Distributed Approach for Solving Time-Dependent Problems in Multimodal Transport Networks

Algorithm 1

Transfer graph approach.

Input: Transfer graph 𝑇 with 𝑚 modes and 𝑛 possible departure times

for 𝑔=1 to 𝑚  do

  for  𝑖=1 to 𝑛  do

   𝑃₊₋←𝐶𝑜𝑚𝑝𝑢𝑡𝑒(𝑃^∗𝑔_+⋅−(𝑡_𝑖),𝑇)

   𝑆𝑡𝑜𝑟𝑒𝐷𝑎𝑡𝑎𝐵𝑎𝑠𝑒(𝑃₊₋,𝐷𝐵)

  end  for

end  for

while  Request(𝑠,𝑑,𝑡)  do

  for  𝑔=1 to 𝑚  do

   𝑃_𝑠𝑑[𝑔]←𝐶𝑜𝑚𝑝𝑢𝑡𝑒(𝑃^∗𝑔_𝑠⋅𝑑(𝑡),𝑇)

   𝑃_𝑠−[𝑔]←𝐶𝑜𝑚𝑝𝑢𝑡𝑒(𝑃^∗𝑔_𝑠⋅−(𝑡),𝑇)

   for  𝑖=1 to 𝑛  do

     𝑃_+𝑑[𝑔]←𝐶𝑜𝑚𝑝𝑢𝑡𝑒(𝑃^∗𝑔_+⋅𝑑(𝑡_𝑖),𝑇)

   end  for

  end  for

  𝑅←𝑅𝑒𝑙𝑒𝑣𝑎𝑛𝑡𝐺𝑟𝑎𝑝ℎ(𝑃_𝑠𝑑,𝑃_𝑠−,𝑃_+𝑑,𝐷𝐵)

 ShortestPath(𝑅,𝑠,𝑑,𝑡)

end  while