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. Daily period A node per minute 1440 nodes per station 20 stations in a section 28800 nodes n=1 n=2................................n=20 222222 112112 111111 11001100 1 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 Passenger trains have absolute priority over freight trains All freight trains are identical Model Schedule 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

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 LR Dn Matrix ACLMatrix ACRMatrix STR Track No 1234 1234 1234 U1100U1100SignallingBUDD D1111D1111Siding/MainSMMS PlatformPPPP Accessibility Matrix

11. Prohibited Interval (for Departure) Track Release Time (for Arrival) Ts = Block Working Time TT= Travel Time TT Ts 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 i ST(J) ET(J) ST(J+1) ET(J+1) TA TAF=Min(TR(J+1, K)) i-1 ST(J) ET(J) TD TDF

14. Algorithm Start I th 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 I th 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 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 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

18. Experiment 1 (change speeds, block working time) BA performs better than AB AB 20 Stations (100 km) 5 km (avg) Expected implications on capacity

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

20. 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 Single track (4 km) River

21. Experiment 3 Arrival 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 P F Time T Express train has to run through siding (loop) because freight is on main E: Express (fast moving) F: Freight P: Passenger (slow moving) P F Time T+Δ E

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