# Speed-Flow-Geometric Relationship for Urban Roads Network
## 4 Results
### Developed Models Features  
As mentioned earlier, 14 regression models for the traffic volume (TV) scenarios in veh/h and pcu/h were developed and summarized in Table 5. Four models were found to be insignificant based on their \(p\)-value above 0.05, representing the surveyed urban roads groups with cross-section parameters features without median, 2-lanes and low side friction [M0, NL2, SF0]; and 1 median, 3-lanes and low side friction [M1, NL3, SF0]. Consequently, 10 succeed models represented the surveyed urban roads groups for cross-section parameters features [M0, NL1, SF0], [M0, NL1, SF1], [M0, NL2, SF1], [M1, NL2, SF0], and [M1, NL2, SF1] for both traffic volume in veh/h and pcu/h. All the final model equations for the cross-section parameters groups were explicitly written for the first time. Clearly, all these models showed reasonable coefficient of determination (R\({}^{2}\)) values that varied in the range of 0.62 to 0.97. In addition, the significant \(p\)-values obtained from the F-test were below 0.05 with small standard errors in the range of 0.64 to 3.37. Figure 5: Percentage quantity of vehicles classes over surveyed urban roads. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{4}{c}{**Group A (TV in veh/h)**} & \multicolumn{4}{c}{**Group B (TV in pev/h)**} & \multicolumn{1}{c}{**Regression Results**} \\ \cline{3-8}
**No. ** & **CSP Category** & \multicolumn{1}{c}{**Model’s Equation**} & \multicolumn{1}{c}{**R\({}^{2}\)**} & \multicolumn{1}{c}{**F-Test Value**} & \multicolumn{1}{c}{**Model’s Equation**} & \multicolumn{1}{c}{**R\({}^{2}\)**} & \multicolumn{1}{c}{**F-Test Value**} & \multicolumn{1}{c}{**(\(\chi\) = Success)**} \\  & & **(Standard Error)** & **(Significance)** & **Model’s Equation** & **(Standard Error)** & **(Significance)** & **(\(\mathcal{O}\) = Full)** \\ \hline
1 & [M0, NL1, SP0] & \begin{tabular}{c} ATS = 39.70 \(-\) 0.017 TV \\ 0.26 AccosD \\ \end{tabular}  & \begin{tabular}{c} 0.71 (1.87) \\ (0.00) \\ \end{tabular}  & \begin{tabular}{c} 42.53 \\ - 0.26 AccosD \\ \end{tabular}  & \begin{tabular}{c} ATS = 39.39 \(-\) 0.02 TV \\ - 0.26 AccosD \\ \end{tabular}  & \ \begin{tabular}{c} 0.78 \\ (1.99) \\ (0.00) \\ \end{tabular}  & \begin{tabular}{c} 58.20 \\ - 0.26 AccosD \\ \end{tabular}  \\ \hline
2 & [M0, NL1, SP1] & \ \begin{tabular}{c} ATS = 34.785 \(-\) 0.01 TV \\ 1.28 TSCD \(-\) 1.26 IntresD \\ \end{tabular}  & 0.87 (2.14) &
\begin{tabular}{c} ATS = 34.50 \(-\) 0.01 TV \\ - 1.47 TSCD \(-\) 1.41 \\ - 1.47 TSCD \(-\) 1. In the evaluation of speed-flow models we considered some additional geometric features of the road other than number of driveways and intersection density like traffic calming speed density (TCSD), right-turn driveway (RTD), number of lanes (NL), median (M), and side friction (SF). The empirical multilinear models were developed using direct values of wide range of geometric and traffic features as observed in the field. The geometric parameters included in the developed models were explicitly described as numerical coefficients. Hence, the proposed models can easily be implemented for the practical purposes depending on any empirical values. The impact of these parameters on the average travel speed (ATS) was evaluated as the values of numerical coefficients in the equations of the models. The successful models provided a correlation between average travel speed (ATS) and three geometric parameters such as traffic calming speed density (TCSD), access driveway density (AccessD) and intersection density (IntersD). The right-turn driveway density (RTD) was found to have no impact on the average travel speed (ATS). In the proposed model, the unification of the cross-section parameters was discerned to influence each coefficient of the longitudinal parameters (AccessD, TCSD, and IntersD) and average travel speed (ATS). Figures 6-8 display the variation of traffic calming speed density (TCSD), access driveway density (AccessD) and intersection density (IntersD) in the five successful models.