Modeling of the Effect of Toll Road Characteristics on Accident Rate

The management, prevention, and control of accidents on toll roads is the obligation of the BUJT (Toll Road Business Entity). A prerequisite that must be met for the toll road to operate is that the initial toll road will be operated in the form of an audit process for the feasibility of the operation and when the toll road has been operated in the form of compliance with the Minimum Service Standards (SPM). In accordance with PM PU No. 16/PRT/M/2014 [3], the substance of toll road MSS can be measured from several elements, including toll road conditions; average travel speed; accessibility; mobility; first aid safety. In addition to the six factors above, in the process of managing safety and preventing traffic accidents on toll roads operationally also includes controls in the form of: Setting the V/C volume/capacity ratio, Setting PHV (Peak Hour Volume), Management of accident rate and fatality rate, Management of construction/pavement, Traffic engineering, Setting the distance of rest areas, Setting the distance of On and Off ramp/distance to toll gates [4]. In its implementation, the Management, Prevention and Control of traffic accidents is carried out as a preventive measure or corrective action.

According to Article 1 number 24 of Law Number 22 of 2009 [5], concerning Road Traffic and Transportation, a traffic accident is an unexpected and unintentional event on the road involving a vehicle with or without other road users resulting in human casualties and/or property loss. Meanwhile, according to WHO (1984), a traffic accident is an incident on road traffic involving at least one vehicle that causes injury or damage or loss to the owner (victim).

Basically, road safety is an interaction between vehicles, people, and roads. It is common to blame the driver for a collision, or the condition of the vehicle being driven. If neither the driver nor the vehicle is to blame, then accidents are often seen as fate, or sheer bad luck. Since then, traffic accidents have always been described as destined collisions [6].

The accident rate is used to measure the accident rate on a road segment or a road point. There are various ways and methods to measure the Accident Equivalent Number (AEN). Some AEN is determined through the segment of the road. The other method is calculated based on the point of occurrence of the accident. Based on the Construction and Building Guidelines Pd T–09–2004–B concerning Handling of Traffic Accident Prone Locations from the Ministry of Public Works and Public Housing of Indonesia [7], the following is the calculation of the accident rate and fatality rate, AEN, and the determination of accident–prone locations (black spots).

(1) Accident rate (AR) [7]

$A R=\frac{A \times 10^8}{d a y \times A A D T \times T \times l}$            (1)

(2) Fatality rate (FR) (Kementerian PUPR, 2004)

$F R=\frac{V D \times 10^\delta}{d a y \times A A D T \times T \times l}$              (2)

The calculation of the equivalent accident number (EAN) is carried out using a weighting system. The accident rate weighted ranking uses a comparison of the monetary value of the accident cost to determine, which refers to the accident cost. The following is an accident weighting value based on the losses caused.

$M: B: R: K=12: 6: 3: 1$              (3)

The AEN value is then calculated for each section on the toll road under review. When you have finished calculating the AEN value in each toll road section, the AEN is sorted in a table starting with the highest number of values to the lowest. For the record, this method does not look at the number of victims, but only the incidence and frequency.

The beginning of determining the blackspot is to identify the location of the blackspot. To begin with, black spots can be intersections, middle block chunks, or cuts in the road. All locations have a history of accidents–some reported, others unreported. To formulate a blackspot, an Accident Equivalent Number (AEN) value is required, as previously explained. One method of determining accident–prone locations (blackspots) is the statistical approach to quality control for inter–city roads, using UCL (Upper Control Limit) as a control chart. A road segment with an accident rate that is above the UCL line is defined as an accident–prone location (blackspot).

$U C L=\lambda+2.576 \sqrt{\left(\frac{\lambda}{m}\right)+\left(\frac{0.829}{m}\right)+\left(\frac{m}{2}\right)}$     (4)

The previous study model used as a reference in this study, the research that is close to this research is the research by Haryadi [8] entitled Exploration of the Toll Road Traffic Accident Rate Model with the GLM (Generalized Linear Modeling) technique. The study locations studied were the Jagorawi Toll Road (Jakarta – Bogor – Ciawi), the Jakarta – Cikampek Toll Road, and the Padaleunyi Toll Road (Padalarang – Cileunyi), with traffic volume and segment length as variables. The model results obtained are as follows:

Linear Regression

Total $=24.59+5.217 \times l+0.0001298 \times A A D T$      (5)

Positive intercept indicates that although there is no traffic and the length of the segment is zero, the model predicts the occurrence of more than 24 accidents per two years. This is of course impossible, so this model cannot be used to show the relationship between the total number of accidents with the length of the segment and the volume of traffic. From statistical analysis, it is known that only the segment length parameter is significant (5%). The linear regression model is based on the assumption of a normal distribution which is a continuous distribution, while the traffic accident data on a road segment at a certain time period is discrete non–negative data that does not follow the normal distribution.

Poisson Regression

$\ln ($Total$)=3.503+0.07792(l)+0.000002622(A A D T)$          (6)

The basic assumption of the Poisson distribution is that the mean and variance are the same. The model developed using the Poisson distribution shows a large overdispersion value, which is an indication that the mean value is much different from the variance value. This violates the most basic of assumptions. From the software output, R shows a large overdispersion symptom. The residual deviance value is 1677.6 with 54 degrees of freedom giving a ratio of deviance divided by degrees of freedom of 31.07. The greater the ratio value, the greater the difference in value between the mean and variance (overdispersion). It also indicates that the data does not match the type of function of the model.

Negative Binomial Regression

$\ln ($Total$)=0.427+0.075(l)+0.382 \times\ln (A A D T)$          (7)

The use of negative binomial distribution to model segment length, traffic volume and total accident solves the problem of overdispersion. The resulting model is similar to the model generated with the Poisson distribution, but the problem of overdispersion is almost completely solved. The value of the deviation divided by the degrees of freedom is 1.1285 (a value of 1.0 indicates that there is no problem with a variance greater than the allowable).

In addition to the Haryadi’s model [8], a study of the previous model that is relevant to this research was also conducted, so this research tries to fill the gap from previous studies with the following developments.

(1) This study tries to explain the relationship between the characteristics of urban toll roads and intercity toll roads on the accident rate by using the Generalized Linear Model (GLM), which includes a Poisson regression model, or a negative binomial distribution if overdispersion is found in the data distribution, namely the condition where the data variance is greater than the average value. Basically, overdispersion does not change conclusions about the relationship between accident rate and traffic volume and road geometry design [9].

(2) This study focuses only on the characteristics of toll roads that affect the accident rate. Based on the mapping of the previous study, no research has been found that has the effect of resting place locations, the distance between toll gates, and blackspot points on the number of accidents that occur. Therefore, in this study, the characteristics of the toll roads that will be reviewed in this study are as follows, taking into account the availability of data [10].

a. Traffic factor:

–Comparison between traffic volume and road capacity (volume capacity ratio).

b. Geometry factor (infrastructure):

–Number of available lanes.

–Toll road shoulder width.

–Location of blackspots.

c. Vehicle factor (means):

–Composition (class) of vehicles on toll roads.

d. Road complementary factors:

–Distance from rest area to toll gate.

–Availability of median barriers.

(3) The data to be used is secondary data obtained from the relevant agencies. Before developing the model, the data will be tested statistically first, namely with a partial test and a data fit test for the proposed model.

(4) In this study, a comparison will be made between the characteristics that affect the rate of accidents on urban toll roads with statistically significant inter–city toll roads.

Secondary data collected from the management agency of each toll road is related to traffic volume, toll road characteristics data, and accident data that occurred on the toll road in a span of five years, namely 2015 – 2019. The data is then processed to become variables in modeling the effect of toll road characteristics on the accident rate. As an example, only one toll road section of the four roads studied will be shown. The following is data obtained from toll road managers that have been processed so that the characteristics of the road sections being reviewed can be known as shown in Table 3 and Table 4.

The grouping of vehicle volumes on toll roads is carried out according to vehicle class based on Bina Marga standards. namely:

Group I: cars, small trucks. and buses;

Group II: trucks with two axles;

Group III: trucks with three axles;

Group IV: trucks with four axles;

Group V: trucks with five axles.

Table 5 and Table 6 show the volume of vehicles on each section of the Cipali Toll Road in 2015.

Table 3. Recapitulation of the characteristics of the Cikopo – Palimanan Toll Road

Table 4. Recapitulation of distance between Cikopo – Palimanan Toll Road facilities

Table 5. Flow rate Tol Cikopo – Palimanan (Route A)

Table 6. Flow rate Tol Cikopo – Palimanan (Route B)

From Indonesian Road Capacity Manual [13] for toll road, road capacity can be calculated by the Eq. (8).

$C=C_o \times F C_w \times F C_{S P}$            (8)

The Cikopo – Palimanan Toll Road with an alignment terrain that tends to be flat. And the type of road divided into four lanes. the Cipali Toll Road has a basic capacity of 2,300 pcu/hour/lane. For each lane width of 3.6 meters. The adjustment factor due to the traffic lane width (FCw) used is 1.012. As for the adjustment factor due to the separation of directions, the value of 1.00 is used, considering that there is a median on the Cipali Toll Road. Therefore, the capacity of the Cipali Toll Road is based on these parameters, namely:

$\begin{gathered}C=C_o \times F C_w \times F C_{S P} \\ \frac{C=2300 \times 1.008 \times 1.00=23,184 \frac{p c u}{ hour }}{ { lane }}\end{gathered}$     (9)

Since 2015, the entire Cipali Toll Road section consists of two lanes for each direction. Therefore, the capacity of this toll road is 4,655 pcu/hour.

Table 7. AADT Tol Cikopo – Palimanan (Route A)

Table 8. AADT Tol Cikopo – Palimanan (Route B)

Table 9. PHV Tol Cikopo – Palimanan (Route A)

Table 10. PHV Tol Cikopo – Palimanan (Route B)

In order to determine the ratio of traffic flow to road capacity. Data on the volume of vehicles at peak hours is needed. Therefore, the annual traffic flow data in the table above needs to be converted into Annual Average Daily Traffic (AADT). AADT is the average number of vehicle traffic that passes one lane of the road for 24 hours which is obtained based on data for one year. An example of the AADT calculation for vehicles moving from Cikopo to Kalijati in 2015 is as follows. Considering that the Cipali Toll Road has been operating since June 13, 2015, the number of operational days for this toll road in 2015 is 201 days.

$\begin{gathered}A A D T\,_{ {cikopo-kalijati }}=\frac{ { Flowrate }\, _ { {Cikopo-kalijati }}}{ { Number\, of \,day \, in \, a \, year }} \\ A A D T\,_{\text {cikopo-kalijati }}=\frac{2,621,686}{201}=13,043 \frac{ { vehicle }}{ { day }}\end{gathered}$     (10)

By performing a similar calculation as in the example above. The 2015 Cikopo – Palimanan (Cipali) Toll Road AADT is obtained as shown in Tables 7 and 8.

Due to data limitations which result in the unavailability of the number of vehicles per hour in one year. The above–mentioned Average Daily Traffic (AADT) data needs to be converted into peak hour vehicle volume using the k factor. The factor k represents the peak hour traffic flow of a road segment in a year, which is defined as the ratio between the hourly traffic volume occurring in the 30th busiest order (or another. For example, 50th or 200th order) to its AADT [14]. According to the Indonesian Road Capacity Manual [13], the k factor value commonly used in Indonesia is 11%.

Calculation of the volume capacity ratio (VCR) is carried out in passenger cars (pcu). Therefore, the peak hour vehicle volume must be multiplied by the passenger car equivalence factor (pcu) for expressways obtained from the Manual [13]. The emp factors used in this study are as follows.

MHV: 1.30 pcu

LB: 1.50 pcu

LT: 2.00 pcu

The following is a formula of calculating the peak hour volume from AADT to PHV in passenger cars unit (pcu). namely:

Peak Hour Volume (PHV)

$P H V=A A D T \times k \times e m p$       (11)

By performing a formula as listed above. The volume of vehicles during peak hours on the Cikopo – Palimanan Toll Road in 2015 is obtained as shown in Tables 9 and 10.

The VCR value can be determined by dividing the volume of vehicles at peak hours by the capacity of the road segment. Capacity of the Cipali Toll Road is 4655 pcu/hour/direction. With the peak hour volume (PHV) on the Cikopo – Kalijati section = 1459 pcu/hour, the following is the VCR value.

Volume Capacity Ratio (VCR)

$V C R=\frac{P H V}{C}$          (12)

In general, the accident rate is used to measure the accident rate on a road segment. Pignataro [15] revealed that the accident rate based on vehicle kilometers traveled can be calculated by Eq. (1).

From the number of accidents in each segment. The accident rate per kilometer for each section of the Cikopo – Palimanan Toll Road section can be calculated, which is shown in the following Table 11 and Table 12.

The fatality rate uses a calculation like the accident rate, only that the number of accidents that is considered is only fatal accidents or those that cause the victim to die. For example, on the Cikopo – Palimanan Toll Road section. The Cikopo – Kalijati section can be calculated using Eq. (2). The number of fatal accidents and the fatality rate per kilometer for each section of the Cikopo – Palimanan Toll Road section is then converted into fatality rates, as shown in Table 13 and Table 14.

Table 11. Accident rate per kilometer Cipali Toll Road (Route A)

Table 12. Accident rate per kilometer Cipali Toll Road (Route B)

Table 13. Fatality rate per kilometer Cipali Toll Road (Route A)

Table 14. Fatality rate per kilometer Cipali Toll Road (Route B)

The method of determining accident–prone locations (blackspots) used in this study is the UCL (Upper Control Limit) approach as a control–chart. The following is an example of the calculation steps for AEN and UCL as mentioned on Eq. (3) in identifying black spots on the Cikampek – Kalijati section of Route A.

$\begin{array}{r}\mathrm{AEN}=(\mathrm{M} \times 12+\mathrm{B} \times 6+\mathrm{R} \times 3+\mathrm{K} \times 1)=1419 \\ U C L=1046.5+2.576 \sqrt{\left(\frac{\lambda}{A E N}\right)+\left(\frac{0.829}{A E N}\right)+\left(\frac{A E N}{2}\right)}=  \mathbf{1 1 1 5 . 1 5} \\ A E N(=\mathbf{1 4 1 9})>U C L(=\mathbf{1 1 1 5 . 1 5}) \rightarrow  { Blackspot }\end{array}$       (13)

Because the AEN value in the Cikampek – Kalijati segment is higher than its UCL. The segment is classified as a blackspot are shown in Table 15.

Table 15. Identification of blackspots in every section of the Cipali Toll Road

After all the data that is owned is processed into variables that are used as the basis for making the model. The data is collected and compiled so that it can be entered and processed with the Python programming language to facilitate data processing. Modeling is intended to predict the AR and FR values, which are rates of the number of accidents or the number of fatal accidents that occur on a toll road. which are normalized by time, segment length, and traffic volume. To find out whether a data has a Poisson distribution or a negative binomial. The data will be tested to see if there is overdispersion, which is a condition when the variance of the response variable is greater than the mean value of the response variable. The estimated dispersion value, namely the residual deviance divided by the degree of freedom, which is greater than 1 indicates that the variance value is greater than the mean value. This indicates overdispersion in the data. After that, it is determined how capable the data is to fit into the model by measuring the deviance goodness of fit (GOF). A small p–value indicates that the model is not able to explain the dataset, which is measured from the deviance of the data, so, the hypothesis H0 is rejected, that the sample comes from a population with a Poisson distribution, so, the model will be developed with negative binomial regression. The results of the software output regarding the dispersion estimate and p–value for the GOF deviance for each modeling with a Poisson distribution are shown in Table 16.

Table 16. Dispersion estimation dan deviance goodness of fit test

Based on the available data from both traffic data and geometric data from the study location, it is possible to calculate the Accident Rate (AR) and Fatality Rate (FR) with the following equations for inner–city toll roads and inter–city toll roads.

Inter–City Toll Road

$L n_{(A R)}=5.251-1.121 \cdot x_1-0.358 \cdot x_3-0.013 \cdot x_6+0.421\cdot x_8+0.362 \cdot x_9$            (18)

$L n_{(F R)}=1.118-2.616 \cdot x_1+3.324 \cdot x_2-0.788 \cdot x_3-0.018\cdot x_6+0.641 \cdot x_9$   (19)

Urban Toll Road

$L n_{(A R)}=23.70-33.287 \cdot x_2-1.18 \cdot x_3+10.119 \cdot x_5-0.255 \cdot x_6-0.752 \cdot x_7+0.917 \cdot x_9$            (20)

$L n_{(F R)}=66.561-114.47 \cdot x_2+28.038 \cdot x_5-0.645\cdot x_6-33.981 \cdot x_7+1.750 \cdot x_9$            (21)

where,

X₁: VCR; (ICT=0.5–0.8), (UT=0.7–0.9)

X₂: % Veh. Type I; (ICT=0.5–0.7), (UT=0.58–0.70)

X₃: Number of toll road lanes; (ICT/UT=2–4)

X₄: Outer shoulder (m); (ICT=2–2.5), (UT=2–3.5)

X₅: Inner shoulder (m); (ICT=1–2.0), (UT=1–1.2)

X₆: Distance I (km); (ICT=25–35), (UT=15–20)

X₇: Distance II (km); (ICT=25–35), (UT=5–10)

X₈: Median barrier; (ICT/UT=Yes=1; No=0)

X₉: Blackspot location; (ICT/UT=0–5)

ICT: Variable for Intercity Toll Road

UT: Variable for Urban Toll Road

With the results of this study, it is expected that the analysis of the calculation of Accident Rate (AR) and Fatality Rate (FR) can be more easily used in improving toll road facilities both on urban toll roads and on intercity toll roads. In addition, each parameter can also provide recommendation to toll road operators to remain focused on traffic safety so that potential accidents can be avoided.

For road planners, especially for toll roads. The results of this study can be used to evaluate the design owned against potential traffic accidents that may occur so that, in the future, sensitivity to traffic safety can be further improved.