## 4 Case Study
### Travel Time Reliability Estimation  
GPS data of 11 bus lines in the case area are collected for fitting analysis. The period of the data is from 6:00 to 11:00 a.m. on Monday. Considering the condition that there is still no EBL in the local area of the case study, to simulate passenger reliability value when the bus is running on an EBL, three bus lines (Line 300 N, Line 300 W, and Line 300 KN) are selected for the case study, which run on the Third Ring Road, completely covered by an EBL during peak hours in Beijing. The sample GPS data are shown on Figure 6. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multicolumn{2}{c}{**IVT**} & \multicolumn{2}{c}{_WT_} & \multirow{2}{*}{\(K\)} & \multirow{2}{*}{\(n\)} & \multirow{2}{*}{\(\beta_{1}\)} \\ \cline{2-2} \cline{5-8}  & \(E\) & \(SD\) & \(E\) & \(SD\) & & \\ \hline \multirow{2}{*}{Value} & 3.38 & min/km & 2.35 min/km & 4.18 min & 6.18 min & 80 & \\  & & & person & & person & 3 & 0.5 \\ \hline \multirow{2}{*}{Parameter} & \multicolumn{2}{c}{\(u\)} & \(u^{\prime}\) & \multicolumn{2}{c}{C} & & \\ \hline \multirow{2}{*}{Value} & Travel time & Travel time reliability & \multirow{2}{*}{\(14.7\)} & \multirow{2}{*}{\(600\)} & \multirow{2}{*}{\(\text{pcu/lane}\)} & \multirow{2}{*}{\(\text{pcu/lane}\)} & \multirow{2}{*}{\(\text{pcu/lane}\)} & \multirow{2}{*}{\(\text{Sangdisan}\)} \\  & yuan/h & yuan/h & & & & & \\ \cline{2-2} \cline{5-8}  & 11.34 & 19.27 & \multirow{2}{*}{\(\text{yuan/km}\)} & \multirow{2}{*}{\(\text{Xinxi}\)} & \multirow{2}{*}{\(\text{Dongbeiwang}\)} & \multirow{2}{*}{\(\text{Shangdiqi}\)} & \multirow{2}{*}{\(\text{Shangdisan}\)} \\ \hline \multirow{2}{*}{Road Name} & \multirow{2}{*}{Xierqi} & \multirow{2}{*}{Houchang Cun} & \multirow{2}{*}{\(\text{N}\)} & \multirow{2}{*}{\(\text{Xinxi}\)} & \multirow{2}{*}{\(\text{Dongbeiwang}\)} & \multirow{2}{*}{\(\text{Shangdiqi}\)} & \multirow{2}{*}{\(\text{Shangdisan}\)} \\  & & & & & & M \\ \hline \multirow{2}{*}{\
\begin{tabular}{c} Traffic Volume \\ (pcu/h/lane) \\ \end{tabular} } & 549 & 1116 & 692 & 160 & 130 & 634 & 420 \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Road Name \\ (pcu/h/lane) \\ \end{tabular} } & \multirow{2}{*}{Shanghaixi} & \multirow{2}{*}{Dongbeiwang W} & \multirow{2}{*}{\(\text{Trafic Volume}\)} & \multirow{2}{*}{\(\text{880}\)} & \multirow{2}{*}{\(\text{201}\)} & \multirow{2}{*}{\(\text{201}\)} \\  & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Key parameters in case study. Figure 6: Sample GPS data. Passenger travel time distributions are fitted to estimate the statistical passenger travel time. Four typical fits for passenger travel time are applied to select the best statistical distribution. As Figure 7 and Table 5 show, results of a Gaussian fit, Weibull fit, Laplace fit, and Lognormal fit are presented. In addition, the fitting results are validated using Root Mean Square Error (RMSE) and R-squared. It is indicated that for Lines 300 N and 300 KN, Lognormal distributions are the best fit. For Line 300 KN, a Gaussian distribution is the best fit. Figure 7: Fitting result. On the basis of the best fit distributions, the IVT of bus lines on an EBL and the IVT and WT of conventional lines are estimated, and the results are shown in Tables 6 and 7. On the EBL, passengers' average expectation and standard deviation of the IVT are 1.59 min/km and 1.15 km, respectively. Off of the EBL, 11 conventional bus lines in the case study area are selected, and results of the IVT and WT are estimated. For IVT, the expectation and standard deviation are distributed from 2.9 min/km to 3.8 min/km, and from 1.9 min/km to 3.3 min/km. For WT, the distributions are from 2.4 min to 5.1 min, and from 5.6 min to 6.8 min. It is indicated that the variation of WT is larger for the waiting process. After the estimation of bus passengers' IVT and WT, reliability can be estimated as Equations (2) and (6) described. Then facing different plans of EBL locations, dynamic demand is estimated considering the reliability conditions in the optimization model.