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. n=1 n=2 ................................ n=20 2 2 2 1 1 1 1 • “Daily” period • A node per minute • 1440 nodes per station • 20 stations in a section • 28800 nodes 1 1 2 1 1 0 0 2

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 • Passenger trains have absolute priority over freight trains • All freight trains are identical Schedule of the Freight Train Model Station Details & Track Details Speed of Freight Trains Block Working Time Desired Starting Time of a Freight Train

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 = Block Working Time • TT= Travel Time Ts Ts TT Prohibited Interval Track Release 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 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 TA TAF=Min(TR(J+1, K)) i ST(J) ET(J) ST(J+1) ET(J+1) 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) • BA performs better than AB • Expected implications on capacity 5 km (avg) A B 20 Stations (100 km)

19. Common Loop • Inappropriate location • 6 stations out of 20 stations • Track #3: common loop – unfavourable to up direction UP 1 UP DOWN 2 DOWN 3

20. Experiment 2 Double track Double track • Effect of changing the single track to double track • No improvement in throughput • Reduction in average travel time possibly due to other bottlenecks Single track (4 km) River

21. Experiment 3Arrival time at destination as a function of departure time at origin

22. Problem of Express Train Path due to Platform Location Passenger train to overtake freight. Hence freight is on non-platform Main line Time T P F 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)

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