A Decision Support System for Improving Railway Line Capacity

1
A Decision Support System for Improving Railway
Line Capacity

• G Raghuram
• VV Rao
• Indian Institute of Management, Ahmedabad

2

• Planning Model
• Not on line
• Objective Maximize line capacity
• Operational Model
• On line
• Objective Minimize train detentions

3
Planning Model

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

4
n1 n2 ................................ n20
2 2 2
1 1 1
1
1 1 2
1 1 0 0
2

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

5
Planning Model

• Regression
• Can only handle a macro measure of capacity
• Level of detail insufficient

6
Planning Model

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

7
Time Distance Diagram
8
(Planning) Model
Schedule of Passenger Trains
Schedule of the Freight Train
Model
Station Details Track Details
Speed of Freight Trains
Block Working Time
Desired Starting Time of a Freight Train

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

9
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

10
Representation of Stations
Up
Up
L
R
Dn
Dn
11
Prohibited Interval (for Departure)Track Release
Time (for Arrival)
Ts
Ts
TT
Prohibited Interval
Track Release Time

• Ts Block Working Time
• TT Travel Time

12
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

13
Case A
TDTA
i
ST(J) ET(J)
ST(J1) ET(J1)
Case B
TA TD
i
ST(J) ET(J)
ST(J1) ET(J1)
Case C
TA TAFMin(TR(J1, K))
i
ST(J) ET(J)
ST(J1) ET(J1)
i-1
ST(J) ET(J)
ST(J) ET(J)
TD TDF
14
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

15
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 interval

Train-1
24 hrs
B Distance A
Train-1
24 hrs
Time
16
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?

17
Experiments

• Effect of average speed and block working time
• Single track vs double track on a bridge
• Effect of departure times on travel time

18
Experiment 1 (change speeds, block working time)

• Expected implications on capacity

5 km (avg)
A
B
20 Stations (100 km)

• BA performs better than AB

19
Common Loop

• Inappropriate location
• 6 stations out of 20 stations
• Track 3 common loop unfavourable to up
  direction

UP
UP
1
DOWN
DOWN
2
3
20
Experiment 2
Double track
Double track
Single track (4 km)
River

• Effect of changing the single track to double
  track
• No improvement in throughput
• Reduction in average travel time possibly due to
  other bottlenecks

21
Experiment 3Arrival time at destination as a
function of departure time at origin
22
Problem of Express Train Path due to Platform
Location
Time T
P
F

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

Time T?
P
F
E
Express train has to run through siding (loop)
because freight is on main E Express (fast
moving) F Freight P Passenger (slow moving)
23
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

24
Policy Issue Optimal length of Freight Train
25
Other Parameters

• Starting time
• Relative priority
• Number of sidings
• Speed of freight
• Slack time
• Change passenger train timings

26
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

27
Operational Model

• Passenger train schedules tracks to be ideally
  occupied
• Minimum stoppage time
• Station section data
• Actual train timings (passenger freight)
• on line input

28
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

29
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

30
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

31
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

32
Thank You