# Highway Travel-Time Forecasting with Greenshields Model-Based Cascaded Fuzzy Logic Systems
## 3 Cascaded Fuzzy Systems Based on Greenshields Models for Vehicle Speed and Travel-Time Prediction
### Cascaded Fuzzy Logic Systems for Travel-Time Prediction  
Since Greenshields models are derived from short-range data collection and analysis, the proposed fuzzy logic system for vehicle speed prediction is effective for specific highway segments. As drivers typically travel along routes composed of several consecutive segments, each segment is equipped with its own dedicated fuzzy logic system for speed prediction. To enable travel-time prediction for an entire route leading to a destination, multiple fuzzy subsystems--each based on the Greenshields model--are linked together in series to form a cascaded system. As illustrated in the flowchart of Figure 15, each pair  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Traffic Flow** & \multicolumn{2}{c}{**Traffic Density**} & \multicolumn{2}{c}{**Vehicle Speed**} \\ \hline If & EL & OR & EL & Then & EF \\ If & EL & AND & VL & Then & EF \\ If & EL & AND & L & Then & VF \\ If & VL & OR & EL & Then & EF \\ If & VL & OR & VL & Then & VF \\ If & VL & AND & L & Then & F \\ If & L & AND & EL & Then & VF \\ If & L & OR & VL & Then & VF \\ If & L & AND & L & Then & F \\ If & Sp & OR & EL & Then & VF \\ If & Sp & AND & VL & Then & VF \\ If & Sp & AND & L & Then & F \\ If & QL & OR & VL & Then & F \\ If & QL & OR & L & Then & F \\ If & QL & AND & Sp & Then & F \\ If & ML & OR & VL & Then & F \\ If & ML & OR & L & Then & Sp \\ If & ML & AND & Sp & Then & Sp \\ If & M & AND & VL & Then & F \\ If & M & AND & L & Then & Sp \\ If & M & AND & Sp & Then & Sp \\ If & MH & OR & L & Then & Sp \\ If & MH & AND & Sp & Then & Sp \\ If & MH & OR & QL & Then & QF \\ If & QH & AND & L & Then & Sp \\ If & QH & AND & Sp & Then & QF \\ If & QH & AND & QL & Then & QF \\ If & De & AND & Sp & Then & Sp \\ If & De & OR & QL & Then & QF \\ If & De & OR & ML & Then & MF \\ If & H & AND & Sp & Then & QF \\ If & H & OR & QL & Then & QF \\ If & H & OR & ML & Then & MF \\ If & VH & OR & QL & Then & MF \\ If & VH & AND & ML & Then & MF \\ If & VH & OR & M & Then & M \\ If & EH & AND & QL & Then & MF \\ If & EH & AND & ML & Then & MF \\ If & EH & AND & M & Then & M \\ \hline \hline \end{tabular}
\end{table}
Table 8: Fuzzy logic rule set in non-congested mode.  
of consecutive fuzzy logic subsystems corresponds to two sequential highway segments. Each subsystem receives current traffic flow and density data from its respective prediction scheme as inputs. Through fuzzy logic processing, the subsystem predicts the vehicle speed for that segment. Using the predicted speed, the travel time for the segment can then be estimated.  
By cascading multiple fuzzy logic subsystems, each with traffic flow and density as inputs and vehicle speed as outputs, complex parameter relationships across a long-range route with multiple segments can be handled and analyzed in real-time, enabling accurate travel-time prediction for long-distance highway paths. An example of the cascaded fuzzy logic system, consisting of four subsystems for current highway traffic status prediction, is shown in Figure 16. Each subsystem predicts the vehicle speed for its corresponding segment, and the required travel time for each segment is then calculated. By summing the travel times for all segments, the estimated total travel time for the specified journey is obtained, with real-time updates based on the current status of the highway.  
The cascaded fuzzy logic system, designed for multiple specified segments, integrates, processes, and updates varying traffic information, thereby improving the accuracy of real-time highway travel-time predictions. This approach not only allows for the processing of long-range traffic data but also dynamically adjusts the predicted travel time in response to changing traffic conditions, enhancing the system's flexibility and adaptability.  
Figure 16: Schematic diagram of a cascaded fuzzy logic system for travel-time prediction.  
Figure 15: Schematic diagram of a single fuzzy logic system for vehicle speed prediction.