# Modeling of Traffic Flows Sustainability on Highway Network Stretches
## 1 Introduction
### Microscopic Models of the Traffic Flows  
Another class of models is traffic flow's microscopic models. Microscopic models are devoted to studies [28; 29; 30; 31; 32; 33; 34; 35; 36; 37; 38]. The models presented in the articles [28; 29; 30] are devoted to studies of automobile driving behind the car in front. Models include the standard deviation of speed and allow reproducing fluctuations in traffic flow. According to the authors of the research, the modeling results can be used in advanced motion control systems in real-time to ensure accurate prediction of delays. In the papers [31; 32; 33; 34], the average heterogeneity effects of automobiles driving in several lanes' presence for travel and the emergence of conflict situations between vehicles when changing lanes were investigated. For example, in the study [32], a factor such as weather conditions is included in the model. In the article [33], such parameters as vehicle acceleration and braking when driving behind an automobile in front are added to the listed factors. The manuscript [34] considers different driving styles and differences in vehicle parameters (speed, acceleration, deceleration, etc.). Such factors were included in the model using principal component analysis and the \(k\)-means clustering method. According to the authors, considering such factors allows for increasing the microscopic mathematical models' adequacy to a real road situation and predicting emergencies and traffic jams occurrence. Microscopic models include models for traffic situation simulation at intersections [35; 36; 37]. Investigation [35] considers an integrated microscopic model of transport flow for modeling vehicle maneuvers in conditions of their interaction. The model is designed on a cluster approach and considers the difference in driver response. The study [36] proposes a new method for vehicle trajectories simulating in two-dimensional space, considering their speed. The study [37] explains delays at unsignaled intersections and their entrance. A simulation was carried out based on technical parameters' data of the road infrastructure (road signs, markings, the presence of barriers reducing the driver visibility, etc.) at the intersections themselves and when approaching unsignaled intersections. Studies [38; 39] show the effect of vehicle stability on traffic flow sustainability while driving. According to the authors, an important aspect is knowing how the vehicle behaves depending on its driving trajectory. The authors show the automobile speed stability in the traffic flow using the example of a two-axle tractor and a semi-trailer. In this case, linear and non-linear wheel slip hypotheses are considered. It was concluded that the studied parameter significantly affects road train speed stability and the entire traffic flow sustainability, mainly if it contains a large percentage of trucks. In papers [40; 41], comparable studies are carried out reproducing a decrease in throughput at exits from highways and entrances to highways. The authors identified one of the main weaknesses of microscopic modeling of traffic at the exit and entrance to the highway--this is a decrease in throughput. The forced lane change model is proposed for vehicles entering the highway. The study [42] proposes a features adaptive-R extended Kalman filter (AREKF) using a specific technique for traffic density estimation. The flow density estimate is selected as the basis criterion for traffic flow sustainability. The simulation was carried out for a highway stretch. This study does not consider the impact of other factors on traffic flow sustainability, which is a limitation. The authors propose a new algorithm for mixed traffic control at unsignaled intersections in the paper [43]. This approach is carried out based on delays accounting during passing intersections. Although the experiment was conducted on a microscopic model, the approach is common and corresponds mainly to macroscopic modeling. The criterion for traffic flow robustness is poorly represented.