A Decision Support System for Improving Railway Line Capacity

G RaghuramVV Rao

Indian Institute of Management, Ahmedabad

• Planning Model– Not on line– Objective: Maximize line capacity

• Operational Model– On line– Objective: Minimize train detentions

Planning Model

• Math Programming

– Can be formulated as a Max Flow Problem– Too large computationally– Time has to be discretized– Level of detail insufficient

• “Daily” period• A node per minute• 1440 nodes per station• 20 stations in a section• 28800 nodes

n=1 n=2 ................................ n=20

2

2

2

1

1

2

1

1

1

1

1

0

0

1

2

Planning Model

• Regression

– Can only handle a macro measure of capacity– Level of detail insufficient

Planning Model

• Simulation

– Can handle a good level of detail– Brute force approach– System is opaque

Time Distance Diagram

Time

Dis

tan

ce

Freight Train

(Planning) Model

• Passenger trains have absolute priority over freight trains• All freight trains are identical

ModelSchedule of Passenger Trains

Station Details & Track Details

Desired Starting Time of a Freight Train

Speed of Freight Trains

Block Working Time

Schedule of the Freight Train

Data

• Passenger train schedules

• Tracks between two stations (single line or double line)

• Station configuration– Accessibility of tracks from left side– Accessibility of tracks from right side– Platform, main or loop

Representation of Stations

Up Up

L R

Dn Dn

Matrix ACL Matrix ACR Matrix STR

Track No

1 2 3 4 Track No

1 2 3 4 Track No 1 2 3 4

U 1 1 0 0 U 1 1 0 0 Signalling B U D D

D 1 1 1 1 D 1 1 1 1 Siding/Main S M M S

Platform P P P P

Accessibility Matrix

Prohibited Interval (for Departure)Track Release Time (for Arrival)

• Ts = Block Working Time• TT= Travel Time

TT Ts Ts

Prohibited Interval

Track Release Time

Moving a Freight Train from Origin to Destination

• Departure Rules (Only one train in between two control points at a time)

• Arrival Rules (Track availability)

• Combination of forward and backward moves

Case A TD=TA

i

ST(J) ET(J) ST(J+1) ET(J+1)

Case B TA TD

i

ST(J) ET(J) ST(J+1) ET(J+1)

Case C

i

ST(J) ET(J) ST(J+1) ET(J+1)

TA TAF=Min(TR(J+1, K))

i-1

ST(J) ET(J) ST(J’) ET(J’)TD TDF

Algorithm

• Start Ith train at station “origin” at desired time• Is it within prohibited interval (PI)?

– If no, proceed to next station– If yes, can it wait till end of PI?– If yes, depart at end of PI to next station– If no, determine first possible arrival time and

backtrack

• If cleared to next station, select track to occupy• Repeat for Ith train until end of section• Repeat for other trains until capacity

Measure of Capacity

• All trains fired at zero hours• Schedule each train in alternate directions• Find how many trains arrive at each

terminal within a 24 hour intervalTrain-1

Train-1

24 hrs

24 hrs

B

Distance

A

Time

Decision Areas

• Where to organize overtakes (and crossings in single track)?

• Which track to use at a station?

• Which track to use in a twin single? line/triple/quadruple section?

• Train stabling for crew change?

Experiments

1. Effect of average speed and block working time

2. Single track vs double track on a bridge

3. Effect of departure times on travel time

Experiment 1 (change speeds, block working time)

• BA performs better than AB

A B

20 Stations (100 km)

5 km (avg)

• Expected implications on capacity

Common Loop

• Inappropriate location• 6 stations out of 20 stations

• Track #3: common loop – unfavourable to up direction

UP UP

DOWN DOWN

1

2

3

Experiment 2

• Effect of changing the single track to double track

• No improvement in throughput

• Reduction in average travel time possibly due to other bottlenecks

Double track Double track

Single track (4 km)River

Experiment 3Arrival time at destination as a function of

departure time at origin

0

5

10

15

20

25

30

35

1 3 5 7 9 11 13 15 17 19 21 23

Departure time at origin

Arr

ival

tim

e at

d

esti

nat

ion

A to B

B to A

Expected(4 hourtransit)

Problem of Express Train Path due to Platform Location

Passenger train to overtake freight. Hence freight is on non-platform Main line

P

F

Time T

Express train has to run through siding (loop) because freight is on mainE: Express (fast moving)F: FreightP: Passenger (slow moving)

P

F

Time T+Δ

E

Use of Model

• Training

• Insights– Loop locations favouring one direction – Bridge not a serious bottleneck– Good departure times– Location of platforms

• Influence on commercial package

Policy Issue: Optimal length of Freight Train

Length of freight train: weight

Th

rou

gh

pu

t: t

on

s/d

ay;

C

apac

ity:

# o

f tr

ain

s

Throughput:tons/day

Capacity: # oftrains

Other Parameters

• Starting time

• Relative priority

• Number of sidings

• Speed of freight

• Slack time

• Change passenger train timings

Limitations and Opportunities for Extensions

• Acceleration, deceleration not considered

• A good path could be based on detention to freight trains

• Priority to passenger trains need not be absolute, but based on a weightage of detention to freight trains

• Resource constraints (loco, crew) can be considered

Operational Model

• Passenger train schedules + tracks to be ideally occupied

• Minimum stoppage time

• Station + section data

• Actual train timings (passenger + freight)[on line input]

Approaches

• A DSS – with graphics interface (absolutely essential)

• Algorithm– A branch and bound procedure with a look

ahead upto four hours or end of section, keeping response time in view

DSS Approach

• Semi structured problem• Interactive: Given many parameters,

decision maker has a role to provide inputs

• Graphical – transparent• Sensitivity analysis – speed of response• In reality, manual charting is used. But

schedules cannot be planned ahead since difficult to try various alternatives quickly

Given Complexity of IR

• Good response times may not be feasible

• But just “drawing support” with linear projections may still relieve the controller of a lot of tediousness

• Generation of statistics possible

DSS Approach

• Benefits of DSS approach for Static Model

– Training tool for schedulers and managers

– Sensitivity of parameters that can be altered – for example: passenger train schedules, slack time, number of sidings etc

– Contingency planning for maintenance etc

Thank You