwsf.f. This suggests that the
observed flow Qwsf.f and predicted flow Qwsf.m does not differ significantly.

TABLE 5.9:
Statistical Evaluation of Paired t-Test between Qwsf.m and Qwsf.f Model

Test Qwsf.m and Qwsf.f

t-statistic -0.11

p-value 0.912

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FIGURE 5.20
Histogram of Differences between Qwsf.m and Qwsf.f Model

Histogram of Differences

(with Ho and 95% t-confidence interval for the mean)
15.0

12.5

10.0

Frequency 7.5

5.0

2.5

0.0 _
-600 X

Ho

-400 -200 0 200 400

Differences

5.8 SUMMARY

This chapter deliberated on model development and validation process. In
model development for weaving section of conventional roundabout, the dynamic
movement activities within the section needs to be understood, which comprises non-
conflicting, conflicting movements and time ideal safe gap for manouver ability. Basic
descriptive statistics and scatter plots of the data were the starting point before data
analysis. From the scatter plots, the limitation of minimum and maximum of each
variable were resolute and the independent variables were determined based on the
relationship with the response variables. Next is to arrived at the most appropriate
integration of variables related to Qncf, Qcf, Tisg and Qwsf were identified using the
sequence application of statistical procedures. In determining the integration between
Qncf, Qcf, Tisg and Qwsf, the stepwise regression of data transformation method was
used and applied in MINITAB software. The final model is then calibrated and tested
with the regression assumption and validity respectively. Model validation is the final
step in regression modeling. In the validation process a new field data set is acquired,
and comparison being made between predicted and observed values. These values

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were tested statistically to 5% level of significance in order to be accepted. The
validation results showed that the newly developed Qwsf model is significant at 5%
level of significance. Hence, a weaving section flow model, Qwsf = 2700 + 0.000028
Qncf3/2.Qcf - 1.22Tisg .Qcf , has been successfully developed, and sensitivity analysis of
the model will be presented in the preceding chapter.

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CHAPTER SIX
SENSITIVITY ANALYSIS AND APPLICATION OF THE

WEAVING SECTION FLOW MODEL

6.1 INTRODUCTION

Basically, a sensitivity analysis is the process of varying model input
parameters over a reasonable range and observing the relative change in model
respond (Saltelli et al., 2004). In this study, the sensitivity analysis is applied using
two to three values within the scope of calibrated data for each input parameter and
plotting the connection between the measured of effectiveness (MOE) as each of the
parameter increased or decreased. The developed model Qwsf with parameters Qcf, Qncf
and Tisg, from Chapter 5 was analyzed thoroughly in order to identify the sensitivity of
the MOE with different of each predictor parameters. The categorized of input
parameters are:

i. MOE stayed within the same LOS for low sensitivity.
ii. MOE jumped not more than one LOS for medium sensitivity.
iii. MOE jumped more than one LOS for high sensitivity.

The sensitivity of the model to uncertainty in values of model input data is one
of the advantages of conducting sensitivity analysis. Sensitivity analyses are also
beneficial in determining the direction of future data collection activities and the data
for which the model is relatively sensitive would require further field characterization
(Saltelli et al., 2004).

6.2 APPROACH TO SENSITIVITY ANALYSIS

The types of three predictors involved in prediction of the respond variable
Qwsf are as follows:

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i. Type A1, A2, A3, A4, A5 and A6: Varying the increment of Qncf parameter
while the other two parameters Qcf and Tisg are fixed under three situations as
shown in Table 6.1 – Table 6.6.

ii. Type B1, B2, B3, B4, B5 and B6: Varying the increment of Qcf parameter and
the other two parameters Qncf and Tisg are fixed under three situations as
shown in Table 6.7 – Table 6.12.

iii. Type C1, C2, C3, C4, C5 and C6: Varying the increment of Tisg parameter and
the other two parameters Qncf and Qcf are fixed under three situations as shown
in Table 6.13 – Table 6.18.

In the calibration of the model, the default values for the three situations are
based on the results of the descriptive statistics (minimum value, mean value and
maximum value in Chapter 5 of Table 5.1). Discussion of the descriptive statistics for
each parameter had been elaborated in Chapter 5. The weaving section capacity Qp,
with the minimum and maximum value of Qp that are taken as indicator value are
2119 pcu/hr and 5298 pcu/hr respectively. These values were deduced and based on
the adoption and simplified Wardrop’s formula in Arahan Teknik (Jalan) 11/87 (1987)
model and others researches works (see Chapter 2, Table 2.3). Basis of using these
values and their explanation are given in Section 6.3.2 of Table 6.21 for clarification.

6.2.1 Analysis for Type A1, A2, A3, A4, A5 and A6

Analysis for Type A1, A2, and A3 are elaborated in Table 6.1 – 6.3
respectively with varying the Tisg and increment of Qncf parameter:

i. Type A1: Based on constant minimum, mean and maximum Tisg, and
minimum Qcf parameter value (see Table 6.1).

105

Model: TABLE 6.1
Configuration of Default Value for Sensitivity Analysis in Type A1

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Value increased Fixed at: 90 Fixed at: 1.000

[1500 to 4500]

2 Value increased Fixed at: 90 Fixed at: 2.500

[1500 to 4500]

3 Value increased Fixed at: 90 Fixed at: 4.000

[1500 to 4500]

ii. Type A2: Based on constant minimum, mean and maximum Tisg and, mean Qcf
parameter value (see Table 6.2).

Model: TABLE 6.2
Configuration of Default Value for Sensitivity Analysis in Type A2

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Value increased Fixed at: 270 Fixed at: 1.000

[1500 to 4500]

2 Value increased Fixed at: 270 Fixed at: 2.500

[1500 to 4500]

3 Value increased Fixed at: 270 Fixed at: 4.000

[1500 to 4500]

iii. Type A3: Based on constant minimum, mean and maximum Tisg , and
maximum Qcf parameter value (see Table 6.3).

106

Model: TABLE 6.3
Configuration of Default Value for Sensitivity Analysis in Type A3

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Value increased Fixed at: 540 Fixed at: 1.000

[1500 to 4500]

2 Value increased Fixed at: 540 Fixed at: 2.500

[1500 to 4500]

3 Value increased Fixed at: 540 Fixed at: 4.000

[1500 to 4500]

As for Type A4, A5 and A6 are elaborated in Table 6.4 – 6.6 respectively with
varying Qcf and increment of Qncf parameter:

i. Type A4: Based on constant minimum, mean and maximum Qcf , and
minimum of Tisg parameter value (see Table 6.4).

Model: TABLE 6.4
Configuration of Default Value for Sensitivity Analysis in Type A4

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Value increased Fixed at: 90 Fixed at: 1.000

[1500 to 4500]

2 Value increased Fixed at: 270 Fixed at: 1.000

[1500 to 4500]

3 Value increased Fixed at: 540 Fixed at: 1.000

[1500 to 4500]

ii. Type A5: Based on constant minimum, mean and maximum Qcf ,and mean Tisg
parameter value (see Table 6.5).

107

Model: TABLE 6.5
Configuration of Default Value for Sensitivity Analysis in Type A5

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Value increased Fixed at: 90 Fixed at: 2.500

[1500 to 4500]

2 Value increased Fixed at: 270 Fixed at: 2.500

[1500 to 4500]

3 Value increased Fixed at: 540 Fixed at: 2.500

[1500 to 4500]

iii. Type A6: Based on constant minimum, mean and maximum Qcf and maximum
Tisg parameter value (see Table 6.6).

Model: TABLE 6.6
Configuration of Default Value for Sensitivity Analysis in Type A6

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Value increased Fixed at: 90 Fixed at: 4.000

[1500 to 4500]

2 Value increased Fixed at: 270 Fixed at: 4.000

[1500 to 4500]

3 Value increased Fixed at: 540 Fixed at: 4.000

[1500 to 4500]

Figures 6.1 – 6.6 show weaving section flows in weaving area of conventional
roundabout at various levels of non-conflicting flow. The other two predictors, Qcf and
Tisg were remaining constant with three situations as described in Table 6.1 – 6.6.
Generally, three situations in these Type A1, A2, A3, A4, A5 and A6 show that the
values of Qwsf increases with increasing of non-conflicting flow. These usual trends
consent with expectations and with traffic flow fundamentals. The minimum and

108

maximum value of Qp that taken as indicator from the adoption and simplified from
those of Wardrop’s formula in Arahan Teknik (Jalan) 11/87 (1987) model and also the
references from others researches are significant be used in Figure 6.1 – 6.6 in order to
addressed the wide range of data results. These results are seems to be in the range of
the minimum and maximum value of Qp.

It is clear that the weaving section flow can goes up to high values when the
non-conflicting flow increased at certain value for any of the three situations. Thus,
these indicated that non-conflicting Qncf as a sensitive predictor parameter for the
respond variable Qwsf. The line plot in Type A1, A2 and A3 of three situations (see
Figures 6.1 – 6.3) seem to be far from each other when the non-conflicting increases
and the conflicting flow vary at 90 pcu/hr, 270 pcu/hr and 540 pcu/hr. This explains
the impact of non-conflicting flow and conflicting flow on operational performance
and thus on the flow of the weaving area and from this analysis the conflicting flow
seems to creates more issues at the weaving section of conventional roundabout.

FIGURE 6.1
Sensitivity Analysis Output for Type A1

Weaving Section Flow, Q wsf (pcu/hr) 6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000

500
0
1500 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500

Non-Conflicting Flow, Qncf (pcu/hr)

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

In situation such as, in high non-conflicting flow and conflicting flow, it is
associated with higher weaving section flow and vice versa. For examples, in Figure
6.2 shows the weaving section flow Qwsf for situation 3 reached Qp minimum when
the non-conflicting flow is 2305 pcu/hr.

109

FIGURE 6.2
Sensitivity Analysis Output for Type A2

Weaving Section Flow, Q wsf (pcu/hr) 6000
5500
Qncf = 2305 pcu/hr5000
4500
4000
3500
3000
2500
2000
1500
1000

500
0
1500 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500

Non-Conflicting Flow, Qncf (pcu/hr)

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

While in Figure 6.3, the weaving section flow Qwsf for situation 1 and 2
reached Qp maximum when the non-conflicting flow Qncf are 3593 pcu/hr and 4288
pcu/hr respectively. Another main observation is that, for different conflicting flow
Qcf values and for different ideal safe gap Tisg would provide different weaving section
flow at conventional roundabout.

FIGURE 6.3
Sensitivity Analysis Output for Type A3

Weaving Section Flow, Q wsf (pcu/hr) 7000
6500
Qncf = 35936000
pcu/hr5500
Qncf = 4288 pcu/hr5000
4500
4000 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500
3500
3000
2500
2000
1500
1000

500
0
1500

Non-Conflicting Flow, Qncf (pcu/hr)

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

110

From Figure 6.4, Type A4 shows that there are increasing lines with different
gradient when the conflicting flow Qcf varies at 90 pcu/hr, 270 pcu/hr and 540 pcu/hr
while ideal safe gap Tisg are fixed at 1.000 sec. Thus, the findings indicate that certain
amount of fix Tisg can define different values of non-conflicting flow Qncf.

FIGURE 6.4
Sensitivity Analysis Output for Type A4

Weaving Section Flow, Q wsf (pcu/hr) 7000
6500
6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000

500
0
1500 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500

Non-Conflicting Flow, Qncf (pcu/hr)

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

From Figures 6.5 and 6.6, Type A5 and A6 show that there are intersect line
when the conflicting flow Qcf varies at 90 pcu/hr, 270 pcu/hr and 540 pcu/hr while
ideal safe gap Tisg are fixed at 2.500 sec and 4.000 sec respectively. Thus, the findings
indicate that certain amount of fix Tisg can define same values of non-conflicting flow.

111

FIGURE 6.5
Sensitivity Analysis Output for Type A5

Weaving Section Flow, Q wsf (pcu/hr) 6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000

500
0
1500 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500

Non-Conflicting Flow, Qncf (pcu/hr)

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

FIGURE 6.6
Sensitivity Analysis Output for Type A6

Weaving Section Flow, Q wsf (pcu/hr) 6000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000

500
0
1500 1800 2100 2400 2700 3000 3300 3600 3900 4200 4500

Non-Conflicting Flow, Qncf (pcu/hr)

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

112

6.2.2 Analysis for Type B1, B2, B3, B4, B5 and B6

For Type B1, B2, and B3 are elaborated in Table 6.7 – 6.9 respectively with
varying the Tisg and increment of Qcf parameter:

i. Type B1: Based on constant minimum, mean and maximum Tisg , and
minimum of Qncf parameter value (see Table 6.7).

Model: TABLE 6.7
Configuration of Default Value for Sensitivity Analysis in Type B1

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Fixed at: 1500 Value increased Fixed at: 1.000

[90 to 540]

2 Fixed at: 1500 Value increased Fixed at: 2.500

[90 to 540]

3 Fixed at: 1500 Value increased Fixed at: 4.000

[90 to 540]

ii. Type B2: Based on constant minimum, mean and maximum Tisg , and mean
Qncf parameter value (see Table 6.8).

Model: TABLE 6.8
Configuration of Default Value for Sensitivity Analysis in Type B2

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Fixed at: 3000 Value increased Fixed at: 1.000

[90 to 540]

2 Fixed at: 3000 Value increased Fixed at: 2.500

[90 to 540]

3 Fixed at: 3000 Value increased Fixed at: 4.000

[90 to 540]

113

iii. Type B3: Based on constant minimum, mean and maximum Tisg , and
maximum Qncf parameter value (see Table 6.9).

Model: TABLE 6.9
Situation: Configuration of Default Value for Sensitivity Analysis in Type B3

1 Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

2 Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

3 Fixed at: 4500 Value increased Fixed at: 1.000

[90 to 540]

Fixed at: 4500 Value increased Fixed at: 2.500

[90 to 540]

Fixed at: 4500 Value increased Fixed at: 4.000

[90 to 540]

For Types B4, B5 and B6 are elaborated in Tables 6.10 – 6.12 respectively
with varying the Tisg and increment of Qcf parameter:

i. Type B4: Based on constant minimum, mean and maximum Qncf , and
minimum of Tisg parameter value (see Table 6.10).

Model: TABLE 6.10
Configuration of Default Value for Sensitivity Analysis in Type B4

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Fixed at: 1500 Value increased Fixed at: 1.000

[90 to 540]

2 Fixed at: 3000 Value increased Fixed at: 1.000

[90 to 540]

3 Fixed at: 4500 Value increased Fixed at: 1.000

[90 to 540]

114

ii. Type B5: Based on constant minimum, mean and maximum Qncf , and mean
Tisg parameter value (see Table 6.11).

Model: TABLE 6.11
Configuration of Default Value for Sensitivity Analysis in Type B5

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Fixed at: 1500 Value increased Fixed at: 2.500

[90 to 540]

2 Fixed at: 3000 Value increased Fixed at: 2.500

[90 to 540]

3 Fixed at: 4500 Value increased Fixed at: 2.500

[90 to 540]

iii. Type B6: Based on constant minimum, mean and maximum Qncf , and
maximum Tisg parameter value (see Table 6.12).

Model: TABLE 6.12
Configuration of Default Value for Sensitivity Analysis in Type B6

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Fixed at: 1500 Value increased Fixed at: 4.000

[90 to 540]

2 Fixed at: 3000 Value increased Fixed at: 4.000

[90 to 540]

3 Fixed at: 4500 Value increased Fixed at: 4.000

[90 to 540]

Figures 6.7 – 6.12 show weaving section flows in the weaving area under
Types B1, B2, B3, B4, B5 and B6 for different stage of Qcf traffic conditions. The
other two predictors, Qncf and Tisg remained constant with three situations as described
in Tables 6.7 – 6.12. The weaving section flow in the weaving area increases linearly
with the increase in weaving section demand as well as with the increase in conflicting
flow demand in Type B1 (situation 1), Type B2 (situation 1 and 2), Type B3 and B4
(situation 1, 2 and 3), Type B5 (situation 2 and 3) and Type B6 (situation 3).

115

6000WeaviWenagviSnegctiSoecntiFolnoFlw,owQ,wsfQw(sfp(cpuc//hhr)FIGURE 6.7
5500 Sensitivity Analysis Output for Type B1
5000 Qcf = 179 pcu/hr
4500 Qcf = 408 pcu/hr140 190 240 290 340 390 440
4000
3500 Conflicting Flow , Qcf (pcu/hr) 490 540
3000 JKR (MAX)
2500
2000
1500
1000

500
0
90

Situation 1 Situation 2 Situation 3 JKR (MIN)

However, if compared with the parameter Qcf as in Type B1 (situation 2 and
3), Type B2 (situation 3), Type B5 (situation 1) and Type B6 (situation 1 and 2), it is
clear that increasing the weaving section flow of roundabout had decreased the
conflicting flow. It seems that the effect of non-conflicting flow and ideal safe gap in
Type B1 (situation 2 and 3), Type B2 (situation 3), Type B5 (situation 1) and Type B6
(situation 1 and 2) give different scenario by comparing with Type B1 (situation 1),
Type B2 (situation 1 and 2), Type B3 and B4 (situation 1, 2 and 3), Type B5 (situation
2 and 3) and Type B6 (situation 3). The reason is because when the non-conflicting
flow decreases, the conflicting flow and ideal safe gap reached its optimum values.

116

WeWaevaivnigngSeScetictoionnFlFlooww,,QQwwssff ((ppcc/uh/r)hr) 6000 FIGURE 6.8
5500 Sensitivity Analysis Output for Type B2
5000 490 540
4500 140 190 240 290 340 390 440 JKR (MAX)
4000
3500 Conflicting Flow , Qcf (pcu/hr)
3000
2500
2000
1500
1000

500
0
90

Situation 1 Situation 2 Situation 3 JKR (MIN)

Thus, there is no more increasing of weaving section flow. As the results, the
weaving section is decreasing. Therefore, it can be concluded that Qcf parameter
depends on Qncf and Tisg parameter in order to predict the weaving section flow
characteristic. For examples, in Figure 6.7 shows the weaving section flow Qwsf for
Type B1 (situation 2 and 3) reached Qp minimum when the conflicting flow Qcf are
408 pcu/hr and 179 pcu/hr respectively. While in Figure 6.9 for Type B3 (situation 1
and 2) are reached Qp maximum when the conflicting flow Qcf are 359 pcu/hr and 481
pcu/hr respectively. This indicates that if the Qcf and Tisg increase, whiles the Qncf
decreases, the Qwsf is decreases and vice versa.

117

FIGURE 6.9
Sensitivity Analysis Output for Type B3

WeWaevaivnigngSeScetcitioonnFFllooww, Qwwssff((ppc/chur/)hr) 7000 Qcf = 359 pcu/hr
6500 Qcf = 481 pcu/hr
6000
5500 140 190 240 290 340 390 440 490 540
5000
4500
4000
3500
3000
2500
2000
1500
1000

500
0
90

Conflicting Flow , Qcf (pcu/hr)

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

WWeeaavviinnggSSeeccttiioonnFlFloow,w,QwQsfw(sfp(c/phcru)/hr) 7000 FIGURE 6.10
6500 Sensitivity Analysis Output for Type B4
6000
5500 140 190 240 290 340 390 440 490 540
5000
4500 Conflicting Flow , Qcf (pcu/hr)
4000
3500
3000
2500
2000
1500
1000

500
0
90

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

118

WWeeaavviinnggSSeecctitioonnFlFolow,w,QwsfQw(sfpc(/phcr)u/hr) 6000 FIGURE 6.11
5500 Sensitivity Analysis Output for Type B5
5000 490 540
4500 140 190 240 290 340 390 440
4000
3500 Conflicting Flow , Qcf (pcu/hr)
3000
2500
2000
1500
1000

500
0
90

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

WeWaevaivinnggSeScetcitioonnFFllooww,, QQwwssff((ppcc/uh/r)hr) 6000 FIGURE 6.12
5500 Sensitivity Analysis Output for Type B6
5000
4500 140 190 240 290 340 390 440 490 540
4000
3500 Conflicting Flow , Qcf (pcu/hr)
3000
2500
2000
1500
1000

500
0
90

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

119

6.2.3 Analysis for Type C1, C2, C3, C4, C5 and C6

For Types C1, C2 and C3 are elaborated in Tables 6.13 – 6.15 respectively
with varying the Qcf and increment of Tisg parameter:

i. Type C1: Based on constant minimum, mean and maximum Qncf , and
minimum of Qcf parameter value (see Table 6.13).

Model: TABLE 6.13
Situation: Configuration of Default Value for Sensitivity Analysis in Type C1

1 Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

2 Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

3 Fixed at: 1500 Fixed at: 90 Value increased

[1.000 to 4.000]

Fixed at: 3000 Fixed at: 90 Value increased

[1.000 to 4.000]

Fixed at: 4500 Fixed at: 90 Value increased

[1.000 to 4.000]

ii. Type C2: Based on constant minimum, mean and maximum Qncf , and mean
Qcf parameter value (see Table 6.14).

Model: TABLE 6.14
Configuration of Default Value for Sensitivity Analysis in Type C2

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Fixed at: 1500 Fixed at: 270 Value increased

[1.000 to 4.000]

2 Fixed at: 3000 Fixed at: 270 Value increased

[1.000 to 4.000]

3 Fixed at: 4500 Fixed at: 270 Value increased

[1.000 to 4.000]

120

iii. Type C3: Based on constant minimum, mean and maximum Qncf , and
maximum Qcf parameter value (see Table 6.15).

Model: TABLE 6.15
Situation: Configuration of Default Value for Sensitivity Analysis in Type C3

1 Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

2 Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

3 Fixed at: 1500 Fixed at: 540 Value increased

[1.000 to 4.000]

Fixed at: 3000 Fixed at: 540 Value increased

[1.000 to 4.000]

Fixed at: 4500 Fixed at: 540 Value increased

[1.000 to 4.000]

For Types C4, C5 and C6 are elaborated in Tables 6.16 – 6.18 respectively
with varying the Qcf and increment of Tisg parameter::

i. Type C4: Based on constant minimum, mean and maximum Qcf , and
minimum of Qncf parameter value (see Table 6.16).

Model: TABLE 6.16
Configuration of Default Value for Sensitivity Analysis in Type C4

Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

Situation: Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

1 Fixed at: 1500 Fixed at: 90 Value increased

[1.000 to 4.000]

2 Fixed at: 1500 Fixed at: 270 Value increased

[1.000 to 4.000]

3 Fixed at: 1500 Fixed at: 540 Value increased

[1.000 to 4.000]

121

ii. Type C5: Based on constant minimum, mean and maximum Qcf , and mean
Qncf parameter value (see Table 6.17).

Model: TABLE 6.17
Situation: Configuration of Default Value for Sensitivity Analysis in Type C5

1 Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

2 Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

3 Fixed at: 3000 Fixed at: 90 Value increased

[1.000 to 4.000]

Fixed at: 3000 Fixed at: 270 Value increased

[1.000 to 4.000]

Fixed at: 3000 Fixed at: 540 Value increased

[1.000 to 4.000]

iii. Type C6: Based on constant minimum, mean and maximum Qcf , and
maximum Qncf parameter value (see Table 6.18).

Model: TABLE 6.18
Situation: Configuration of Default Value for Sensitivity Analysis in Type C6

1 Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )

2 Qncf (pcu/hr) Qcf (pcu/hr) Tisg (sec)

3 Fixed at: 4500 Fixed at: 90 Value increased

[1.000 to 4.000]

Fixed at: 4500 Fixed at: 270 Value increased

[1.000 to 4.000]

Fixed at: 4500 Fixed at: 540 Value increased

[1.000 to 4.000]

Tables 6.13 – 6.18 summarized the selected Tisg in situation 1, 2 and 3 for
Types C1, C2, C3, C4, C5 and C6. Figures 6.13 – 6.18 illustrate the variation of
weaving section flows Qwsf in the weaving area under Types C1, C2, C3, C4, C5 and
C6 with respect to ideal safe gap at different Qncf and Qcf demand. The parallel

122

declined lines state different scenarios of traffic condition. The earliest observation is
that, weaving section flow decreases linearly with ideal safe gap.

From Figure 6.13, it is clear that at low traffic flow condition that is for Type
C1 (situation 1, 2 and 3) the ideal safe gap shows less impact on the weaving section
flow in the weaving area, as the conflicting flow is generally within the low flow
condition.

FIGURE 6.13
Sensitivity Analysis Output for Type C1

WWeeaavivinnggSSeeccttiioonn FFlloow,w,QwQsfws(fp(cp/chru)/hr) 6000
5500
5000 1.500 2.000 2.500 3.000 3.500 4.000
4500
4000 Ideal Safe Gap, Tisg (sec)
3500
3000 Situation 2 Situation 3 JKR (MIN) JKR (MAX)
2500
2000
1500
1000

500
0
1.000

Situation 1

Figure 6.14 and Figure 6.15 show the weaving section flow Qwsf for Type C2
(situation1) and C3 (situation 1) are reached Qp minimum when the ideal safe gap Tisg
are 3.097 sec and 2.215 sec respectively. The line plot in Types C1, C2 and C3 of
three situations seems to be far from each other when the ideal safe gap increases and
the conflicting flow vary at 90 pcu/hr, 270 pcu/hr and 540 pcu/hr.

123

In comparing the level of sensitivity of Tisg parameter relative to the Qncf and
Qcf values, it can be concluded that the Tisg parameter is considered decreasing with
different input values of Qncf, and Qcf.

FIGURE 6.14
Sensitivity Analysis Output for Type C2

6000WeWaeavivinnggSSeectcitioonn FFloww,, QQwswfsf((ppc/chur/)hr)
5500
5000 Tisg = 3.097 sec
4500
4000 1.500 2.000 2.500 3.000 3.500 4.000
3500
3000 Ideal Safe Gap, Tisg (sec)
2500
2000 Situation 2 Situation 3 JKR (MIN) JKR (MAX)
1500
1000

500
0
1.000

Situation 1

While in Figure 6.15 for Type C3 (situation 3) is reached Qp maximum when
the ideal safe gap Tisg is 2.985 sec. Thus, this indicate that the situation where the
conflicting flow and ideal safe gap was high, the number of vehicles within the non-
conflicting flow decreases and this contribute to the decrease of weaving section flow
of the weaving area and vice versa.

124

FIGURE 6.15
Sensitivity Analysis Output for Type C3

7000WeWaevaivingngSeScetcitioonnFFllooww, QQwwsfsf((ppc/chur/)hr)
6500
6000 Tisg = 2.215 sec
5500 Tisg = 2.985 sec
5000
4500 1.500 2.000 2.500 3.000 3.500 4.000
4000
3500 Ideal Safe Gap, Tisg (sec)
3000
2500 Situation 2 Situation 3 JKR (MIN) JKR (MAX)
2000
1500
1000

500
0
1.000

Situation 1

In line plot of Types C4 and C5 (see Figure 6.16 and 6.17) show that there are
intersect line when the conflicting flow Qcf are vary at 90 pcu/hr, 270 pcu/hr and 540
pcu/hr while non-conflicting flow Qncf are fixed at 1500 pcu/hr and 3000 pcu/hr
respectively. Thus, the findings indicate that the certain amount of fix Qncf can define
same values of ideal safe gap Tisg.

125

FIGURE 6.16
Sensitivity Analysis Output for Type C4

WeWaeviavnigngSeScetictoionnFlFlooww,, QQwwssff((ppcc/hu/r)hr) 6000
5500
5000 1.500 2.000 2.500 3.000 3.500 4.000
4500
4000 Ideal Safe Gap, Tisg (sec)
3500
3000 Situation 2 Situation 3 JKR (MIN) JKR (MAX)
2500
2000
1500
1000

500
0
1.000

Situation 1

FIGURE 6.17
Sensitivity Analysis Output for Type C5

WWeeaavivinnggSSeectctiioonnFFllooww,, QQwwsfsf((ppc/chur/)hr) 6000
5500
5000 1.500 2.000 2.500 3.000 3.500 4.000
4500
4000 Ideal Safe Gap, Tisg (sec)
3500
3000 Situation 2 Situation 3 JKR (MIN) JKR (MAX)
2500
2000
1500
1000

500
0
1.000

Situation 1

126

From Figure 6.18, it is clear that at high traffic flow condition that is for Type
C6 (situation 1, 2 and 3) the ideal safe gap shows more impact on the weaving section

flow in the weaving area, as the conflicting flow is generally within the high flow
condition.

FIGURE 6.18
Sensitivity Analysis Output for Type C6

WeWaevaivnigngSeScetictoinonFlFloow,w,QQwwsfsf((ppcc/u/hrh)r) 7000
6500
6000 1.500 2.000 2.500 3.000 3.500 4.000
5500
5000
4500
4000
3500
3000
2500
2000
1500
1000

500
0
1.000

Ideal Safe Gap, Tisg (sec)

Situation 1 Situation 2 Situation 3 JKR (MIN) JKR (MAX)

6.3 INTEGRATION BETWEEN THE Qwsf MODEL WITH THE ARAHAN
TEKNIK (JALAN) 11/87 (1987) Qp MODEL WHICH ADAPTED FROM
WARDROP (1957) MODEL

In the following section, weaving section flow model developed from this
study and model from Arahan Teknik (Jalan) 11/87 (1987) which adopted and
simplified from those of Wardrop’s formula were examined, analyzed and integrated.
As had been noted earlier that Arahan Teknik (Jalan) 11/87 (1987) capacity model
solely consider geometrical parameters; The relationship between Qwsf and Qp in
predicting the weaving section flow (parameter of non-conflicting flow, conflicting
flow and ideal safe gap) and weaving section capacity (parameter of weaving section
length L, width of weaving section W and average entry width e), the integration can

127

be made to both models in order to get more information of the traffic volume
conditions at the weaving section of conventional roundabout in relating to geometric
design and traffic performance. The following sections and paragraphs would explain
the development of LOS chart, as a result of the combination of models Qwsf and Qp
(as shown in Appendix F). Subsequent to the development of the LOS chart, the
following paragraphs would provide application examples of the models and the
weaving section flow level of service chart.

The output from model developed in this study Qwsf and the model from the
Arahan Teknik (Jalan) 11/87 (1987) Qp is showed in Table 6.19. The variables from
Weaving Section Flow (Qwsf) model are Qncf, Qcf and Tisg and from Arahan Teknik
(Jalan) 11/87 (1987) Qp are W (width of weaving section), e (average entry width) and
L (length of weaving section). These geometrical values were site measurements
(study area). Although both models do not use same parameters, but the findings or
outputs are based at weaving section of conventional roundabout. To provide the basis
for comparing the models, analyses were undertaken using trial values (see Table 6.20
and Table 6.21) for each of the input predictor parameters and the output of the
respond variable is plotted on Figures 6.19 – 6.22 for ease of explanation.

Type of Models TABLE 6.19
Model for Predicting Weaving Section Flow

Equation Models for predicting at weaving section, Q (pcu/hr)

Model developed Qwsf = 2700 + 0.000028 (Qncf 3/2 . Qcf ) - 1.22 (Tisg . Qcf )
from this study
Equation (5.3)

Arahan Teknik Qp 160W 1 + e 
(Jalan) 11/87 = W
(1987) which 1 +  W 
was adapted  L
from Wardrop
(1957) model.

128

6.3.1 Analysis of Weaving Section Flow Model, Qwsf

In Figure 6.19, basically it shows that the weaving section flow (Qwsf) is
almost in the range of capacity of weaving section from Arahan Teknik (Jalan) 11/87
(1987) (adapted from Wardrop (1957) model) and other studies of Kimber (1980),
Hagring (1998), Wan Ibrahim and Hamzah (1999) and Federal Highway
Administration (2000) (see Chapter 2, Table 2.3) which depends on the value of non-
conflicting flow (Qncf), conflicting flow (Qcf) and ideal safe gap (Tisg). Based on
studies from Polus et. al. (2003) and the sensitivity analysis output for Types A, B and
C, the studies and the results show that increasing of weaving section flow (Qwsf) had
effect the decreasing of the ideal safe gap (Tisg). Thus, the range of trial value in Table
6.20 is according to the sensitivity analysis output and the analysis of descriptive
statistics from the calibration database as discussed in Chapter 5. Bear in mind that
weaving section capacity Qp from Arahan Teknik (Jalan) 11/87 (1987) is not
considering the flow and gap but basically on fix geometrical configuration of
roundabout. Therefore the plot line for weaving capacity from Arahan Teknik (Jalan)
11/87 (1987) is as base or indicator to be compared with the new model (Qwsf) which
based on flow and gap. Figure 6.19 shows that the weaving section flow (Qwsf)
decreases when the ideal safe gap (Tisg) increases from 1.000 to 4.000 seconds.
However, the weaving section flow (Qwsf) increases due to the increment of non-
conflicting flow (Qncf). Figure 6.19 also indicates the minimum 1.590 second and
maximum 3.810 second of the ideal safe gap (Tisg) that correspond to Qp(min) and
Qp(max) respectively. The passenger car equivalent (pce) factor that use for this study
is 1.0595 where the pce of weaving section (e.g. Persiaran Raja Muda (North) in
Bulatan Bistari) calculation is shown in Appendix A. Therefore, the unit conversion
of this study are used in order to determine unit vh/hr to pc/hr that come from Qp(min)
and Qp(max). The plot line of Qwsf in Figure 6.19 was simplified by the add trend line of
exponential using the statistical analysis, where from this add trend line it was found
that the R2 is almost near 1 in comparing with others add trend line (e.g. polynomial,
logarithmic and etc.).

129

TABLE 6.20
Configuration of Trial Values for Comparison Analysis for Qwsf and Qp

Non- Conflicting Ideal Safe Weaving Qp(jkr) Qp(jkr)
Conflicting Flow, Qcf Gap, Tisg Section (Pcu/hr) (Pcu/hr)
Flow, Qncf (pcu/hr) Flow, Qwsf Minimum Maximum
(sec) (pcu/hr)
(pcu/hr) 540 2119 5298
540 1.000 6605 2119 5298
4500 540 1.100 6540 2119 5298
4500 540 1.200 6474 2119 5298
4500 540 1.300 6408 2119 5298
4500 540 1.400 6342 2119 5298
4500 540 1.500 6276 2119 5298
4500 540 1.600 6210 2119 5298
4500 540 1.700 6144 2119 5298
4500 540 1.800 6078 2119 5298
4500 270 1.900 6013 2119 5298
4500 270 2.000 3283 2119 5298
3000 270 2.100 3250 2119 5298
3000 270 2.200 3218 2119 5298
3000 270 2.300 3185 2119 5298
3000 270 2.400 3152 2119 5298
3000 270 2.500 3119 2119 5298
3000 270 2.600 3086 2119 5298
3000 270 2.700 3053 2119 5298
3000 270 2.800 3020 2119 5298
3000 270 2.900 2987 2119 5298
3000 90 3.000 2954 2119 5298
3000 90 3.100 2506 2119 5298
1500 90 3.200 2495 2119 5298
1500 90 3.300 2484 2119 5298
1500 90 3.400 2473 2119 5298
1500 90 3.500 2462 2119 5298
1500 90 3.600 2451 2119 5298
1500 90 3.700 2440 2119 5298
1500 90 3.800 2429 2119 5298
1500 90 3.900 2418 2119 5298
1500 4.000 2407
1500

130

Qwsf (pcu/hr) FIGURE 6.19
Output of Integration from Trial Values

Tisg (sec)

6.3.2 Analysis of Arahan Teknik (Jalan) 11/87 (1987) Model, Qp
Figure 6.20 describes the geometric parameters of conventional roundabout

from previous researchers where the minimum, mean and maximum values are
evaluated from the studies of Kimber (1980), Arahan Teknik (Jalan) 11/87 (1987)
which adapted from Wardrop (1957), Hagring (1998), Wan Ibrahim and Hamzah
(1999) and Federal Highway Administration (2000) (see Chapter 2, Table 2.3).

131