# Heuristic Fuzzy Approach to Traffic Flow Modelling and Control on Urban Networks
## 6 Conclusions  
Depending on the desired outcome, the fuzzy or the classical controller should be used. If the goal is to minimise total travel time and maximise the flow, the classical controller would be a better choice. However, if the delay in travel time per car unit is considered, the choice of preference should be the fuzzy controller with Fuzzy Controller 3 (three-valued logic for inputs and five-valued logic for outputs). Overall, Fuzzy Controllers 1 and 2 (two-valued logic for inputs) show the worst results compared with Fuzzy Controllers 3 and 4 (three-valued logic of inputs) and compared with the classical controller. For this study, the benchmark was the classical controller. The goal of the research was to design a network of intersections represented as a hierarchical system of traffic \begin{table}
\begin{tabular}{c c c c c c} \hline  & **Fuzzy Controller 1** & **Fuzzy Controller 2** & **Fuzzy Controller 3** & **Fuzzy Controller 4** & **Classical Controller** \\ \hline Flow (veh/h) & 3121 & 3111 & 3121 & 3115 & 3125 \\ \hline Total travel time (h) & 61.73 & 63.64 & 60.84 & 64.25 & 59.1 \\ \hline Delay (s/km) & 66.6 & 67.35 & 59.68 & 61.32 & 60.51 \\ \hline Travel time (s/km) & 133.19 & 133.95 & 126.27 & 127.91 & 127.1 \\ \hline \end{tabular}
\end{table} 
Table 21: Traffic indicators for the five controllers. Figure 7: Travel time per car measured in seconds per kilomet. light-regulated intersections managed by fuzzy controllers. These fuzzy controllers were designed and simulated separately in the hierarchical network according to traffic indicators such as flow, delay, travel time and total travel time. Overall, the fuzzy controllers lead to better results for the individual units of vehicles, while the classical controller leads to better results in terms of system-wide behaviour. The main contribution of this study is the development of a hierarchical transport network for an urban environment with interconnected junctions and the use of a traffic light control system for this network by using four different fuzzy controllers and one classical controller. The main novelty of the study is that it examines, in a heuristic setting, the performance of the four different fuzzy controllers on the hierarchical system and compares them with a classical controller that is used as a benchmark. The main relevance and significance of this study in relation to previous works is its systematic approach that guarantees the good capability of the associated expert based heuristics and makes it potentially useful for policy decisions in the chosen application area. Future research will focus on the generalizability and scalability of the experiment so that larger or more complex urban networks can be simulated and tested with this method. It will also consider data-driven optimisation techniques for the fuzzy controllers in the context of scenarios that are different from the one investigated in this paper, as well as more robust statistical analysis of the data. It will also focus on a more advanced implementation of the current fairly basic heuristic fuzzy approach that will be complemented with an associated learning process based on machine learning techniques. Conceptualisation, A.G., B.V., Y.B. and A.I. ; methodology, A.G., B.V. and A.I. ; software, B.V. and Y.B. ; validation, B.V. and Y.B. ; formal analysis, A.G.; investigation, B.V. and Y.B. ; resources, Y.B. ; data curation, B.V. and Y.B. ; writing--original draft preparation, B.V. and Y.B. ; writing--review and editing, A.G. and B.V.; visualisation, B.V. and Y.B. ; supervision, A.G.; project administration, A.G.; funding acquisition, not applicable. All authors have read and agreed to the published version of the manuscript.