# Speed-Flow-Geometric Relationship for Urban Roads Network
## 4 Results
### Models Application  
The final speed-flow-geometric model from Table 6 was used for predicting the average travel speed (ATS) values on the Johor roads segment. Each surveyed urban road group model enclosed a set of independent variables (longitudinal parameters, LP) with estimated free-flow speed (FFS), and range of traffic volume (TV) as shown in Table 7. A pre-specified range of values was used for the longitudinal parameters (LP) for each surveyed urban road groups of the urban roads segment. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameters**} & \multirow{2}{*}{**Group 1**} & \multirow{2}{*}{**Group 2**} & \multirow{2}{*}{**Group 3**} & \multirow{2}{*}{**Paired _t_-Test between the**} & \multirow{2}{*}{**Paired _t_-Test between the**} & \multirow{2}{*}{**Paired _t_-Test between the**} & \multirow{2}{*}{**Estimated _ATS Using MOM**} & \multirow{2}{*}{**Final Model**} \\  & & **Observed** & & & & **(veh/h) and the** & \\  & & **Model A (veh/h)** & & & **Using Model B (pcu/h)** & & \\ \cline{2-8}  & & **\(t\)-Value** & _p_**-Value** & _t_**-Value** & _p_**-Value** & _p_**-Value** & \\ \hline
[M0, NL1, SF0] & \(-\)1.05 & 0.304 * & \(-\)1.958 & 0.065 * & 2.35 & 0.03 & Model B (pcu/h) \\ \hline
[M0, NL1, SF1] & \(-\)0.418 & 0.682 * & 0.847 & 0.411 * & 1.356 & 0.197 * & Model A (veh/h) \\ \hline
[M0, NL2 SF1] & \(-\)0.525 & 0.609 * & \(-\)2.35 & 0.037 & Ineligible & Ineligible & Model A (veh/h) \\ \hline
[M1, NL2, SF0] & \(-\)0.94 & 0.368 * & 1.081 & 0.308 * & 3.95 & 0.003 & Model B (pcu/h) \\ \hline
[M1, NL2, SF1] & 1.00 & 0.339 * & 3.546 & 0.005 & Ineligible & Ineligible & Model A (veh/h) \\ \hline \hline \end{tabular}  
* _p_-value > 0.05, the difference is not significant.  
\end{table} 
Table 6: Summary of models’ validation results for the five successful models based on the paired _t_-test. A series of linear trend lines for each value of the longitudinal parameters (LPs) were used to illustrate the variation of the average travel speed (ATS) against the traffic volume (Figures 9-11). These lines were obtained by substituting the measured values of traffic calming speed density (TCSD), intersection density (InterSD), and access driveway density (AccessD) parameters into the developed speed-flow-geometric relationship equations for the five categories of cross-sectional parameters (median, number of lanes, and side friction conditions). These longitude parameters were assumed to have values within a certain range between two extremities. The highest value did not exceed the intercept value of the developed equation. This was due to the fact that only the intercept value in the equation had positive sign whereas all other longitudinal parameters in addition to the traffic volume (TV) had negative signs. Consequently, if they were bigger than the intercept, the estimated average travel speed (ATS) became zero (or negative), indicating that this speed-flow-geometric relationship equation is inapplicable. Parallel to the definition of the highest applicable value of the longitudinal parameter in the equation, a line of the speed-flow relationship could be drawn if we solve the equation for average travel speed (ATS) and traffic volume (TV) (in the case where the traffic volume is zero and the average travel speed is zero). Next, for each model, a sensible decrease in the greatest value of the longitudinal parameter, this incline line of speed-flow relationship might be traced many times downward. When the inclined speed-flow relationship line provided an irrationally small value of average travel speed (ATS), this iteration ended. In short, for each of the five urban road's category, distinct series inclined lines of speed-flow relationship were developed.