## 3 Model Formulation
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Parameter** & **Description** & **Unit** \\ \hline \(C_{oT}\) & Train operation cost & ($/h) \\ \(C_{oF}\) & Feeder access cost & ($/h) \\ \(C_{oT}\) & Train access cost & ($/h) \\ \(C_{uF}\) & Feeder waiting cost & ($/h) \\ \(C_{uT}\) & Train waiting cost & ($/h) \\ \(C_{uF}\) & Feeder user in-vehicle cost & ($/h) \\ \(C_{uiT}\) & Train user in-vehicle cost & ($/h) \\ \(C_{oF}\) & Feeder operating in-vehicle cost & ($/h) \\ \(C_{uT}\) & Train operating in-vehicle cost & ($/h) \\ \(C_{uFi}\) & Feeder maintenance cost & ($/h) \\ \(C_{mT}\) & Train maintenance cost & ($/h) \\ \(C_{pF}\) & Feeder personnel cost & ($/h) \\ \(C_{pT}\) & Train personnel cost & ($/h) \\ \(C_{pT}\) & Feeder fixed cost & ($/h) \\ \(C_{fT}\) & Train fixed cost & ($/h) \\ \(A_{F}\) & Average frequency of feeder bus system & (veh-h) \\ \(T_{PK}\) & Total passenger-km & (passenger-km) \\ \(T_{VK}\) & Total vehicle-km & (vehicle-km) \\ \(\mu_{a}\) & Passenger access cost & ($/passenger-h) \\ \(\mu_{a}\) & Passenger waiting cost for arrival of transit mode & ($/passenger-h) \\ \(\mu_{I}\) & Passenger riding cost on transit mode & ($/passenger-h) \\ \(\lambda_{J}\) & Fixed cost of feeder bus & ($/veh-h) \\ \(\lambda_{I}\) & Vehicle operating cost of feeder bus & ($/veh-h) \\ \(\lambda_{T}\) & Vehicle operating cost of train & ($/veh-h) \\ \(\lambda_{m}\) & Maintenance cost of feeder bus & ($/veh-km) \\ \(\lambda_{p}\) & Personnel cost of feeder bus & ($/veh-h) \\ \(\lambda_{s}\) & Social cost of feeder bus & ($/veh-km) \\ \(V\) & Average operating speed of feeder bus & (km/h) \\ \(S_{ij}\) & Slack time route \(k\) at station \(j\) & (h) \\ \(t_{aF}\) & Average access time to reach the feeder station & (h) \\ \(t_{aTj}\) & Average access time to the rail station \(j\) & (h) \\ \(t_{aT}\) & Dwell time for boarding and alighting from the train & (h)/passenger) \\ \(t_{Tj}\) & Linked riding time between station \(j\) and the destination of the train & (h) \\ \(t_{aF}\) & Dwell time for boarding and alighting from the feeder bus & (h)/passenger) \\ \(t_{in}\) & Linked in-vehicle time between nodes \(i\) and h of the feeder bus & (h) \\ \(F_{opt,k}\) & Optimum frequency of feeder bus on route & (veh/h) \\ \(F_{mq,k}\) & Required frequency of feeder bus on route \(k\) & (veh/h) \\ \(F_{k}\) & Frequency of feeder bus on route \(k\) & (veh/h) \\ \(F_{T}\) & Frequency of trains & (veh/h) \\ \(f_{min}\) & The minimum frequency & (veh/h) \\ \(f_{max}\) & The maximum frequency & (veh/h) \\ \(N\) & Total fleet size of feeder bus & (veh) \\ \(LF\) & Load factor of feeder bus & (passenger/seat) \\ C & Capacity of feeder bus & (passenger/veh) \\ \(l_{min}\) & The minimum length of one route & (km) \\ \(l_{max}\) & The maximum length of one route & (km) \\ \(V_{T}\) & Average operating speed of train & (km/h) \\ \(T_{T}\) & Train link travel time from node 56 to node 59 & (h) \\ \(n_{k}\) & Number of stops in route \(k\) & - \\ \(q_{i}\) & Demand of node \(i\) & (passenger/h) \\ \(Q_{k}\) & Demand of route \(k\) & (passenger/h) \\ \(l_{iR}\) & Distance from node \(i\) to \(h\) & (km) \\ \(L_{iR}\) & Link travel distance from each stop \(i\) to station \(j\) in route \(k\) & (km) \\ \(L_{k}\) & Length of route \(k\) for the feeder bus & (km) \\ \(X_{\text{alk}}\) & Binary variable; value of 1 if stop \(i\) precedes stop \(h\) on bus route \(k\) & - \\ \(Y_{ij}\) & Binary variable; value of 1 if stop \(i\) is assigned to station \(j\) & - \\ \(I\) & Number of stops & - \\ \(J\) & Number of stations & - \\ \(K\) & Number of routes & - \\ \(H\) & All nodes containing stops and stations & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: _Cont._