Rake Linking For Suburban Train Services

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


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


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

Technology

Rake Linking For Suburban Train Services