## 3 Methodology
### Notation
#### 3.2.2 Model for Express Cargo  
The sets and parameters related to the construction of the spatio-temporal network for the express cargo part are described in detail in Table 3. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Variable Symbol** & **Symbol Definition** \\ \hline \multirow{7}{*}{Set Data} & \(S\) & The set of stations, \(s\), \(s^{\prime}\in S\) \\  & \(S_{i}\) & The set of stations on the path of the train \(i\), \(S_{i}\subset S\) \\  & \(T\) & The set of available times for train travel, \(t\), \(t^{\prime}\in T\) \\  & \(I\) & The set of trains, \(i\in I\) \\  & \(N\) & The set of nodes in a spatio-temporal network, \((s,t)\), \((s^{\prime},t^{\prime})\in N\) \\  & \(N_{i}\) & The set of train \(i\) nodes in a spatio-temporal network, \(i\in I\) \\  & \(\sigma_{i}\) & The set of virtual starting points for train \(i\) in a spatio-temporal network, \(i\in I\), \(\sigma_{i}\in N\) \\  & \(\theta_{i}^{a}\) & The set of arrival nodes of train \(i\) at station \(s\) in a spatio-temporal network, \(s\in S\), \(i\in I\), \(\theta_{i}^{a}\subset N\) \\  & \(\theta_{i}^{a}\) & The set of departure nodes of train \(i\) at station \(s\) in a spatio-temporal network, \(s\in S\), \(i\in I\), \(\theta_{i}^{a}\in N\) \\  & \(\theta_{i}^{a}\) & The set of virtual endpoints of train \(i\) in a spatio-temporal network, \(i\in I\), \(\theta_{i}^{a}\in N\) \\  & \(A_{i}\) & The set of arcs in spatio-temporal networks, \((s,t,i;s^{\prime},t^{\prime})\in A\) \\  & \(A_{i}\) & The set of arcs corresponding to train \(i\) in a spatio-temporal network, \\  & \(A_{i}\subset A\), \(A_{i}=A_{i}^{start}+A_{i}^{turbel}+A_{i}^{turbel}+A_{i}^{turbel}+A_{i}^{turbel}\) \\  & \(A_{i}^{start}\) & The set of train starting arcs corresponding to train \(i\) in a spatio-temporal network, \(A_{i}^{start}\subset A_{i}\) \\  & \(A_{i}^{turbel}\) & The set of train running arcs corresponding to train \(i\) in a spatio-temporal network, \(A_{i}^{turbel}\subset A_{i}\) \\  & \(A_{i}^{turbel}\) & The set of train dwell arcs corresponding to train \(i\) in a spatio-temporal network, \(A_{i}^{turbel}\subset A_{i}\) \\  & \(A_{i}^{end}\) & The set of train end arcs corresponding to train \(i\) in a spatio-temporal network, \(A_{i}^{turbel}\subset A_{i}\) \\ \hline \multirow{7}{*}{Index Data} & \(s\) & Station Index \\  & \(t\) & Time Index \\  & \((s,t,i)\), \((s^{\prime},t^{\prime},t^{\prime})\) & Spatio-temporal network node \\  & \((s,t,i;s^{\prime},t^{\prime},t^{\prime})\) & Spatio-temporal network arc \\ \hline \multirow{7}{*}{Parameter Data} & \(o_{i}\) & Starting station of train \(i,i\in I\) \\  & \(d_{i}\) & Terminating station of train \(i,i\in I\) \\ \cline{1-1}  & \(t_{i}^{s}\) & Train arrival time of scheduled train \(i\) at station \(s\) \\ \cline{1-1}  & \(t_{i,s}^{s}\) & Departure time of train at station \(s\) for scheduled train \(i\) \\ \cline{1-1}  & \(L_{(s,s^{\prime})}^{a}\) & Station spacing from station \(s\) to station \(s^{\prime}\) \\ \cline{1-1}  & \(C^{pa}\) & High-speed train capacity \\ \cline{1-1}  & \(f_{i}^{xx}\) & Expected passenger transport demand for train \(i\) \\ \cline{1-1}  & \(e^{\mu}\) & Revenue per unit of passenger transport \\ \cline{1-1}  & \(U\) & Extremely large number \\ \hline \multirow{7}{*}{Decision Variables} & \(x_{i}^{u}\) & 0–1 variable, which is \(1\) if train \(i\)’s transport organization mode is \(w\); otherwise, it takes the value \\ \cline{1-1}  & \(x_{i}^{u}\) & 0, \(i\in I\), \(w\in W\) \\ \cline{1-1}  & \(loss_{i}^{pa}\) & 0–1 variable indicates the judgement of whether there is a loss of passengers in train \(i\), \(1\) indicates whether there is a loss of passengers in train \(i\), and \(0\) indicates otherwise. \(i\in I\) \\ \cline{1-1}  & \(v\) & An integer variable indicating the number of special high-speed rail trains running \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Explanation of train symbols.