# Highway Travel-Time Forecasting with Greenshields Model-Based Cascaded Fuzzy Logic Systems
## 5 Conclusions  
Accurate travel-time prediction is a fundamental component of ITS, enabling efficient route planning, reducing delays, optimizing traffic flow, and minimizing fuel consumption and environmental impact. This paper proposes a cascaded fuzzy logic system based on the Greenshields traffic flow model for highway travel-time prediction. The system consists of multiple fuzzy inference subsystems, each designed to estimate vehicle speed and travel time for specific highway segments under either congested or uncongested traffic conditions. By leveraging the mathematical relationship among traffic flow, density, and vehicle speed defined by the Greenshields model, each subsystem generates localized, real-time speed estimates that are subsequently integrated to produce long-range travel-time forecasts. Non-parametric approaches, such as machine learning methods, often require extensive data preprocessing and frequent retraining to maintain accuracy. In \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Segments of** & **Dingjin to** & **Rende to** & **Tainan to** & **Xiaying to** \\
**Highway** & **Rende** & **Tainan** & **Xiaying** & **Chiayi** \\
**System** & **Segment** & **Segment** & **Segment** & **Segment** \\ \hline Segment & & & & \\ Distance & 32 & 15 & 16 & 27 \\ (km) & & & & \\ \hline Traffic & & & & \\ Conditions & Congested & Congested & Non- & Congested \\ \hline Traffic & & & & \\ Flow & 21 & 58 & 21 & 67 \\ (\%) & & & & \\ \hline Traffic & & & & \\ Density & 85 & 78 & 20 & 25 \\ (\%) & & & & \\ \hline Predicted & & & & \\ Vehicle & 28 & 43 & 106 & 85 \\ Speed & & & & \\ (Km/h) & & & & \\ \hline Predicted & & & & \\ Travel & 68 & 21 & 9 & 19 \\ Time & & & & \\ (Minutes) & & & & \\ \hline Total & & & & \\ Required & & 1 h and 57 min & & \\ Travel & & & & \\ Time & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Predicted travel time from Dingjin System to Chiayi System. contrast, parametric models like regression analysis can offer a high predictive accuracy with statistically significant coefficients and low standard errors, but they are generally static and less adaptable to dynamic traffic conditions. The proposed fuzzy logic system overcomes these limitations by effectively handling uncertainty and imprecise input data, without requiring large training datasets. Furthermore, the system's modular and flexible structure allows easy adjustments to parameters, making it highly scalable and well-suited for dynamic, data-constrained environments. These characteristics make fuzzy logic a more practical and efficient choice for real-time ITS applications. Extensive simulations were conducted using traffic data from the Sun Yat-Sen Highway of Taiwan. The fuzzy logic model, tailored for both congested and non-congested scenarios, accurately captured the interrelationships between traffic density, flow, and speed--enabling the system to reflect real-time traffic conditions. To assess the performance of our proposed fuzzy logic system, we compare it with a traditional regression model using the same real-world dataset. In validation tests, the predicted vehicle speeds closely aligned with those generated by polynomial regression models, with discrepancies typically below 1%. The experimental results show that both the fuzzy logic and regression models produce consistent and reliable outputs. Further simulations evaluated the performance of the cascaded fuzzy logic framework for travel-time prediction along a multi-segment route from Dingjin to Chiayi during morning peak hours. Each segment was managed by a dedicated fuzzy logic subsystem, and the total travel time was obtained by summing the predicted times across segments. This segment-wise prediction strategy, based on localized traffic conditions, ensured that the system remained responsive and accurate in the face of evolving traffic patterns. Results demonstrated that the proposed framework effectively captured spatial variations in traffic flow, delivering reliable long-distance travel-time predictions.