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

Algorithm 2

Input: 𝐺(𝑉,𝐸), origin city 𝑥, destination city 𝑦, departure time 𝑇₀, total number of passengers 𝑃.

Output: The set of the path 𝐿(𝑙₁,𝑙₂,…,𝑙_𝑘), the generalized cost 𝐶(𝑙_𝑘) of path 𝑙_𝑘 and passenger volume 𝑃(𝑙_𝑘) of path 𝑙_𝑘.

Step  1. Set 𝑉_𝑜(𝑣𝑖𝑑(𝑂) = 0, 𝑐𝑖𝑑(𝑂)=𝑥, 𝑣𝑡𝑦𝑝𝑒 = “𝑂”), 𝑉_𝑑(𝑣𝑖𝑑(𝐷) = 𝑛+1, 𝑐𝑖𝑑(𝐷) = 𝑦, 𝑣𝑡𝑦𝑝𝑒 = “D”).

     for (𝑗=1,𝑗≤𝑛,𝑗++)

     if (𝑐𝑖𝑑(𝑗) = 𝑥 && 𝑣𝑡𝑦𝑝𝑒(𝑗) = “de” && 𝑣𝑡𝑖𝑚𝑒 > 𝑇₀)

      𝑁[0][𝑗]← Maxnum, 𝐶[0][𝑗]←0;

     for (𝑖=1,𝑖≤𝑛,𝑖++)

     if (𝑐𝑖𝑑(𝑖)=𝑦 && 𝑣𝑡𝑦𝑝𝑒(𝑖) = “ar”)

      𝑁[𝑖][𝑛+1]← Maxnum, 𝐶[𝑖][𝑛+1]←0;

      set 𝑘=1;

Step  2. From origin node 𝑂, use Dijkstra algorithm to search the optimal path 𝑙_𝑘 according to the generalized cost of the arc.

     And calculate the generalized cost 𝐶(𝑙_𝑘) of this path.

if 𝐶(𝑙_𝑘)≥ Maxnum, delete 𝑙_𝑘, end;

otherwise 𝑙_𝑘: 𝑉_𝑜→𝑉_𝑖→⋯→𝑉_𝑗→𝑉_𝑑 is deposited to the set 𝐿.

Step  3. Sort the arcs by residual train capacity in path 𝑙_𝑘, set the minimal arc capacity is capacity

   of the path 𝑙_𝑘, namely 𝑁_min(𝑙_𝑘); set passenger volume of path 𝑙_𝑘: 𝑃(𝑙_𝑘)=𝑁_min(𝑙_𝑘);

   set 𝑁[𝑖][𝑗]←𝑁[𝑖][𝑗]−𝑁_min(𝑙_𝑘),𝑃←𝑃−𝑁_min(𝑙_𝑘); if the arc in the path 𝑙_𝑘

    𝑁[𝑝][𝑞]=0, set 𝐶[𝑝][𝑞]← Maxnum.

Step  4. Reconstruction of the passenger travel network:

   set 𝐶[𝑖][𝑝]← Maxnum, 𝐶[𝑞][𝑗]← Maxnum;

   if 𝑃≤0, set 𝑃(𝑙_𝑘)←𝑃+𝑃(𝑙_𝑘), end;

   otherwise 𝑘←𝑘+1, go to Step  2.