# Modeling of Traffic Flows Sustainability on Highway Network Stretches
## 1 Introduction
### Macroscopic Models of the Traffic Flows  
Modeling of heterogeneous traffic flows is presented in the works [17; 18]. The authors of [17] have developed a new macroscopic model of a heterogeneous transport flow with partial connection to an automated environment based on the theory of a potential security field. In the study [18], the macroscopic model of heterogeneous transport flow considers the velocity gradient and the driver's delay time in making decisions. The research study [19] suggested a macroscopic model that utilizes the relaxation time parameter. This parameter is used as a characteristic of traffic flow density change. According to research results, vehicle interaction in traffic affects relaxation time. Relaxation  
Figure 2: Research flowchart (main steps). times include driver behavior that affects the perception and handling of road situations and related activities. Research [20] considers data set on the flows and vehicle speeds driving along the highway, accumulated by fixed sensors and classified by lanes and vehicle classes. The authors extrapolate two important pieces of data with a neural network-based learning model: the traffic jams prediction and total vehicle quantity that presumably passes through a controlled section of the route. This information is used for improving simulation accuracy. The studies [21; 22] conclude that stochastic factors significantly contribute to the destabilization of the traffic flow. The research study [21] investigated the stochastic impact on transport flow sustainability using [PERSON]'s method. Based on the obtained results, the authors concluded that the stochastic presence destabilized macroscopic models and modeling results. In the research study [22], a critical condition of transport flow sustainability was obtained. The motion of the density wave is simulated, which affects the occurrence of traffic jams. The authors of the research [23] note that successfully using macroscopic models requires calibration. According to the scientists who developed these models, it is necessary to calibrate and check real data of traffic flows. Model calibration determines the optimal set of parameters that minimizes the discrepancy between simulation results and actual data. In addition, model validation is performed to confirm calibrated model accuracy. A sustainable control model [24] considers uncertainties that could arise while driving (vehicle entrance/exit from the highway, traffic jams occurrence, and other factors.). The model defines the management effect that wholly improves transport network functioning and considers only traffic features. In our opinion, it is not enough to fully assess the traffic flow robustness. The authors propose to use the ensemble method for short-term forecasting of traffic parameters [25]. Therefore, the success of this method relies heavily on the quantity of data gathered regarding the traffic flow. The model considers speed, density, occupancy, and a sufficient degree of traffic. The state of the road infrastructure and driver behavior are not considered. The study proposed combines multitask learning (MTL) with a graph convolution network [26]. The current model is combined since it includes several graphs characterizing the state of the transport network at different intervals. In our opinion, the approach is interesting but requires significant resources to accumulate traffic information. Also, the model becomes bulkier every time. It complicates the efficiency of calculating the traffic flow robustness. The paper [27] proposes a deep-learning architecture using models of folded sparse auto-encoders (SAE). It gives possibilities to accurately assess the traffic flow by the whole network with an already deployed set of sensors. Despite the promise, the model requires accurate and fine-tuning. Unfortunately, this is not always possible.