A preliminary analysis of base saturation flow rate during first loss time and saturated time at pretimed signalized intersections

. Saturation flow rate is a key parameter essential for assessing signalized intersection capacity. The reference often used for signalized intersection planning in Indonesia is Indonesian Highway Capacity Guidelines (PKJI, 2023). In heterogeneous traffic environments, it has been observed that driver characteristics and behaviors exhibit significant variations. Therefore, this study aimed to investigate the prevailing saturation flow rate conditions at signalized intersections within Banda Aceh City. This exploration unfolded through two distinct scenarios, namely saturated time with and without initial lost time. For data acquisition, the focus was set on four signalized intersections, namely Jambo Tape, Pocut Baren, AMD Batoh, and Lhong Raya. This extraction procedure aimed to uncover insights into vehicle composition, movement patterns, and field saturation flow rate at these signalized intersections. In the aspect of analysis, a simple linear regression approach was adopted to recalibrate saturation flow rate coefficient of signalized intersections. This recalibration took into account vehicle compositions at the observation locations. The culmination of this analysis showed that in the scenario devoid of lost time under prevailing conditions, flow rate yielded S0 = 352 x Le. Meanwhile, for the scenario entailing lost time, the calculation produced was S0 = 294 x Le.


Introduction
An intersection is a point within highway network where different streams of vehicles converge and cross paths.These intersections are categorized into two types, namely signalized and unsignalized.Signalized intersections, which are commonly found on main roads in Banda Aceh City, aim to minimize traffic conflicts and manage traffic flow efficiently.[1] These intersections serve as pivotal junctures in highway network, facilitating the convergence and redirection of vehicles from diverse directions.Consequently, intersections often give rise to various traffic challenges.Highway Capacity Manual 2000 [2], developed by the Transportation Research Board (TRB, 2000), stands as the principal manual widely embraced by numerous developed and developing countries, including Indonesia, which adopted its earlier iteration.
In Banda Aceh City, signalized intersections are primarily planned according to guidelines outlined in the 1997 Indonesian Highway Capacity Manual (MKJI, 1997) [3].Presently, the design of signalized intersections in Indonesia adheres to the Indonesian Highway Capacity Guidelines (PKJI 2023) [4].Extensive studies on calibrating saturation flow rate have been conducted by Munawar (2006) [5], Susilo and Solihin (2011) [6], Meloh (2011) [7], and Masykur (2014) [8].The results indicated variations, highlighting that the distinct characteristics of each intersection contributed to the differing saturation flow rate values observed.This study centers on signalized intersections with comparable attributes but varying approach widths within Banda Aceh City.The objective is to scrutinize the correlation between the variance in approach width and the field saturation flow rate, thereby providing insight into the current conditions prevalent in the location.

Area of Study, Data Collection, and Processing
The selection of study locations was based on observations made both prior to the analysis of saturation flow rate and during the implementation phase.The study site was selected from the various intersection options with similar attributes, namely signalized and four-legged intersections.As a result, four signalized four-legged intersections in Banda Aceh City were identified.These intersections stood out due to their intricate traffic movements, diverse patterns, and differing approach widths.The selected intersections included Jambo Tape, Pocut Baren, AMD Batoh, and Lhong Raya.The data collection methodology employed centered on a survey approach, encompassing the measurement of geometric conditions at the intersections.This included acquiring the approach highway widths through direct on-site measurements.To facilitate this process, survey forms and measuring tape were used.Observations were strategically conducted during off-peak hours to minimize interactions between vehicles and surveyors.The collection of traffic flow data encompassed each intersection approach.Surveys were performed during the morning peak hours (from 06:45 to 08:30 WIB) and the evening (from 16:45 to 18:30 WIB).To record data, a drone was optimally positioned to observe departing traffic from designated approaches.A single drone was employed for this purpose, necessitating battery replacements every 20 minutes due to the limited battery lifespan.Signal timing data was directly obtained through field observation, with the surveyor using a digital stopwatch to record timings.This approach was also applied consistently to measure initial lost time.
The next step is to tabulate the data obtained from video recordings for several cycles of each intersection arm that have been extracted.The saturation time of the cycle is obtained by subtracting the end time with the start time of the cycle time.The start time of the cycle is recorded when the vehicle moves past the stop line when the green signal is on, the end time indication is recorded when the last vehicle in line has left the stop line before the red signal turns on.Saturated current data obtained from the data extraction process will be used as input data in linear regression analysis.Saturated current data input is divided into two scenario, namely saturated current data without initial loss time and saturated current data with initial lost time.
The variance in vehicle types was standardized into Passenger Car Units (PCU) using the Equivalent Passenger Car Unit (EPCU) approach from the Indonesian Highway Capacity Guidelines [4], thereby converting saturation flow rate unit to PCU.By using the linear regression approach, the averaged saturation flow rate (S0) and effective lane width data were analyzed to establish saturation flow rate (S 0 ) model.It should be noted that the model developed in this study was designed to be straightforward, aligning with its purpose for comparative analysis with saturation flow rate model [4].This alignment was consistent with the concept of simplicity underpinning the basic model in the manual, which solely incorporated the effective lane width as the independent variable.
The estimation of regression parameters was conducted using Microsoft Excel.The calibration of prediction model parameters for intersection saturation flow rate relied on data from four signalized intersections, encompassing a total of 16 intersection approaches.The produced model was subsequently validated against observed saturation flow rate through comparison with the [4] model.The result of this regression will be compare with saturation flow rate (S0) [4] and the new model of saturation flow rate (S 0 ) can represent current condition in Banda Aceh City.

Analysis method
The study employed the straightforward linear regression approach for analysis.This approach entailed quantifying the count of each vehicle type passing the signalized intersection stop line in relation to the observed saturation time in the field.The analysis method used to ascertain the vehicle composition in terms of PCU adhered to the EPCU Indonesian Highway Capacity Guidelines (PKJI 2023) [3].EPCU values, as shown in Table 1, were derived from PKJI [4], with validation for motorized pedicabs based on Sugiarto S (2021) [5].In accordance with PKJI (2023) [4], capacity of a signalized intersection was computed by multiplying the intersection saturation flow rate (J) by the total green time within a single cycle (WH) and then dividing the result by the cycle time (s).This calculation was expressed as equation (1).

C= J x (1)
Flow rate for signalized intersections was determined by multiplying J 0 by correction factors accounting for deviations from ideal conditions.In this context, J 0 represented saturation flow rate under optimal traffic and geometric conditions, leading to correction factors for J 0 equaling one.The formula for the signalized intersection saturation flow rate employed a model that incorporated adjustment factors, including the side friction (F HS ), Urban Area (F UK ), Grade (F G ), stop-line distance (F P ), left-turn (F BKi ), and right-turn (F BKa ).This saturation flow rate calculation was represented by equation ( 2).J = J 0 x F HS x F UK x F G x F P x F BKi x F BKa (2) According to PKJI 2023 [4], the basic saturation flow rate for signalized intersections stood at 600 x Le, though this value was not absolute.The value could be tailored based on the effective approach width of the intersection arms.The calibration coefficient value of 600 stemmed from empirical data drawn from diverse cities in Indonesia.This context underscored the need for a study to analyze saturation flow rate at multiple four-legged intersections.The linear regression analysis model captured relationships between two or more variables.In this model, dependent variables (y) manifested a functional correlation with one or more independent variables (xi).As per Tamin (2000) [10], the simplest form of this relationship could be expressed in equations 3 and 4: This linear regression model established a numerical connection, shedding light on how the simple regression of variables interrelated.In this context, Y signified the dependent variable, X represented the independent variable, A indicated the intercept or regression constant, B denoted the regression coefficient, and ε signified the Residual (error term).

Results and discussion
After conducting field observations, the analysis of traffic flow composition indicated that saturation flow rate were obtained during the evening peak hours.Therefore, the analysis presented in this section was based on observations made during the evening peak hours.The four intersections under observation exhibited varying cycle lengths and approach widths.Figure 2 -Figure 5 showed the existing traffic signal data (Cycle Time) for all four intersections, encompassing red, yellow, and green times.The analysis input is the approach width, shown in Table 2 capturing data for signalized intersections.This paper delved into the analysis of vehicle composition, encompassing both saturated time and first lost time conditions.Given the variability in initial lost time across intersections, a survey was necessary.Initial lost time shown in table 3. Vehicle compositions were categorized into four types, with Table 4 showing the percentages during saturated and first lost time conditions.
Motorcycles (MC) dominantly constituted the vehicle composition during saturated time at all four signalized intersections in Banda Aceh City.This dominance of MC composition persisted during the first lost time condition, although there was a rise in the percentage of light vehicles (LV) due to the clearing of MC from the intersection during the initial lost time.The field saturation flow rate, as the dependent variable, was regressed against the independent variable of approach width.Vehicle composition of saturation flow rate was divided into two scenarios, namely without initial lost time and with initial lost time.Table 5 showed the field saturation flow rate data, while Table 6 showed a summary of saturation flow rate at the intersection.The developed model in this study simplified the analysis of saturation flow rate.A simple model was chosen for comparative study with the baseline saturation flow rate model [4].This model lacked a regression constant, signifying its reliance solely on the effective approach width of the intersection.The equation for saturated time was y = 352 x in the model S0 = 352 x Le.The equation for First Lost Time took the form y = 294 x in the model S 0 = 294 x Le.The R2 value served as a parameter to assess the linearity of the equation.An R 2 value nearing 1 signified a better fit for the model.The R2 for first lost time 0,88 and R2 saturated time 0,90.Table 7 showed recapitulation of Signalized Intersection Saturation Flow Rate.The result showed the different model between comparative study with the baseline saturation flow rate model [4].The analysis results unveiled disparities between saturation flow rate values from PKJI 2023 [4] and those acquired through field analysis in Banda Aceh City.This discrepancy underscored variations between guidelines of PKJI 2023 [4] and those observed at the study location.

Conclusion
In conclusion, this study presented saturation flow rate representing four-legged signalized intersections in Banda Aceh City, based on PKJI 2023 [4].By using the simple linear regression approach, the analysis recalibrated saturation flow rate coefficient considering the approach width.Both vehicle compositions, namely "without initial lost time" and "with initial lost time," observed at the study locations were considered.The analysis results showed that under current conditions, the calculation of saturation flow rate "without initial lost time" and "with initial lost time" produced S 0 = 352 x Le and 294 x Le.

Table 2 .
Approach Width

Table 3 .
Initial Lost Time

Table 6 .
Summary Output of Saturation Flow Rate

Table 7 .
Recapitulation of Signalized Intersection Saturation Flow Rate