# Modeling of Traffic Flows Sustainability on Highway Network Stretches
## 4 Discussion  
By analyzing Equation (11), which is caused as a criterion for transport flow robustness, one can identify the parameters that impact sustainability. Regarding the above mathematical formulations by which the \(K_{2}\) gain coefficients are calculated, the transport flow sustainability is \(K_{3}\) affected by traffic density and intensity. These parameters should be calculated according to Equations (7) and (9) for each stretch of the road network or highways, which should be investigated and substituted into Equation (11). The time constants \(T_{1}\), \(T_{2}\), and \(T_{3}\) depend on driver qualification and psychophysiological properties, the fatigue rate, the dynamic properties of vehicles, and traffic conditions. The values for these parameters can be calculated using Equations (2)-(4) and then plugged into Equation (11). If the criterion value equals one, the traffic flow functions on the verge of sustainability loss. If the traffic flow sustainability is lost, the criterion value would be less than one, resulting in traffic coming to a halt due to traffic jams occurring. When the criterion value exceeds one, it indicates that the traffic flow is sustainable and operates smoothly without any disruptions or congestion. The bigger criterion value means a greater sustainability margin. The \(RR\) robustness criteria should be applied when analyzing the road network for delays during traffic and traffic jams and when designing a new urban highways network. The obtained result differs from previous studies in this field because it allows for determining sustainability loss limits by modeling--traffic jams occurring. Limit values determining transport flow density and intensity and their gradients will allow designing measures to prevent traffic jams considering multi-lane driving. These results are based on previous research discussed in papers [56; 57]. The accounting of process development dynamics is the main difference in the current study from others in the same scientific sphere. In addition to velocity and density gradients of traffic flows that are used in these researchers, the dynamic features of vehicles and the multi-lane highway nature, as well as delay time at pedestrian crossings and traffic lights, are considered. Based on theoretical studies, it has been found that the mathematical model for traffic flow sustainability has restrictions to its application. Limitations are related to source data finding for the simulation. On the controlled highway stretch, it is necessary to determine flow density and intensity, vehicles' speed, and their acceleration in traffic. Modern electronic controllers are capable of providing such measurements. In addition, statistically determined values are drivers' reaction time to changes in traffic and the appearance of pedestrian crossings and traffic lights on monitored highway stretches. It is important to acknowledge that the proposed approach has several limitations in application:  
* The study of factors that impact traffic flow sustainability was only conducted in the values range presented in Table 1;
* robustness criterion assessment was only applied for a highway stretch with a fixed length equal to one kilometer;
* the group of factors characterizing weather conditions was not considered when determining the dependencies of factors that impact the target function \(RR\);
* the robustness criterion is only applicable to evaluating traffic flow sustainability on a particular highway section and cannot be used to assess the entire urban transport network;
* \(RR\) did not directly consider the vehicle intensity, although the traffic flow density and speed gradients were used among the estimated factors. * We hope these limitations do not reduce the scientific and practical significance of the proposed approach. The next step in the research should focus on creating reliable models to measure transportation flow density and intensity. These models should also be able to predict changes in vehicle density and speed within the traffic.