The model validation for trip assignment using all or nothing and user’s equilibrium method

In transportation planning, an accurate transportation model is crucial. The trip-based approach is widely used, which relies on the four-step model (FSM) for transportation modeling. The model generates an origin-destination (O-D) Matrix as the starting point, which is then used to determine traffic flow on the road network through a trip assignment. This approach is superior because the (O-D) Matrix is a result of the interaction between land use and accessibility. In Boyolali Regency, research was conducted using traffic volume data that reflected the conditions at the beginning of 2023. The gravity model was used to determine trip distribution for this study, and the Least Squares method and negative exponential function calibrated the model. The study aim is to compare the performance of All or Nothing and User’s Equilibrium assignment methods using the EMME/3 software. The results showed that All or Nothing had a higher R2 value of 0.913 compared to User’s Equilibrium’s 0.911, suggesting that the All or Nothing assignment method is more suitable for Boyolali Regency. The research predicted that the total movement of Boyolali Regency in 2023 would be 12,354 pcu/hour, with most of the movement being external-external. As Boyolali Regency is a transit area, vehicles only pass through it.


Introduction
The balance between transportation supply and travel demand is the main objective of transportation planning.Transportation planning involves the process of making decisions about future regional road infrastructure developments.Estimation of demand is an essential process in transportation planning.Some tool analysis can be used to estimate demand, one of which is transportation modeling [1].One of the most popular methods used in transportation modeling is the four-step model (FSM), which is used to estimate traffic flows in accordance with a network and travel demand representation.This model is commonly used in developing transportation policy [2].A sequential FSM is a way developed to handle the complexity of road networks.In the first step, trips are represented as trip ends, trip productions, and trip attractions, this step is called trip generation.Next, in trip distribution, trip production is distributed to match the distribution of trip attraction and to represent travel impediments (time and/or cost), resulting in a trip table.Next, in mode choice, the trip tables are essentially calculated to represent the relative proportion of trips by alternative modes.Finally, in route selection, the trip tables are assigned to the transportation network [3].
In the second stage of the current FSM, there were various methods employed.Among these, two were the Wardrop user's equilibrium and the All or Nothing approach.The user's equilibrium concept was introduced in 1976 and was applied to road networks in cities such as Winnipeg and the Parkway East.This approach was discussed in numerous articles, focusing on its implications for usage [4]- [7].The user's equilibrium is sensitive to traffic congestion.In addition, another method called The All or Nothing method has been applied in many pieces of research since All or Nothing phenomena still widely occurred [8].By implementing the All or Nothing traffic assignment in logistic transport routes, urban planners can optimize their planning and design using this algorithm.This results in a more efficient and effective logistic transport route for transportation and logistics [9].All or Nothing is not suitable for areas with heavily congested road networks [10].
In general, study locations are often identified where user's equilibrium and the All or Nothing method are analyzed for traffic assignment.However, comparing these methods can result in a more reliable model.Therefore, the aim of this research is to compare performance resulting from traffic assignment using the All or Nothing and User's Equilibrium method to get a reliable model.By integrating a valid and accurate basic transportation model with FSM, transportation planners can make more precise predictions and design more effective transportation plans.Implementing this test in Boyolali Regency is expected to guide transportation planners in having an excellent model to consider transportation policy in transportation planning.

Gravity Model
The gravity model is a commonly used and well-known model due to its simplicity.It states that the movement between the starting point (i) and the destination (d) is directly proportional to the size of the starting point (Oi) and the size of the destination (Dd), while being inversely proportional to the distance between the two.This can be expressed mathematically in Equation 1.
=   .  .  .  .(  ) dimana, Tid = The number of trips from origin zone i to destination zone d, Ai = The balancing factor for each origin zone i, Bd = The balancing factor for each destination zone d, Oi = Total moves from home zone i, Dd = Total moves from home zone d, f(Cid) = Barrier function or measure of accessibility between zones of origin and destination.

Least Squares Estimation Method
The Least Squares estimation method is a technique for calibrating the β parameters in the gravity model.Its main approach is to minimize the square of the difference between the observed data and the modeling results for calibrating unknown parameters.Equation 2 presents the system of simultaneous equations with unknown parameter β. (2)

Traffic Assignment
In the trip distribution stage, traffic assignment entails taking an origin-destination matrix and inputting it into the road network to determine the current flow on each road segment, and the total number of trips on the network being analyzed.Traffic assignment can be performed using various methods, some of which are listed below.
3 1.3.1.All or Nothing.This assignment method assumes that individuals will select a route based solely on the shortest distance without considering the impact of traffic congestion.Under the All or Nothing loading model, all travellers will have a uniform understanding of the optimal route (the shortest, fastest, or most cost-effective).However, this approach is not suitable for areas with heavily congested road networks [9]- [11].
User's Equilibrium.The first principle of the Wardrop Equilibrium Law is the self-regulation of traffic when congestion is present.This principle takes into account the impact of traffic jams and assumes that drivers are unable to alter their routes in order to reduce travel expenses during periods of congestion.

Statistical Test Indicator
To assess the performance of each estimation method, statistical test indicators were used.The coefficient of determination (R 2 ) was the indicator used, and it was calculated using Equation 3.This helped to compare the results of the different methods in terms of their statistical indicators.
The range of R 2 values is based on presented in Table 1.

EMME (Equilibre Multimodal Multimodal Equilibrium)
EMME, which stands for Equilibre Multimodal or Multimodal Equilibrium, is a professional software that is utilized to fulfil transportation modelling needs.It serves as a travel demand modelling system that can forecast transportation on an urban, regional, and national level.The research being conducted in this instance specifically employs the EMME/3 software.

Research Location
This study was conducted in Boyolali Regency and used primary arterial, collectors, and toll roads.The region was divided into 15 zones, consisting of eight internal and seven external zones.Internal zones were created through zone aggregation, merging multiple zones based on traffic movement distribution or area size.This study combined several districts to form each internal zone since not all roads reach every sub-district.External zones were located along the border of the Boyolali Regency.A map of the region used in this study can be found in Figure 1.

Research Data
While, in theory, travel is linked to people's activities, one possible way to start collecting data is to focus on the starting and ending points of trips instead of specific activities.Additionally, traffic flow data for certain roads on the road network can be the first input for this model.This research incorporates both primary and secondary data.The primary data comprises traffic flow statistics gathered from 15 survey points located in the field during morning peak hours.The survey lasted 2 hours, from 06.00 to 08.00 WIB, with readings taken at 15-minute intervals.The secondary data was obtained from various agencies in Boyolali Regency and included administrative maps, road network data and maps, road section data, population data, and land function data.

Results and Discussion
This study obtains the parameter β through the Least Squares estimation method.The resulting value for β is 0.0702, which can be used to describe the average trip cost in the resistance function.This value indicates that the average travel cost is higher than the initial assumption, with a β parameter value of 0.08.The β parameter value obtained from this study can be used to estimate (OD) Matrix in the future [13].
Based on the study conducted, it has been estimated that the total movement estimation of the Boyolali Regency by 2023 would be 12,354 pcu/hour.The study reveals that the most significant movements in the region are related to external-external travel, as depicted in Figure 2. Additionally, the figure also displays movements between zones within the Boyolali Regency.External movements accounted for the largest share of movement in Boyolali Regency, with a total of 5,432 pcu/hour or 43.97% of the total movement.This is due to the fact that Boyolali Regency serves as a transit area where vehicles simply pass through.
In Boyolali Regency, the external-internal movement was the second most significant movement, accounting for 3,540 pcu/hour or 28.65% of the total movement.This movement was because many residents who live outside the Boyolali Regency work there.Boyolali Regency has various industrial areas, likely to attract labour from outside the region.The presence of industrial and trade areas also causes people from outside the region to enter, which affects the external-internal movements within the region.
The Internal-External movement is the third largest movement in Boyolali Regency, with 2,247 pcu/hour or 18.19% of the total movement.This movement is mainly caused by residents of Boyolali Regency who work outside of the area.The main attraction for this movement is towards Surakarta City and its surrounding areas, which has seen progress in the economic, cultural, and tourism sectors and increased population.
The smallest type of movement within Boyolali Regency is internal-internal movement.In 2023, the total number of internal movements in the regency is expected to be 1,135 per hour, which accounts for 9.19% of all movements in the area.These internal movements are primarily for school commutes in the morning, as many schools are close to students' homes within Boyolali Regency.After the trip distribution process, the (OD) Matrix is charged to the road network during the trip assignment process.In this study, EMME/3 software facilitates the All or Nothing and User's Equilibrium loading methods.The validity of traffic loading is determined by comparing the R 2 value of each loading method.

Zone
In this study, traffic flow was modeled using two loading methods: All or Nothing and User's Equilibrium.The traffic flow obtained from the All or Nothing method was assigned using the EMME/3 software in the first iteration, based on the shortest path.For the User's Equilibrium method, the traffic flow was modeled through trip assignment using EMME/3 software in autoassignment mode.
Traffic assignment using the All or Nothing and User's Equilibrium loading methods produces an R 2 of 0.913 and 0.911, as shown in Figure 4 and Figure 5.The value of R2 is obtained by comparing observed and modeled traffic flows using EMME/3 software.The R 2 generated from these two methods is included in the category of very high validity.The modelled traffic flows using the All or Nothing and User's Equilibrium loading methods are highly similar to the observed traffic flows.
Road users in Boyolali Regency still take the shortest route from origin to destination without considering alternatives.One of the factors that cause Boyolali Regency to have a tendency towards the All or Nothing method of imposition is that most of the roads in Boyolali Regency have yet to experience congestion.Therefore, the All or Nothing loading method for areas that are not jammed is correct.Another factor that makes Boyolali Regency tend towards the All or Nothing approach of imposition is the road network, which is less complex than in big cities, so the All or Nothing loading method can still be used.In comparison, when analysing the R 2 values of the All or Nothing method, it was discovered that the values for metropolitan areas were lower than those of big cities.In the Bandung metropolitan areas, the R 2 value ranged from 0.519 to 0.557 [14], [15], whereas for this research with the location study in Boyolali as a big city, it was 0.913.In the case of the user's equilibrium method, the R 2 value for the Bandung Metropolitan area varied from 0.76 to 0.791 [14][15], while for the big cities (Surakarta, Sukoharjo, Boyolali), it was between 0.80 to 0.91 [16]- [19].These findings align with prior research.
To confirm that Boyolali Regency has yet to experience congestion, this study calculates the degree of saturation (DS) for the collector, arterial, and toll roads.The result is shown in the Figure 6.The survey was conducted during the morning peak hour.Of the 126 roads surveyed, only 12 had congested traffic.

Conclusion
The value of the β parameter obtained in this study is 0.0702.According to the gravity model, the estimated traffic movement distribution in Boyolali Regency for 2023 is 12,354 pcu/hour.As Boyolali Regency serves as a transit area, the most significant traffic movement will be from one external zone to another.All or Nothing and User's Equilibrium methods have high validity, with R 2 values of 0.913 and 0.911, respectively.The R 2 value for loading using the All or Nothing method is higher compared the User's Equilibrium method.This suggests that Boyolali Regency leans towards the All or Nothing method.Some people still prefer the shortest route, the trend towards the All or Nothing method could be due to the lack of congestion.
External -Internal Internal -External Internal -Internal Total Movement Movement Type

Figure 3
Figure 3 displays the desire line, which portrays the results of the movement.

Figure 3 .
Figure 3.The Desire Line of total trip of Boyolali Regency in 2023.

Figure 4 .
Figure 4. Comparison of Traffic Flows from Field Observation and Developed Model Using All-or-Nothing Assignment Method.

Figure 5 .
Figure 5.Comparison of Traffic Flows from Field Observation and Developed Model Using User's Equilibrium Assignment Method.

7 Figure 6 .
Figure 6.The Degree of Saturation of Roads in Boyolali Regency.