Figures (7)  Tables (5)

    • Figure 1. 

      Operation of a unidirectional URT line.

    • Figure 2. 

      All-stop and skip-stop plan. (a) All-stop, (b) skip-stop.

    • Figure 3. 

      Passenger arrival distribution.

    • Figure 4. 

      Optimization results of evaluation indicators for each plan.

    • Figure 5. 

      Distribution of waiting density by scenario. (a) Plan A, (b) Plan B1, and (c) Plan B2.

    • Figure 6. 

      Train timetable for Plan B2.

    • Figure 7. 

      Sensitivity analysis of maximum number of skipped stations.

    • Parameters Meanings
      I Set of stations, I = {1, 2, 3, ..., N}
      I' Set of skipped stations, $ \ I' \subset I $
      K Set of trains, K = {1, 2, 3, ..., |K|}
      i Station index, $ \forall i \in I $
      j Skipped station index, $ \forall j \in I' $
      k Train index, $ \forall k \in K $
      ak,i Arrival time of train k at station i
      dk,i Departure time of train k from station i
      λk,i Number of waiting passengers at station i when train k arrives
      $ \lambda'_{k,i} $ Number of waiting passengers at station i when train k departs
      ηk,i Actual number of passengers on train k upon its arrival at station i
      $ f_{k,i}^a $ Number of passengers alighting from train k at station i
      $ f_{k,i}^b $ Number of passengers boarding train k at station i
      hmin Minimum safe headway
      ρk,i Passenger density at station i when train k arrives at station i
      $ \rho'_{k,i} $ Passenger density at station i when train k departs from station i
      Wk,i Total waiting time when train k arrives at station i
      $ {\bar \rho '_j} $ Average waiting density for each train leaving station j
      D Train stopping time
      Si Platform area of station i
      C Train rated capacity
      Nmax Maximum number of skipped stations
      ri Passenger arrival rates at station i
      rk,i Proportion of passengers alighting from train k at station i
      ni Initial number of waiting passengers at station i
      ti Train running time between station i and i+1
      tmin Minimum headway
      tmax Maximum headway
      Evaluation indicators
      $ \bar t $ Average train operation time
      q Total stop density during operation
      $ {\tilde \rho '_j} $ Density variance of waiting passengers when each train depart from station j
      β Passenger carrying capacity per second during the operation
      W Average waiting time during operation

      Table 1. 

      Parameters and symbols.

    • Parameters Value
      ti [158.00, 112.00, 158.10, 109.00, 145.00, 92.00, 121.00, 114.00, 109.10, 105.00, 164.00, 125.00, 146.00, 138.00, 107.00, 132.00]
      ni [2209, 239, 368, 1865, 699, 208, 64, 114, 119, 52, 93, 118, 834, 96, 99, 80, 0]
      ri [3.209, 0.797, 1.228, 2.408, 2.331, 0.694, 0.214, 0.381, 0.397, 0.173, 0.309, 0.392, 0.667, 0.318, 0.330, 0.268, 0.000]
      rk,i [0.000, 0.110, 0.120, 0.130, 0.140, 0.116, 0.192, 0.163, 0.125, 0.064, 0.199, 0.194, 0.522, 0.312, 0.224, 0.266, 1.000]

      Table 2. 

      Parameter settings.

    • Stopping mode Plan Objective function Weight settings
      All-stop A − −
      Skip-stop Without considering station crowding balance B1 Eqns (1), (2) ω1 = 0.01, ω2 = 0.01, ω3 = 0.98
      Considering station crowding balance B2 Eqns (2), (3) ω1 = 0.01, ω2 = 0.01, ω3 = 0.98, ω4 = 0.01, ω5 = 0.99, j = 5

      Table 3. 

      Optimize plans settings.

    • Train Station 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
      1 1 1 1 0 1 1 1 1 1 1 1 1 0 1 0 1 1
      2 1 1 1 1 1 1 1 0 0 1 0 1 1 1 1 1 1
      3 1 1 1 1 1 1 0 1 0 1 1 1 1 1 0 1 1
      4 0 1 1 1 1 1 1 1 1 0 1 0 1 0 1 1 1
      5 1 1 1 1 1 0 1 1 1 1 1 1 1 0 0 1 1
      6 0 1 1 0 1 0 0 1 1 1 1 1 1 1 1 1 1
      7 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 1
      8 0 1 1 1 1 1 1 1 1 1 1 0 1 1 0 1 1
      9 0 1 0 1 1 1 1 1 1 1 1 1 1 0 1 1 1
      10 1 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

      Table 4. 

      Decision-making variables for Plan B2.

    • Adjacent train number 1−2 2−3 3−4 4−5 5−6 6−7 7−8 8−9 9−10
      Departure interval (s) 151 128 131 93 164 149 149 150 142

      Table 5. 

      Departure headways variables for Plan B2.