a decision support system for improving railway line capacity g raghuram vv rao indian institute of...
TRANSCRIPT
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