Optimal Path Choice in Railway Passenger Travel Network Based on Residual Train Capacity

Algorithm 1

Input: Standard train timetable (Table 1), minimum transferring time 𝐾[𝑠𝑖𝑑(𝑖)][𝑠𝑖𝑑(𝑗)],

     transferring fare M[𝑠𝑖𝑑(𝑖)][𝑠𝑖𝑑(𝑗)] and parameters 𝛼,𝛽.

Output: 𝐺(𝑉,𝐸), 𝑉(𝑣𝑖𝑑,𝑐𝑖𝑑,𝑠𝑖𝑑,𝑡𝑖𝑑,𝑣𝑡𝑦𝑝𝑒,𝑣𝑡𝑖𝑚𝑒) and 𝐸(𝑒𝑖𝑑,𝑁[𝑖][𝑗],𝐶[𝑖][𝑗]).

Step  1. Initialize node set 𝑉, define total number of nodes 𝑛 according to train timetable.

Step  2. Establish 𝑡𝑖𝑑 and the time among arcs.

 for (𝑖=1, 𝑖≤𝑛,𝑖++)

  if tid(𝑖) = tid(𝑖+1), set 𝑇[𝑖][𝑖+1]←𝑣𝑡𝑖𝑚𝑒(𝑖+1)−𝑣𝑡𝑖𝑚𝑒(𝑖).

Step  3. Establish all transferring arcs

 for (𝑘=1, 𝑘 ≤ amount of cities, 𝑘++)

  for (𝑗=1,𝑗≤𝑛, 𝑗++)

  if (𝑐𝑖𝑑(𝑗)=𝑘 && 𝑣𝑡𝑦𝑝𝑒(𝑗) = “de”)

   for (𝑖=1,𝑖≤𝑛,𝑖++)

   if (𝑐𝑖𝑑(𝑖)=𝑘 && 𝑣𝑡𝑦𝑝𝑒(𝑖)= “ar” && (𝑡𝑖𝑑(𝑖)! = 𝑡𝑖𝑑(𝑗)))

    set 𝑝←𝑣𝑡𝑖𝑚𝑒(𝑗)−𝑣𝑡𝑖𝑚𝑒(𝑖)

    if (𝑝≥𝐾[𝑠𝑖𝑑(𝑖)][𝑠𝑖𝑑(𝑗)])

    set 𝑁[𝑖][𝑗]← maxnum, 𝑇[𝑖][𝑗]←𝑝,𝐹[𝑖][𝑗]←𝑀[𝑠𝑖𝑑(𝑖)][𝑠𝑖𝑑(𝑗)],

     𝐶[𝑖][𝑗]← 𝛼𝑇[𝑖][𝑗]+𝛽𝐹[𝑖][𝑗];

    otherwise 𝑁[𝑖][𝑗]← 0, 𝑇[𝑖][𝑗]← maxnum.

Step  4. Set capacity of all stopping arcs.

 for (𝑖=1,𝑖≤𝑛,𝑖++)

  if 𝑣𝑡𝑦𝑝𝑒(𝑖) = “ar”, set 𝑁[𝑖][𝑖+1]← maxnum.

Step  5. Set capacity and fare of all running arcs.

 for (𝑖=1,𝑖≤𝑛,𝑖++)

 if 𝑣𝑡𝑦𝑝𝑒(𝑖) = “de”

 set 𝑁[𝑖][𝑖+1],𝐶[𝑖][𝑖+1]←𝛼𝑇[𝑖][𝑖+1]+𝛽𝐹[𝑖][𝑖+1];

 if 𝑁[𝑖][𝑖+1]=0, set 𝐶[𝑖][𝑗]← maxnum; end.