Rake Linking for Suburban Train Services

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Rake Linking for Suburban Train Services
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Rake-Linker

• The Rake-Linker assigns physical trains (rakes)
  to services that have been proposed in a
  timetable
• Services will be linked directly at terminals or
  indirectly by proposing new services between
  terminals
• New services can then be run as empty movements
  or as additional commercial services

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Typical use of the rake linker

• Step 1 Find the minimum number of rakes required
  to run all the services
• Step 2 Minimize the number of new services
  (including empty rake movements), with the same
  number of rakes as in Step 1
• Step 3 Minimize the number of rakes and
  proposed/empty rake movements further by
  perturbation and sensitivity analysis.
• Step 4 Check the constraints on stations and
  line segments for the feasibility and allot
  platforms to rakes at each station.

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Modeling

• Construction of service graph
• Vertices services
• Edges possible direct and indirect successors to
  each node
• Rake Cycle construction
• Stated as minimum chain decomposition problem
• Step 3 Min Cost Flow formulation
• Modification of service graph
• Each node is spilt into two nodes
• 4 dummy source and 4 dummy sinks
• Allocation of suitable capacities, lower bounds
  and costs to all the edges in the network

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Direct and Indirect Edges

• Direct edges corresponds to linking of a service
  at one terminus to other services at the same
  terminus maintaining car-shed/ stabling/turn-aroun
  d constraints
• Indirect edges corresponds to linking of a
  service at one terminus to other services at a
  different terminus by proposing an empty rake
  movement between them and maintaining
  car-shed/stabling/turn-around constraints at both
  the stations

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MCF Network
Self edge
9car source
9Car sink
Dummy source
Dummy Sink
Super source
Super Sink
12Car Sink
12Car source
Unused rake edge
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The overall system view
SCHEDULER
Inputs Set Of Constraints
Utilities
TIME TABLE OR PARTIAL TIME TABLE
RAKE-LINKER
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Features of the Rake Linker

• Finds rake links for various scenarios
• (by changing parameter values)
• Outputs the minimum no. of rakes and minimum no.
  of empty rake movements
• Gives output suitable for viewing individual
  rake-links and rake-cycles as well as the
  timetable format
• Gives stable table, occupancy table and charts
  for every terminus

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Features (contd.)

• Can also link the rakes in FIFO fashion at every
  terminus
• Consideration of different types of rakes during
  assignment e.g., 9 Car, 12 Car
• AC rakes, AC-DC rakes

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Inputs for Rake Linker

• Partial Time Table (obtained from scheduler)
• Station Table
• Inter Terminal Transit Time Matrix
• Parameter Table

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Partial Time Table

• The rake linker uses
• Terminal locations and start and end timings for
  each service
• Service attributes such as rake type of the
  service (e.g. 9 Car/12 Car)
• Any rake links that must be maintained

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Partial Time Table
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Hold Resource (Station) Table
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Inter Terminal Transit Time Matrix
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Parameter Table
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Outputs of the Rake Linker

• Partial time table (Modified) updated RakeLinkId
  and Distance
• RakeTable (detailed rake cycles)
• RakeServTable (short form of Rake Table)
• Stable Table (stabling requirements)
• Occupancy Table (platform requirements)
• Platform Occupancy Chart (visual scenario)

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Partial time table (Modified)
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Rake Table
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Platform Allocation

• Problem Given platform preferences, allocate a
  platform to each service.
• Algorithm
• Start with all platforms as empty.
• In increasing order of time, if a train arrives
  or departs, generate new possible allocations.
• Repeat till all the train arrival and departure
  complete.
• Trace the path back to root to get a possible
  allotment of platforms

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Platform Allocation

• Three platforms at a Hold Resource.
• Order of events
• arrival of service 1
• arrival of service 2
• departure of service 1
• Platform preferences of train 1, 2 1,2,3
• Initially all platforms empty

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Platform Allocation
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Platform Occupancy Chart
Rake Linker
generates
Platform Occupancy Table with Platform Preferences
After Checking Feasibility at all Stations
Generates final Occupancy table With assigned
Platform number
Platform Occupancy Chart
generates
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Platform Occupancy Chart
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Perturbation and Sensitivity analysis of Rake
Linker

• Computes the change in the rake linking objective
  (minimum no. of rakes, minimum no. of empty rake
  movements) for small changes in operating
  parameters (turn-around time, run time,
  prepone/postpone)
• Modeling
• Residual network additional edges
• Finds negative cost cycles
• Saturates negative cost cycles
• Outputs new Rake Table

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Perturbation and Sensitivity analysis (contd.)

• Examples
• At Vasai Road (BSR) in WR, if we permit
  turn-around time of one service from 10 mins to 9
  mins, we can save a rake
• At Bandra (BA), if we permit turn-around time of
  two services from 6 mins to 5 mins, we can save
  one empty-rake movement
• Savings are also possible with perturbing either
  run-times or preponing/postponing the timings of
  a few services

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Applications and Examples

• Validated on full scale Western Railway Mumbai
  Suburban network
• Outputs 62 rakes and 10 empty movements for 963
  services
• WR uses 64 rakes (22 are 12 Car rakes) and 70
  empty rake movements
• Useful application
• During maintenance block time
• To check optimality

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FIFO Rake Linker

• It assigns rakes to each service in First-In
  First-Out fashion at every terminus
• Features
• outputs a detailed rake table in Time table
  format
• Run time (3 secs for number of rakes, 10 secs for
  rake table)
• Used for analyzing and comparing rake links with
  those generated by MCF-solver