# Modeling of Traffic Flows Sustainability on Highway Network Stretches
## 3 Results
Please note that the robustness range is reduced by half compared to changes in vehicle length and does not exceed a value of \(RR=20\). Loss of traffic flow sustainability occurs at higher values of gradients. The vehicle engine power is the third most important factor that affects traffic flow robustness. Figure 6 showcases the dependencies of traffic flow robustness for varying density and velocity gradients, considering alterations in vehicle engine power. According to the presented dependencies, increasing the vehicle engine power increases the traffic flow robustness. However, the level of impact is minimal and does not surpass \(RR=7\). Loss of traffic flow sustainability occurs at even high values of gradients. Vehicle length, Figure 4, vehicle weight, Figure 5, and Vehicle engine power, Figure 6, constitute a group of design factors that characterize the vehicle and its effect on traffic flow robustness. The next set of factors can be named temporary factors that consider: the driver's reaction time to the traffic situation, Figure 7; vehicle maneuver time according to traffic situation changes, Figure 8; the total delays time driving the route, Figure 9.  
Figure 5: Dependencies of traffic flow robustness range for different values of density and speed gradients when changing vehicle weight: 1—\(M=2000\) kg; 2—\(M=10,000\) kg; 3—\(M=18,000\) kg. Figure 6: Dependencies of traffic flow robustness range for different values of density and speed gradients when changing vehicle engine power: 1—\(N_{e}=100\) kW; 2—\(N_{e}=150\) kW; 3—\(N_{e}=200\) kW. Figure 8: Dependencies of traffic flow robustness range for different values of density and speed gradients when changing vehicle maneuver time according to traffic situation changes: 1—\(t_{2}\) = 4 s; 2—\(t_{2}\) = 7 s; 3—\(t_{2}\) = 10 s.  
Figure 7: Dependencies of traffic flow robustness range for different values of density and speed gradients when changing the driver’s reaction time to the traffic situation: 1—\(t_{1}\) = 0.6 s; 2—\(t_{1}\) = 1.0 s; 3—\(t_{1}\) = 1.4 s.  
The average impact rate on the traffic flow's robustness range can be determined by analyzing the dependencies presented. Factors such as the driver's reaction time to the road situation (\(t_{1}\)) and the total delay time when driving the route (\(t_{3}\)) play a significant role in the current study. Note, that the robustness range of \(t_{1}\) and \(t_{3}\) does not exceed \(RR\) = 20. Loss of sustainability in traffic occurs at average gradients' values. The extent of the Impact on the duration for maneuver, \(t_{2}\), which can use vehicles when traffic situation changes, is presented in Figure 8. If a vehicle driver has more time to maneuver (according to curve 3), then traffic flow robustness will increase. When there is limited time for maneuvering, traffic will inevitably come to a stop (as shown in Curve 1). The robustness test value at the change of density and velocity gradient values does not exceed 6 units. The third group of factors considers features of road environment design. Such factors include lane quantity on the roadway, Figure 10; pedestrian crossings, and traffic light quantities in the controlled stretch, Figure 11.  
Figure 4:0 Dependencies of traffic flow robustness range for different values of density and speed gradients when changing lanes quantity on the roadway: 1—\(nt\) = 4; 2—\(nt\) = 2; 3—\(nt\) = 1. Figure 4:1 Dependencies of traffic flow robustness range for different values of density and speed gradients when changing total delays time driving route: 1—\(t_{3}\) = 50 s; 2—\(t_{3}\) = 150 s; 3—\(t_{3}\) = 250 s.  
Based on the displayed data, it appears that adding more lanes in the roadway results in an increased robustness criterion to \(RR\) = 22, as shown by curve 1. It helps to enhance traffic flow sustainability across a wide range of density and velocity gradients. Therefore, the probability of traffic jams is minimal.