### A Decision Support System for Improving Railway Line Capacity

```A Decision Support System for
Improving Railway Line Capacity
G Raghuram
VV Rao
Indian Institute of Management,
• 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
n=1
2
n=2
1
1
2
1
2
1
1
1
2
................................
1
2
1
0
0
•
•
•
•
•
“Daily” period
A node per minute
1440 nodes per station
20 stations in a section
28800 nodes
n=20
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
Distance
Time Distance Diagram
Freight Train
Time
(Planning) Model
Schedule of
Passenger Trains
Schedule of
the Freight
Train
Model
Station Details &
Track Details
Desired
Starting
Time of a
Freight
Train
Speed
of
Freight
Trains
Block
Working
Time
• Passenger trains have absolute priority over freight trains
• All freight trains are identical
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
TT
Prohibited Interval
Track Release Time
• Ts = Block Working Time
• TT= Travel Time
Ts
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)
Case B
TA
ET(J+1)
TD
i
ST(J)
ET(J)
ST(J+1)
Case C
TA
ET(J+1)
TAF=Min(TR(J+1, K))
i
ST(J)
ET(J)
ST(J)
ET(J)
ST(J+1)
ET(J+1)
i-1
TD
TDF ST(J’) ET(J’)
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 interval
Train-1
24 hrs
B
Distance
A
Train-1
24 hrs
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?
• 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)
• Expected implications on capacity
5 km (avg)
A
B
20 Stations (100 km)
• BA performs better than AB
Common Loop
• Inappropriate location
• 6 stations out of 20 stations
• Track #3: common loop – unfavourable to
up direction
UP
1
DOWN
2
3
UP
DOWN
Experiment 2
Double track
River
Double track
Single track (4 km)
• Effect of changing the single track to
double track
• No improvement in throughput
• Reduction in average travel time possibly
due to other bottlenecks
Experiment 3
Arrival time at destination as a function of
departure time at origin
35
Arrival time at
destination
30
A to B
25
20
B to A
15
10
Expected
(4 hour
transit)
5
0
1 3
5
7
9 11 31 51 71 91 12 32
D ep ar t ur e t ime at o r ig in
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+Δ
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)
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
Throughput: tons/day;
Capacity: # of trains
Policy Issue: Optimal length of
Freight Train
Throughput:
tons/day
Capacity: # of
trains
Length of freight train: w eight
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
```