Model development of road performance indicator-related travel time using international roughness index: a case study national road network of Sulawesi

. The International Roughness Index (IRI) is widespread in measuring road performance. However, travel time is a more critical benchmark in measuring road performance and the transportation system's performance. Therefore, new studies and models are needed to determine the relationship between IRI and travel time to obtain a segment performance function model influenced by road conditions. The study begins with a traffic condition survey to obtain vehicle travel time data on various road conditions. Assessment of road conditions uses the value of road surface flatness obtained from the results of Hawkeye measurements by carrying out actual travel throughout the national road network of Sulawesi Island. The study results show that the IRI value greatly influences the achievement of travel time as a road performance indicator in Indonesia. The equation of the relationship function of the vehicle travel time in free flow with the value of the flatness of the road surface is 𝑦 = −6,062𝑥 2 + 1,068𝑥 − 1,0873 with R2 0,9314. At the same time, the equation of travel time as a function of road performance is 𝑡𝑎 = 𝛼 1 ( 𝑣 𝑐 ) 𝛽 + 𝛼 1 ( 𝑣 𝑐 ) − 6,062𝑥 2 + 1,068𝑥 − 1,0873 .


Introduction
The road is a means of transportation that is vital in life.It can facilitate the economy, culture, and distribution of goods and services, become an access link between regions, and improve the people's economy and standard of living [1].It is a land transportation infrastructure that includes all parts of the road, including complementary buildings and equipment intended for traffic on the ground.The road network is a crucial land transportation infrastructure, especially for the sustainable distribution of goods and services [2].Transportation intentionally moves goods and services from one place to another.An excellent level of road service facilitates the movement of people and goods.So, road damage can affect economic activity, quality of life, and the environment in an area [3].Optimization in road maintenance is needed to obtain proper pavement conditions even with limited funds using a knowledgebased planning strategy [4].
The primary function of road pavement is to spread the wheel load to the surface area to provide a solid structure for support traffic loads, a flat surface, and skid resistance on the pavement surface.However, pavement damage is caused by exceeding the capability limits of each road pavement element.Therefore, road conditions must remain prime to provide safety and comfort for users [5].According to WHO, nearly one million people are killed annually, three million are disabled for life, *Corresponding author: hera@ce.its.ac.id and thirty million are injured in road accidents.By 2020, road accidents are expected to be the third most important contributor to the global burden of disease and injury [6].
It has been discussed previously that travel time is an essential benchmark in measuring traffic conditions and is generally used in assessing the performance of transportation systems [7].However, although many studies on travel time have been carried out, few studies are related to the factors that affect travel time on roads in developing countries such as Indonesia.In addition, studies related to the influence of external factors outside the vehicle and the driver have not been found that reach the influence of road surface conditions, especially road surface flatness.This situation is understandable because there is generally a locus of research in developed countries whose road conditions generally have excellent and uniform roughness values.
As the Main Performance Index in measuring service levels in Indonesia, travel time highly depends on various supporting factors.In addition to connectivity and terrain conditions, road pavement conditions significantly affect this achievement.Various studies have stated that Roughness can measure the surface condition of road pavement.Parameters of road pavement conditions, such as the International Roughness Index (IRI) and Road Damage Value (NK), are very commonly used to determine the performance of road services in addition to parameters from the traffic side [8].Another function of a good IRI value is to increase the safety of road users [9].The ease and popularity of using IRI as an initial indicator in determining the level of road performance can be a further model to realize an optimal level of road performance.Various latest technologies have been used in measuring IRI with computer vision-based methods [10].The selection of IRI associated with time travel will be interesting if it is made in a dynamic model.
An excellent national road network must be able to provide a quality level of service.The condition of the road structure, with the increase in traffic volume and natural disturbances, is expected on Sulawesi Island.This condition can cause a decrease in the quality of the road surface.The decrease in the road surface quality, as measured by Roughness, will reduce the level of safety and comfort for road users.In response to the decline in road quality, drivers will drive their vehicles at a lower speed.The decrease in roughness value has the potential to increase travel time and affect the level of road performance.So, we need a new study and modeling to determine the relationship between IRI and travel time to obtain a model of the segment performance function influenced by road conditions.

Literature review 2.1 Travel time reliability
Time travel can be defined as the elapsed time when a vehicle moves between two spatial positions.Of course, this definition applies to all modes of transport (or a combination thereof) regardless of the inherent differences.This is expected because travel time is usually understood as a one-dimensional quantity.Furthermore, the travel time can be divided into several components depending on the analyst.For example, the travel time of public transport modes tends to be divided into waiting time, time in the vehicle, transfer time, and other variables [11].Based on the difference in the road network, travel time can be divided into two components: free-flow time and total time.The former refers to the time the driver takes to arrive at his destination without experiencing any (or very little) traffic.The latter refers to increased travel time due to variations in traffic conditions.This variation can be predictable, like rush hour traffic jams, or unpredictable, like vehicle accidents [12].
Predictable changes in travel time, such as traffic jams, are easy for travelers to respond to this condition.Various adjustments can be made to offset additional costs (e.g., leaving early to avoid arriving late at work).Traffic jam events that cause variations in travel time are exciting topics in traffic theory science [13].In transportation research, morning peak hour congestion is considered a classic trip scheduling problem under deterministic traffic conditions.Several recent studies have presented solutions to problems with a single deterministic congestion model between origin and destination, fixed and homogeneous travel requests, and departure times [14].Variations that cannot be predicted are directly related to the uncertainty of travel time, consisting of several main variables.This uncertainty has been divided into three elements: traffic flow, weather, and incident [15].
Travel time reliability is closely related to unpredictable variations.This situation suggests that travelers choose under an uncertain environment as they may need to predict the exact time of travel before scheduling their trip, such as choosing a departure time [16].However, regarding predictable variation, travelers can adjust their preferred departure time and remain confident of arriving on time at their destination.This condition applies even in transportation systems with high traffic jams.Therefore, different approaches have been proposed for the travel time reliability model by conducting various studies with other variables [17].
Several studies conclude that factors can affect travel time, including increased traffic, traffic demand, poor weather, and Traffic Accidents [18].Furthermore, the literature study was expanded by exploring other research on travel time, especially related to factors affecting travel speed or time.Several types of research have been conducted for at least 15 years.At the same time, they are aimed at providing a review of various research that have been and are being carried out related to travel time reliability [19].Two main focuses of research related to travel time variability are studied, namely travel behavior and transport networks.The first type is behavior that influences decision-making, individuals' choices, and the considerations involved with these factors.The second is in the transport network and system performance appraisal, where regular or irregular variations such as transport network accidents are still considered [20].

Speed average and time travel
This section briefly shows the relationship between travel time, reliability, and average travel speed.Various studies have shown a strong correlation between vehicle travel time and average travel speed.For example, some studies show that during off-peak hours, speed and travel time are at their free-flow values [21].However, during peak hours, the average speed decreases to less than half the free-flow speed, and travel time increases to 4 times the free-flow value.On the other hand, even though the average speed at night is lower than the freeflow speed, the travel time is still close to the free-flow value [22].Since, at night, fewer vehicles are contributing to the average segment speed, a single vehicle traveling at a speed slower than the main traffic flow can significantly reduce the average speed [23].
A place far away may not necessarily be said to have low accessibility, or a place nearby has high accessibility because there are other factors in determining accessibility, namely travel time [24].Travel speed is the average traffic flow speed (km/hour) calculated from the road length divided by the average travel time of vehicles passing through the road segment.Travel time is the vehicle's average time to travel a road segment of a certain length, including all stop-time delays.
The procedure for trip loading on the road network can use various methods, including the capacity restrained method, which is a loading technique that balances the volume on each road segment that is charged based on the conditions and characteristics of the road used as a counterweight.Travel time conditions and volume on the road segment largely determine this method.The relationship between travel time and the volume of a road segment describes the type and characteristics.This relationship is generally a function of road segment performance.The road segment performance function approach model developed is based on the graph in the Indonesian Highway Capacity Manual (ICHM), which is mathematically stated as Equation 1.

Roughness
International Roughness Index is a parameter to determine road surface flatness.The Roughness parameter is presented on a scale that describes the unevenness of the pavement surface felt by the driver.IRI is one of the functional pavement performances which is very influential on riding quality.The IRI value is the value of the surface unevenness, which is the cumulative length of the surface up and down per unit length expressed in m/km [25].Parameters of road pavement conditions, such as the International Roughness Index (IRI) and the Damage Value (NK) in Indonesia, are very commonly used to determine road service performance in addition to parameters from the traffic side [8].
The value of road surface roughness is obtained with the NAASRA measuring instrument and then calibrated using a dipstick calibration tool to produce the IRI value in m/km.NARA stands for National Association of Australian State Road Authorities, which created a method for measuring road surface roughness.The measurement method known in general is the NAASRA method using the NAASRA rough meter measuring instrument to measure the unevenness of the road surface [26].This tool is mounted on the rear axle of the test vehicle wheel.The basic principle of this tool is to measure the amount of vertical movement of the rear axis at a certain speed.The vertical movement at a certain distance is expressed in IRI in meters per kilometer [27].
This tool is installed on a station wagon-type vehicle; if this type of vehicle is unavailable, it can be replaced with a four-wheel-drive Jeep vehicle or a pickup with a cover on the tub.Before surveying the road surface's unevenness, it is necessary to measure the longitudinal profile with the Dipstick Floor Profiler [28].Testing on the segment is carried out at least eight times, selected from roads with very flat to very uneven surfaces with a segment length of 300 meters plus 50 meters each at both ends.After the test is carried out, the correlation equation between the Dipstick Floor Profiler and the NAASRA measuring instrument is determined on the IRI value [27].The survey vehicle was run at a 30 km/h speed to record the road surface's unevenness.

Methodology
This research was conducted on the national road network of Sulawesi Island because almost all have the same character.The road corridor data that becomes the research locus can be seen in Table 1.The primary data needed is the vehicle's travel time, which serves as input for calculating the vehicle's travel time in free flow.Furthermore, the volume of vehicle traffic serves as an input for calculating the travel time of vehicles in free flow.Primary data collection is done by documenting the traffic in the segment under study for later recording and observing the value of vehicle travel time in free flow.The vehicle travel time and traffic flow from traffic documentation videos were obtained using Hawkeye survey vehicles.At the same time, the secondary data needed are maps, general road data, IRI, and pavement serviceability.Analysis of the relationship between IRI and travel time in free flow (ta') is carried out on the data needed to input the calculation of vehicle travel time in free flow.The calculation of vehicle travel time results in free flow, and road grades are carried out through polynomial regression of order 2. The parameters in this model consist of International Roughness Index (IRI), Vehicle Travel Time in Free Flow (ta'), traffic volume (v), road capacity (c), and vehicle travel time (ta).The input data used is the IRI value from the survey results of road conditions and travel time on Free Flow which is calculated based on the road segment performance function based on the IHCM graph.Road corridors and characteristics can be seen in Table 2.The traffic survey was carried out under Free Flow Speed (FV) conditions.According to IHCM, FV is the speed at zero current when the driver chooses to drive a motorized vehicle without being influenced by others.FV data were obtained through field observations, where the regression method determined the relationship between free flow velocity with geometric and environmental conditions.The free flow speed of light vehicles has been chosen as the essential criterion for the current road segment performance (Q) = 0.The free flow speed for heavy vehicles and motorcycles is also a reference.The free flow rate for passenger cars is usually 10-15% higher than other types of light vehicles.
As an indicator, the IHCM is a guide for the analysis, planning, design, and operation of road traffic facilities in Indonesia, a product of empirical research conducted in several places that are considered representative of characteristic traffic conditions in the territory of Indonesia.The resulting analysis parameter values are not absolute numbers and may change occasionally and from location to location.The period since the publication of the conditions experienced by road transport infrastructure and its users, both in quantity and quality, is now following traffic characteristics and infrastructure conditions at that time.This condition is expected to change the analysis parameters in IHCM.In addition, parameter non-conformance analysis can produce technical design results that may need to be revised.
Trip distribution estimates based on the traffic database are mostly concentrated in Makassar, Manado, Palu, Gorontalo, and Kendari.Trips from and to Makassar constituted the highest number of trips, while the number of long-distance trips between provinces, for example, Makassar to Manado, is tiny.Estimated traffic generation and pull-by zone show that Makassar City has the highest traffic generation/attraction.The city, which is located adjacent to Makassar City, is a city with almost the same value.The highest traffic generation/attraction at the provincial level is in South Sulawesi, including Makassar City.
Analyzing intermodal relations is quite challenging, as well as obtaining maximum results regarding transportation in and around Sulawesi Island.This condition occurs mainly because air and water traffic on Sulawesi Island covers many inter-island and international movements.Therefore, using intermodal transportation by residents of Sulawesi Island is difficult to obtain due to limited data and information.Another factor that causes this difficulty is the limited time and funds to conduct large-scale surveys.
In addition to the survey, this paper also analyzes the average space speed (U-SMS) for all links on the researched road segment.The estimated travel time of the vehicle in this study uses the Instantaneous model method based on spot speed data that has been processed into two-speed variables, namely the average time speed (TMS) and the average space speed (SMS).The estimated travel time of the vehicle is carried out for these two-speed parameters.The travel time for each link is calculated as the link length divided by the local average speed.The calculation of the vehicle's estimated travel time based on the average speed data is 2.31 hours/100 km with a standard deviation of 0.16.
Pay attention to the various theories underlying this research and the visual and graphic analysis results in Fig. 2. In that case, IRI closely correlates with vehicle speed in each corridor.The better the road conditions, the smaller the Roughness, and the higher the vehicle speed.By using vehicle speed in free flow on a road segment that has a specific IRI value, an analysis of the relationship between the IRI value and vehicle speed will be carried out.The input data for the analysis can be seen in Table 3.International Roughness Index is a parameter used to determine the road surface's unevenness level.The roughness parameter is presented on a scale that describes the unevenness of the road pavement surface felt by the driver.The unevenness of the pavement surface is a function of the longitudinal and transverse sections of the road surface.Besides these factors, Roughness is also influenced by vehicle operational parameters, including wheel suspension, vehicle shape, vehicle level position, and speed.These conditions directly affect the vehicle's speed, as seen in Fig. 3.

Fig. 3. Relationship between speed and IRI.
Based on the analysis of the equations obtained using a polynomial order two approaches, we get an Equation 2 that describes the relationship between the IRI value and the speed that vehicles can achieve on the corridors of national roads on the island of Sulawesi. = −6,062 2 + 1,068 − 1,0873 (2) y = speed (km/hours) x = IRI (m/km)

Travel time in free flow
The value of Vehicle Travel Time in Free Flow on the researched road segment results from calculating the road segment performance function based on the ICHM graph.Analysis of capacity uses Equation 1 with the data obtained and adjusted from the survey results.
It can be seen in Table 3 that the Manado-Gorontalo, Parepare-Makassar, and Makassar-Watampone Road segments are the road segments with the highest road capacity compared to other road segments.This difference is because the road segment has a higher side resistance value than others.Furthermore, the calculation of travel time on free flow is based on the equation of the road performance function based on the ICHM graph.The results of the ta' analysis based on the data above and the values of 1 α1, α2, and β are the results of interpolation using equation 1 can be seen in Table 3.

Model of relationship roughness and travel time
Furthermore, the relationship between IRI and travel time travel on free flow is analyzed.This analysis is slightly different from the previous analysis, which only includes data on the average speed of each segment.In this analysis, the actual traffic flow conditions in the field have been considered.Based on the IRI and ta' data in Table 3 for the road segment under study, the relationship between the two can be analyzed using Polynomial Order 2. The graph of the relationship between IRI and travel time in Free Flow (ta') can be seen in Fig. 4.
The Roughness value that affects travel speed can be developed into a road performance model.The road segment performance function based on the ICHM graph changes the travel time of vehicles on free flow by including the relationship function between travel time in free flow and the value of road surface flatness (Equation 3). = −6,062 2 + 1,068 − 1,0873 (3) y = free-flow travel time (hours/100 km) x = IRI (m/km) Meanwhile, the segment performance function based on the Indonesia Highway Manual Capacity chart and the relationship between free-flow travel time and IRI (Equation 4).In Fig. 4, the free-flow travel time is related to the value of the road surface flatness.The higher the value of the flatness of the road surface, the more travel time required by a vehicle.The equation of the relationship function of vehicle travel time in free flow with the value of road surface flatness can be seen in Equation 3and road performance in Equation 4.

Conclusions
Based on the calculations and analyses that have been carried out based on data obtained from the national road corridor on the island of Sulawesi with the assumption that they have the same characteristics.Vehicle travel time in free flow is related to the road surface flatness value.The higher the value of the flatness of the road surface, the longer the travel time on free flow required by a vehicle.The equation of the relationship function of the vehicle travel time in free flow with the value of the flatness of the road surface is  = −6,062 2  There is a limitation to this paper because only ten characteristic indexes are analyzed.In future studies, more characteristic indexes should be selected to explore the impact of the characteristic indexes on the time travel of road networks.In addition, simulation should still be extended, providing a further detailed comparison.
) ta = Travel time ta' = Free flow travel time v = Volume c = Capacity , = Parameter

4 Result and analysis 4 . 1
Travel time variabilityThe traffic volume, speed, and travel time surveys were conducted for five days on weekdays in the first semester of 2022.The traffic volume survey started at 07.00 WIB for 12 hours.The location of observations in the collection of traffic volumes is carried out on all corridors of national roads on the island of Sulawesi.Based on the results of field observations, the traffic volume on the existing road conditions is then grouped into ten main corridors.The average travel time and vehicle speed results of traffic surveys conducted on weekdays can be seen in Fig.1.

+ 1 ,
068 − 1,0873 with R 2 0,9314.At the same time, the equation of travel time as a function of road performance is

Table 3 .
Capacity analysis and free flow travel time.