Rake Linking For Suburban Train Services
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Rake Linking for Rake Linking for Suburban Train ServicesSuburban Train Services
Rake-LinkerRake-Linker
The Rake-Linker assigns physical trains (rakes) The Rake-Linker assigns physical trains (rakes) to services that have been proposed in a to services that have been proposed in a timetabletimetable
Services will be linked directly at terminals or Services will be linked directly at terminals or indirectly by proposing new services between indirectly by proposing new services between terminalsterminals
New services can then be run as empty New services can then be run as empty movements or as additional commercial servicesmovements or as additional commercial services
Typical use of the rake linkerTypical use of the rake linker
Step 1: Find the minimum number of rakes required Step 1: Find the minimum number of rakes required to run all the servicesto run all the services
Step 2: Minimize the number of new services Step 2: Minimize the number of new services (including empty rake movements), with the same (including empty rake movements), with the same number of rakes as in Step 1number of rakes as in Step 1
Step 3: Minimize the number of rakes and Step 3: Minimize the number of rakes and proposed/empty rake movements further by proposed/empty rake movements further by perturbation and sensitivity analysis.perturbation and sensitivity analysis.
Step 4: Check the constraints on stations and line Step 4: Check the constraints on stations and line segments for the feasibility and allot platforms to segments for the feasibility and allot platforms to rakes at each station.rakes at each station.
ModelingModeling
Construction of service graphConstruction of service graph Vertices: servicesVertices: services Edges: possible direct and indirect successors to Edges: possible direct and indirect successors to
each nodeeach node
Rake Cycle constructionRake Cycle construction Stated as minimum chain decomposition problemStated as minimum chain decomposition problem
Step 3: Min Cost Flow formulationStep 3: Min Cost Flow formulation Modification of service graphModification of service graph
Each node is spilt into two nodesEach node is spilt into two nodes4 dummy source and 4 dummy sinks4 dummy source and 4 dummy sinks
Allocation of suitable capacities, lower bounds and Allocation of suitable capacities, lower bounds and costs to all the edges in the networkcosts to all the edges in the network
Direct and Indirect EdgesDirect and Indirect Edges
Direct edges corresponds to linking of a service Direct edges corresponds to linking of a service at one terminus to other services at the same at one terminus to other services at the same terminus maintaining car-shed/ stabling/turn-terminus maintaining car-shed/ stabling/turn-around constraintsaround constraintsIndirect edges corresponds to linking of a Indirect edges corresponds to linking of a service at one terminus to other services at a service at one terminus to other services at a different terminus by proposing an empty rake different terminus by proposing an empty rake movement between them and maintaining car-movement between them and maintaining car-shed/stabling/turn-around constraints at both the shed/stabling/turn-around constraints at both the stationsstations
MCF NetworkMCF Network
Self edge
Unused rake edge
9car source
12Car source
Dummy source
Super source
Super Sink
9Car sink
12Car Sink
Dummy Sink
The overall system viewThe overall system view
SCHEDULER
RAKE-LINKER
Inputs&
Set Of
Constraints
UtilitiesTIME TABLE
ORPARTIAL TIME TABLE
Features of the Rake LinkerFeatures of the Rake Linker
Finds rake links for various scenariosFinds rake links for various scenarios (by changing parameter values)(by changing parameter values)
Outputs the minimum no. of rakes and minimum no. of Outputs the minimum no. of rakes and minimum no. of empty rake movementsempty rake movementsGives output suitable for viewing individual rake-links Gives output suitable for viewing individual rake-links and rake-cycles as well as the timetable formatand rake-cycles as well as the timetable formatGives stable table, occupancy table and charts for every Gives stable table, occupancy table and charts for every terminusterminus
Features (contd.)Features (contd.)
Can also link the rakes in FIFO fashion at Can also link the rakes in FIFO fashion at every terminusevery terminus
Consideration of different types of rakes Consideration of different types of rakes during assignment e.g., 9 Car, 12 Carduring assignment e.g., 9 Car, 12 Car
AC rakes, AC-DC rakesAC rakes, AC-DC rakes
Inputs for Rake LinkerInputs for Rake Linker
Partial Time Table (obtained from Partial Time Table (obtained from scheduler)scheduler)
Station Table Station Table
Inter Terminal Transit Time MatrixInter Terminal Transit Time Matrix
Parameter TableParameter Table
Partial Time TablePartial Time Table
The rake linker usesThe rake linker uses
Terminal locations and start and end Terminal locations and start and end timings for each servicetimings for each service
Service attributes such as rake type of the Service attributes such as rake type of the service (e.g. 9 Car/12 Car)service (e.g. 9 Car/12 Car)
Any rake links that must be maintainedAny rake links that must be maintained
Partial Time TablePartial Time Table
Hold Resource (Station) TableHold Resource (Station) Table
Inter Terminal Transit Time MatrixInter Terminal Transit Time Matrix
Parameter TableParameter Table
Outputs of the Rake LinkerOutputs of the Rake Linker
Partial time table (Modified): updated Partial time table (Modified): updated RakeLinkId and DistanceRakeLinkId and Distance
RakeTable (detailed rake cycles)RakeTable (detailed rake cycles)
RakeServTable (short form of Rake Table) RakeServTable (short form of Rake Table)
Stable Table (stabling requirements)Stable Table (stabling requirements)
Occupancy Table (platform requirements)Occupancy Table (platform requirements)
Platform Occupancy Chart (visual Platform Occupancy Chart (visual scenario)scenario)
Partial time table (Modified)Partial time table (Modified)
Rake TableRake Table
Platform AllocationPlatform Allocation
Problem: Given platform preferences, allocate a Problem: Given platform preferences, allocate a platform to each service. platform to each service.
Algorithm : Algorithm : 1.1. Start with all platforms as empty. Start with all platforms as empty.
2.2. In increasing order of time, if a train arrives or departs, In increasing order of time, if a train arrives or departs, generate new possible allocations. generate new possible allocations.
3.3. Repeat till all the train arrival and departure complete. Repeat till all the train arrival and departure complete.
4.4. Trace the path back to root to get a possible allotment of Trace the path back to root to get a possible allotment of
platformsplatforms
Platform AllocationPlatform Allocation
Three platforms at a Hold Resource. Three platforms at a Hold Resource.
Order of events: Order of events:
1.1. arrival of service 1 arrival of service 1
2.2. arrival of service 2 arrival of service 2
3.3. departure of service 1 departure of service 1
Platform preferences of train 1, 2 = 1,2,3 Platform preferences of train 1, 2 = 1,2,3
Initially all platforms empty Initially all platforms empty
Platform AllocationPlatform Allocation
Rake Linker
Platform OccupancyChart
generatesPlatform OccupancyTable with Platform PreferencesAfter Checking
Feasibility at all Stations
Generates finalOccupancy table With assigned Platform number
generates
Platform Occupancy Chart
Platform Occupancy ChartPlatform Occupancy Chart
Perturbation and Sensitivity Perturbation and Sensitivity analysis of Rake Linkeranalysis of Rake Linker
Computes the change in the rake linking Computes the change in the rake linking objective (minimum no. of rakes, minimum no. of objective (minimum no. of rakes, minimum no. of empty rake movements) for small changes in empty rake movements) for small changes in operating parameters (turn-around time, run operating parameters (turn-around time, run time, prepone/postpone)time, prepone/postpone)
Modeling:Modeling: Residual network + additional edgesResidual network + additional edges Finds negative cost cyclesFinds negative cost cycles Saturates negative cost cyclesSaturates negative cost cycles Outputs new Rake TableOutputs new Rake Table
Perturbation and Sensitivity analysis Perturbation and Sensitivity analysis
(contd.)(contd.)Examples:Examples: At Vasai Road (BSR) in WR, if we permit turn-around At Vasai Road (BSR) in WR, if we permit turn-around
time of one service from 10 mins to 9 mins, we can time of one service from 10 mins to 9 mins, we can save a rakesave a rake
At Bandra (BA), if we permit turn-around time of two At Bandra (BA), if we permit turn-around time of two services from 6 mins to 5 mins, we can save one services from 6 mins to 5 mins, we can save one empty-rake movementempty-rake movement
Savings are also possible with perturbing either Savings are also possible with perturbing either run-times or preponing/postponing the timings of run-times or preponing/postponing the timings of a few servicesa few services
Applications and ExamplesApplications and Examples
Validated on full scale Western Railway Mumbai Validated on full scale Western Railway Mumbai Suburban networkSuburban network Outputs 62 rakes and 10 empty movements for 963 Outputs 62 rakes and 10 empty movements for 963
servicesservices WR uses 64 rakes (22 are 12 Car rakes) and 70 WR uses 64 rakes (22 are 12 Car rakes) and 70
empty rake movementsempty rake movements
Useful application:Useful application: During maintenance block timeDuring maintenance block time To check optimalityTo check optimality
FIFO: Rake LinkerFIFO: Rake Linker
It assigns rakes to each service in First-In It assigns rakes to each service in First-In First-Out fashion at every terminus First-Out fashion at every terminus Features:Features: outputs a detailed rake table in Time table outputs a detailed rake table in Time table
formatformat Run time (3 secs for number of rakes, 10 secs Run time (3 secs for number of rakes, 10 secs
for rake table)for rake table) Used for analyzing and comparing rake links Used for analyzing and comparing rake links
with those generated by MCF-solver with those generated by MCF-solver