## 7 Conclusions  
In summary, the proposed TSMA algorithm was used to develop a transport network model. The presented case study covered three main origin nodes and one destination node. Based on the characteristics of the transport links, a numerical analysis of the traffic flow distribution problem was presented using nonlinear programming. The developed deterministic model of the transport system made it possible to optimize the distribution of the traffic flows within the road network. Minimizing travel time along assumed movement routes was adopted as the objective function for both approaches: the Nash equilibrium and the Stackelberg equation. The analysis presented in this paper has highlighted the utility of the proposed TSMA algorithm and nonlinear programming based on Nash equilibrium and the Stackelberg approach in solving optimisation problems related to the road transport networks. Based on three scenarios, it was found that the proposed approaches make it possible to accurately determine the optimal distribution of traffic flows in the transport network according to the adopted criteria. Increased traffic volume on individual routes in the transport system has been observed to lead to a decrease in traffic volume on some links of the road network. In the analyzed road network, the increase in traffic on the link (6.7) causes congestion and significant travel delays. This means changes in the distribution of traffic flows for the O-D pair (2,8) between the route containing the link (6,7) and the routes composed of other connections. Therefore, the \(p_{5}\) route is taken by a small number of traffic users, which results in a reduction in traffic on the (5,6) link, which is only part of the \(p_{5}\) route. This phenomenon is not intuitive and requires examining the elements that make up road networks in a systems approach, taking into account the complex mechanisms of traffic flow. A drawback of the developed transport system model is its deterministic character and the failure to take into account planned and random events that affect the distinguishing functions of the elements of the road network. Such important events include collisions, road accidents, road infrastructure renovations, and extremely adverse weather conditions. Therefore, in the next stage of the research, we will try to develop a dynamic model corresponding to a real (variable) road situation. Moreover, we hope to apply fuzzy logic to the decision-making problem, which reflects uncertainty and random components. Expanding the developed transport system model onto a larger area (than the one discussed in the paper) of the Warsaw agglomeration might also be also an appropriate direction of research. Conceptualization, M.O. ; methodology, M.O. and J.Z. ; software, M.O. ; validation, M.O. and A.L. ; formal analysis, M.O. ; investigation, M.O. ; resources, M.O. ; data curation, M.O. and J.Z. ; writing--original draft preparation, M.O. ; writing--review and editing, M.O., J.Z., J.M. and A.L. ; visualization, M.O. ; supervision, J.Z. and J.M. ; project administration, M.O. and J.M. ; funding acquisition, J.M. All authors have read and agreed to the published version of the manuscript. This research received no external funding. **Informed Consent Statement:** Not applicable. **Data Availability Statement:** Not applicable. **Acknowledgments:** This research was funded by the Military University of Technology, grant number UGB 22-835. This support is gratefully acknowledged. **Conflicts of Interest:** The authors declare no conflict of interest. **Appendix A**  
**Table A1. Abbreviations and acronyms. ** \begin{tabular}{c c} \hline \hline
**Abbreviation/Acronym** & **Meaning** \\ \hline EC-TEP & Environmentally constrained traffic equilibrium problem \\ GDDKiA & General Directorate for National Roads and Motorways \\ GPR & General Traffic Measurement \\ MST & Transport system model \\ O-D & Origin–Destination \\ PoA & Price of Anarchy \\ TSMA & Transport system model creation algorithm \\ \hline \hline \end{tabular}   
**Table A2. Notations.