# Modeling of Traffic Flows Sustainability on Highway Network Stretches
## 1 Introduction
### General Models for Solving the Real-Time Traffic Management Problem and Predicting Traffic Flows  
In the topic's context of our research, several prominent works can be distinguished on creating models [7; 8; 9; 10] and modeling traffic flows in urban highway network sections [11; 12; 13; 14; 15; 16]. Approach [7] proposes to unify two commonly used evaluations of traffic flow sustainability: probabilistic analysis of driving instability, accounting random nature of traffic speed, and analysis of non-fatal accidents. The method is used due to online monitoring by highway network stretches. It is acceptable on a road network that is equipped with appropriate controls. However, the approach falls short of a comprehensive sustainability assessment, considering the road environment and driver's behavior. Study [8] presents traffic-changing possibilities, considering visibility on highway sections near intersections. The authors proposed a 3D model evaluating changes in the traffic flow parameters based on road infrastructure at intersections. The study offers only one sustainability criterion. Papers [9; 10] describe traffic sustainability dependencies on truck delays during route passes on urban highways. Regrettably, these studies only relate to sustainability indirectly because criteria for assessing traffic flow robustness weren't established. However, these studies identified a group of factors that slow down other vehicles in traffic. Today, using intelligent transport systems is carried out not only for assessing traffic flow parameters but also for forecasting. Studies [11; 12] describe how during predicting traffic flow, one can consider the geometric speed of the driver's driving in different weather and climatic conditions (fog, clear weather, fog with an on-board detection system, etc.) [11]. The second research in the same direction was carried out on the indirect road section, considering the driver's behavior simulation due to poor visibility, particularly fog. The results of these two studies are shown in examples of Brazilian highways. In  
Figure 1: Classification of methods and models for solving traffic management problems. our opinion, despite approach innovation, it evaluates traffic flow sustainability only from one perspective. Traffic forecasting is carried out by comparing the expected active traffic management schemes for the four busiest highways in England [13]. This approach will improve sustainability and energy independence. The study shows only a general assessment and directions for finding solutions to increase robustness. Specific criteria are not applied, which is a lack. Applying neural networks for driving speed prediction is another direction to improve traffic flow sustainability. The study is promising due to the smart cities' concept [14]. However, significant statistics are needed for such an assessment. The challenges of implementing neural networks are often linked to issues that arise during their training, such as self-learning duration and tuning quality. The solution is a hybrid algorithm using, considering data lack and factors restrictions [15]. Prediction of traffic flow parameters is provided according to signal retrospective [16]. In this case, the model accuracy could be doubted, especially when there are no signals or have hopping values that exceed the extreme traffic flow behavior. The above-described models are general and have several restrictions on application but further highlight the significance of chosen research direction. Therefore, the criterion design for transport flow robustness should be based on different groups of factors, their modeling, assessment, and ranking due to each value. Therefore, it is essential to examine each mathematical model type depicted in Figure 2 in greater detail. Because our research is completely correlated with such an approach. According to the above, it is possible to clearly identify knowledge gaps in current scientific papers devoted to traffic flow sustainability assessment based on mathematical modeling.