Urban Rail Transit Line Rescheduling and Rolling Stock Circulation in Case of Complete Blockade

1. Train rescheduling and rollingstockcirculation in case of complete blockade for an urban rail transit line Yihui Wang Beijing Jiaotong University 2018.11.06 yihui.wang@bjtu.edu.cn

2. OUTLINE • Background • Model • Solution approach • Case study • Conclusions yihui.wang@bjtu.edu.cn

3. OUTLINE • Background • Model • Solution approach • Case study • Conclusions yihui.wang@bjtu.edu.cn

4. 1.Background Huge passenger demand Large scale network Disruptions serious impacts for passengers and operators High levelofautomation Small headway yihui.wang@bjtu.edu.cn

5. 1.Background In 2017, Jul-Aug, 8 disruptions occurred 07:14 Failure of equipment (25min,Line 10) 08:19 Failure of turnout equipment (15min,Line 1) 18:52 Failure of trains (15min,Line 9) 07:14 Failure of signal (30min, Line 10) 07.03 07.04 07.14 07.17 08.03 07.07 07.28 08.22 07:33 Failure of signal (40min, Line 5) 19:52 Passenger entering the track (15min, Line 2) 13:46 Passenger entering the track (30min,Line 2) 08:27 Failure of signal (15min, Line 6) 5 yihui.wang@bjtu.edu.cn

6. 1.Background On-board congestion Passenger flow limitation Traffic jams outside • Disruptions cause trains stopping in opentracks(passenger cannot get off) • Disruptions cause passenger waitingoutside the station(capacity is limited) • Disruptions cause disordered operation of metro network, even trafficjamsinthearea Effectivereschedulingisimportantforenhancingsubwayperformanceunderdisruptions 6 6 yihui.wang@bjtu.edu.cn

7. 1.Background 2017/5/13 ,12:50, suicide occurred at station PGY in Line 1 • Measuresandeffects(dispatchers) • Power cutoffforcontact rails • Manual driving in section with accident • Power supply recoveredat 12:58 • 1 service cancelled, 7 services delayed, 1 services added and 13 servicesadjusted 5 trains delayed >2min PGY GC BJ Down direction …… BBS …… JB MXD GC BJ PGY yihui.wang@bjtu.edu.cn

8. OUTLINE • Background • Model • Solution approach • Case study • Conclusions yihui.wang@bjtu.edu.cn

9. 2. Model Set-up • Acompleteblockadeforbothtracks • Longblockingtime,e.g.,30min,1hourormore • Short-turningservicesshouldbeprovidedforbothparts • Expectedheadwaysbasedonpassengerdemand,rollingstocks,etc. yihui.wang@bjtu.edu.cn

10. 2. Model Objective • Minimize deviations between optimized headways and expected headways • Minimize variations between consecutive headways • Minimizenumberofrollingstocks yihui.wang@bjtu.edu.cn

11. 2. Model Objective function yihui.wang@bjtu.edu.cn

12. 2. Model Departure and arrivalconstraints i: train service in the up direction l: train service in the down direction j: station yihui.wang@bjtu.edu.cn

13. 2. Model Departure and arrivalconstraints Atrain can only enter a station when apredecessortrain has left yihui.wang@bjtu.edu.cn

14. 2. Model Headwayconstraints • Calculation of headways • Maximumandminimumheadways The maximumheadway between train services largely depends on the disruptions not include in themodel yihui.wang@bjtu.edu.cn

15. 2. Model Rollingstockcirculationconstraints(turnaroundstation) i l yihui.wang@bjtu.edu.cn

16. 2. Model Turnaroundtimeconstraints(turnaroundstations) i l yihui.wang@bjtu.edu.cn

17. 2. Model Rollingstockcirculation constraints(disruptedstation) • Train order at station K , i arrives after l departing • At most two trains dwell at station K • and are the number of train services which arrive at or depart from station K before the arrival of train service i, respectively • , • Dwell time at station K , q : minimal dwell time at station K • Dwell time at station K involves the time for passenger boarding/alightingand the change-endtime yihui.wang@bjtu.edu.cn

18. 2. Model Rollingstockcirculation constraints(disruptedstation) • Safety headway for turnaround at station K • Rollingstockfortrain service i must turnaround at station K yihui.wang@bjtu.edu.cn

19. 2. Model Inventory constraintsforthedepot • Limited rollingstocksavailable in the depot • ---number of exiting operations before the departure of train service i at station 1 • ---number of enteringoperations before the departure of train service i at station 1 yihui.wang@bjtu.edu.cn

20. OUTLINE • Background • Model • Solution approach • Case study • Conclusions yihui.wang@bjtu.edu.cn

21. 3. Solution approach——MILP Transformation properties • A logical variable times a real-valued variable Consider , , By introducing a new real-valued variable , then nonlinear expression is equivalent to • Statement By introducing a new auxiliary logical variable , then , , , . ε is a small positive number yihui.wang@bjtu.edu.cn

22. 3. Solution approach——MILP Transformation properties • Absolute function We consider introduce two new auxiliary real-valued variables and , the absolute function is equivalent to: yihui.wang@bjtu.edu.cn

23. OUTLINE • Background • Model • Solution approach • Case study • Conclusions yihui.wang@bjtu.edu.cn

24. 4. Case study • Blockade starts at 7:10am and lasts to 8:30am at least • Turnaround time should be between 120s and 720s • The minimal headway is 120s(normalcase) • The expected headway during disruption period is setas300s yihui.wang@bjtu.edu.cn

25. 4. Case study The reaction time of dispatcher is 5min • Trainsareforcedtostopatstationsuntildispatchertakesactions • Longerreactiontimeresultslargerdelays The reaction time of dispatcher is 10min yihui.wang@bjtu.edu.cn

26. 4. Case study The reaction time of dispatcher is 5min • Dwell times of train services at stations are much longer in the beginning of the disruption • 6 rollingstocksarerequired to satisfy the expected headway(sameasrollingstocksontheline) • Longerturnaroundtimesforthestationbeforethedisruptedarea(up down) The reaction time of dispatcher is 10min The reaction time of dispatcher is 300s yihui.wang@bjtu.edu.cn

27. 4. Case study The reaction time of dispatcher is 5min • Alongerreactiontimeresultsbiggerheadwayvariations • Thenumbersofaffectedtrainservicesarethesame • Theexpectedheadwaycanbereached The reaction time of dispatcher is 10min yihui.wang@bjtu.edu.cn

28. OUTLINE • Background • Model • Solution approach • Case study • Conclusions yihui.wang@bjtu.edu.cn

29. Conclusions • Effectivedisruptionmanagementalgorithmsareimportantforthedailyoperations • Amodelisproposed to integratethe train rescheduling and rollingstockcirculation in case of complete blockade • The problemis transformed into an MILP problem andsolvedbyCPLEX • A smallcasestudy based on the Beijing Yizhuang line is performed yihui.wang@bjtu.edu.cn

30. Conclusions yihui.wang@bjtu.edu.cn

31. Thankyouforyourattention! Yihui Wang Beijing Jiaotong University yihui.wang@bjtu.edu.cn