a.dariano@dia.uniroma3.it

Dynamic Control of Railway Traffic A state-of-the-art real-time train scheduler based on optimization models and algorithms 20/06/2013 a.dariano@dia.uniroma3.it 1

The Aut.O.R.I. Lab (Rome Tre University) The Laboratory of Automation and Operations Research in Industry at the Roma Tre University has an international reputation for its excellence in research and teaching. It strives to maximise the relevance of its research to the marketplace through problem anticipation and solving, development of new optimization solutions, and dissemination. Mission: Ensure education and advanced research in Operations Research and Industrial Automation. Aim towards improved efficiency of transportation services and industrial organization through better operations management. Research: Oriented towards the development of new mathematical models and algorithms for solving practical scheduling problems. Main problems addressed in the last 10 years concern real-time railway management, from capacity optimisation to speed control. Permanent development of tools based on most recent research. Education: Operations Research, Industrial Automation, Combinatorial Optimization, Optimization in Public Services, Logistics Optimization, Managerial Decision Support Systems. 2

Members The RailOptGroup at the Aut.O.R.I. Lab 1 full professor: Dario Pacciarelli, head of the Aut.O.R.I. Lab 1 assistant professor: Andrea D Ariano 1 Ph.D. student: Marcella Samà 2 external collaborators (among others): Marco Pranzo (University of Siena) Francesco Corman (T.U. Delft) Main achievements in the railway domain Publications on the top international journals on transportation Funded Projects: National (SAT, GENESI) and European projects (COMBINE). Prizes at Railway Application Section of Informs, IEEE Intelligent Transportation Systems Society, International Association of Railway Operations Research, Italian Association of Operations Research, TRAIL Research School. Committee Members: ATMOS, TRB, MT-ITS, IAROR, IEEE ITS 3

Presentation contents Introduction Traffic management models AGLIBRARY solver Alstom case study ROMA dispatching system 4

Research project Context: Keep service intentions in case of unexpected events Aim: Development of novel railway traffic management systems for a precise and effective train traffic regulation in terms of punctuality increase Tool: Flexible rail operations via advanced models and algorithms for train sequencing, routing and timing Application: Recover real-time railway traffic disturbances such as multiple delayed trains and blocked tracks 5

Station A Timetable Station B Station C Recovery time Station D Station E Minimum headway Buffer time Station F Time 6

Station A Real-time Initial delay Station B Station C Conflicts Station D Station E Delay Station F Currenttime Time 7

Station A Real-time Initial delay Timetable sequence Station B Station C Station D Consecutive delay Station E Delay Station F Currenttime Time 8

Station A Real-time Initial delay FIFO sequence Station B Station C Station D Consecutive delay Station E Delay Station F Currenttime Time 9

Maximum consecutive delay for a typical instance is 16 min and the average initial delay is 1.24 min Timetable sequence With rescheduling Comulative consecutive delay in all stations is 3093 min when using the timetable sequence and 1611 min if consecutive delays are minimized by optimal train rescheduling

State-of-the-art: Open issues No advanced dispatching support tool exists to reschedule vehicle movements during operations. In fact, there is still a lack of: Precision: Models and algorithms must include the variability of vehicle dynamics and must respect specific problem constraints; Robustness: Existing dispatching systems are able to provide viable solutions only for small instances and simple disturbances; Quality: A set of good solutions can be computed only if global conflict resolution is considered when computing orders, routes and times of the vehicles running in the studied railway area; Efficiency: The development of novel optimization algorithms must include the constraints due to limited computation times. 11

Presentation contents Introduction Traffic management models AGLIBRARY solver Alstom case study ROMA dispatching system 12

Blocking time theory Clearing point Block sections Sight & Reaction time Running time Minimum headway time Time Space Clearing & Switching time Switching time 13

Conflict detection and resolution (CDR) Stop Weight of fixed arcs Weight of alternative arcs 0 Time 0 Weight of fixed arcs Space Time 14

G = (N,F,A) Alternative Graph (AG) N = Set of nodes F = Set of fixed arcs A= Set of pairs of alternative arcs Max consecutive delay n [Pacciarelli EJOR 2002] Time t0 0 Selection S = Choose at most one arc from each pair in A, thus obtaining a graph G(S)=(N,F S) Problem= Find a complete selection S such that the longest path from 0 to n in G(S) is minimum 15

From AG to MILP t n t1 w8,1 t2 t3 w9,n w0,1 w12,n t7 w0,7 t8 t9 w4,9 t4 t5 t6 t10 0 t0 Min f(t,x) s.t. t1 w0,1 t7 w0,7 t4 w0,4 t10 w0,10 t2 t1 + w1,2 t12 t11 + w11,12 t1 t8 + w8,1 M (1 X8,1_2,7) t7 t2 + w2,7 MX8,1_2,7 t11 X8,1_2,7= 1 X9,2_3,8= 1 X10,3_4,9 = 1 X11,4_5,10 = 1 X12,5_6,11 = 1 t12 16/14

+ + x M w t t F j i w t t x t f hk ij ij i j ij i j ) (1 ), ( ), ( min, MILP ( MILP (Mixed Mixed-Integer Integer Linear Linear Programming Programming) model model FIXED ROUTES FIXED ROUTES 17 = + + selected is k h if selected is j i if x A k h j i Mx w t t x M w t t hk ij hk ij hk h k hk ij ij i j ), ( 0 ), ( 1 ), ),(, (( ) (1,,,

MILP (Mixed-Integer Linear Programming) model FLEXIBLE ROUTES (D Ariano et al. 2013) min f ( t, x, r t t ns = 1 j k y rs t t i = 1 + w y) t j t i + w ij M (1 y rs ) + w M (1 x ) M (1 y h ij hk Mx ij, hk ij, hk M (1 y rs rs ) M (1 ) M (1 y uv ) y uv ) ( i, s = 1,..., nt j ) F rs, r, s (( i, j),( h, k) A x ij, hk = 1 0 if if ( i, j) is selected ( h, k) is selected y rs = 1 0 if route r of train s is otherwise selected ns: number of routes of train s nt: number of trains 18

Presentation contents Introduction Traffic management models AGLIBRARY solver Alstom case study ROMA dispatching system 19

Optimization software: AGLIBRARY XML input file: Timetable Infrastructure Data Train Train routes Data Passable Traveltimes Routes Infeasible Schedule Train (Re)Scheduling CDRFR*algorithms: Heuristics (e.g. FCFS, AMCC, JGH) Branch and Bound (B&B) Feasible Schedule Rerouting Alternatives? No Rerouting or Time Limit Reached Xml output: Optimal Orders Optimal Routes Possible Improvements New Routes Train Rerouting CDR algorithms: Local Search (LS) Tabu Search (TS) *Conflict Detection and Resolution with Fixed Routes 20

Illustrative example (1) CDRFR formulation of a small example with three trains TA 1 2 3 4 TB 7 8 9 10 5 6 TC 11 12 13 14 60 TA 1 10 2 10 3 10 9 10 12 10 13 10 14 10 out -131 0 0 TB 20 20 7 8 20 9 10 20 5 20 6 20 out -160 n 40 TC 11 10 8 10 9 10 10 10 5 10 6 10 out -122 Each alternative pair is used to order two trains on a block section 21

Illustrative example (2) Optimal CDRFR solution computed by the B&B algorithm 1 2 3 4 7 8 9 10 5 6 TC TB 11 12 13 14 local rerouting available... TA 60 TA 1 10 2 10 3 10 9 10 12 10 13 10 14 10 out -131 0 0 TB 7 20 8 20 9 20 10 20 5 20 6 20 out -160 n 40 TC 11 10 8 10 9 10 10 10 5 10 6 10 out -122 Max cons. delay = 8 A conflict-free deadlock-free schedule is a complete consistent selection S 22

1 Illustrative example (3) Optimal solution to the compound CDR problem 2 3 4 New output sequence! 7 8 9 10 5 6 TB TC 11 12 13 14 TA 60 TA 1 10 2 10 3 10 4 10 5 10 13 10 14 10 out -131 0 0 TB 7 20 8 20 9 20 10 20 5 20 6 20 out -160 n 40 TC 11 10 8 10 9 10 10 10 5 10 6 10-122 out Max cons. delay = 0 A new route for TA and a new complete consistent selection S are shown 23

Test on Utrecht-DenBosh dispatching area Utrecht-Den Bosch railway network (50 km long, including 21 station platforms) 40 running trains per hour (timetable 2007) Rolling stock connections are located in Zaltbommel and Den Bosch stations Rerouting is performed in stations and corridors (356 local routes) 24

Results on the compound CDR problem (1) [Transp. Science 2008] Percentage of maximum consecutive delays for four ROMA(AGLIBRARY) config. ARI + Default Routing ARI + Routing Optimization* B&B + Default Routing B&B + Routing Optimization* 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% Average Default Routing Routing Optimization Results Delay Delay Time Delay Delay Time Max Avg Tot Max Avg Tot ARI 489.4 66.9 0.6 417.0 60.5 8.1 B&B 279.8 50.4 2.1 245.3 44.8 33.9 (in seconds) * *Routing Optimization by the local search algorithm 25

Results on the compound CDR problem (2) [TRpB 2010] * * * * * Perturbations are multiple train delays Disruptions are tracks which are blocked * * * * * *Routing Optimization by the tabu search algorithm 26

Presentation contents Introduction Traffic management models AGLIBRARY solver Alstom case study ROMA dispatching system 27

Alstom Strategy Conflict Detection And Resolution LOCAL Alternative routes near the conflicts detected Current status Timetable Manager Infrastructure Manager Rolling Stock Manager ICONIS DSS New schedule Current status AGLibrary 28

Railway network (nearby London) 29

Example 1 of disruption 30

Set of 10 small instances ID Alstom Time horizon Average number for resources per train Total number of alternative routes Num of trains Num of alt pairs Num of arcs Num of nodes 1 15 20 22 33 489 2236 1055 2 15 19 9 37 684 2842 1191 3 15 19 21 41 873 3263 1291 4 15 15 14 38 1833 5511 1544 5 15 17 3 40 1003 3569 1327 6 15 18 6 34 1047 3548 1249 7 15 20 6 36 835 3079 1201 8 15 22 8 32 890 3293 1289 9 15 19 11 33 2068 6003 1599 10 15 17 10 37 1638 5179 1566 31

Set of 9 medium instances ID Alstom Time horizon Average number for resources per train Total number of alternative routes Num of trains Num of alt pairs Num of arcs Num of nodes 11 30 18 33 40 2283 6862 1959 12 30 17 31 48 2897 8380 2203 13 30 12 17 54 5475 14088 2641 14 30 13 7 52 3845 10575 2450 15 30 15 4 49 3670 10051 2339 16 30 16 7 42 3007 8473 2106 17 30 17 10 44 2798 8079 2120 18 30 17 11 43 2697 7894 2121 19 30 17 13 41 4003 10691 2305 32

Set of 10 large instances ID Alstom Time horizon Average number for resources per train Total number of alternative routes Num of trains Num of alt pairs Num of arcs Num of nodes 20 55 12 29 58 9405 23149 3726 21 55 12 29 59 9166 22669 3641 22 55 13 26 57 8759 21815 3639 23 60 11 16 64 11642 27993 4058 24 60 12 33 58 10925 26415 3915 25 60 12 31 66 11640 28063 4124 26 60 8 38 90 22188 50682 5483 27 60 12 5 59 11012 26644 3982 28 60 8 19 85 26081 59044 6030 29 60 12 13 61 11450 27550 3998 33

Computational results Intel Core 2 Duo E6550 (2.33 GHz), 2 GB di RAM, Windows XP Scheduling & routing problem (CDR problem) : 29 instances CPLEX (algorithm: 1 hour of computation): [MILP formulation solved by IBM LOG CPLEX MIP 12.0] 6 fails, 22 optimum, avg comp time (algo) best sol 1011.7 sec AGLIBRARY (algorithm: 20 sec of computation): [Branch & Bound (EJOR, 2007) + Tabu Search (TRpartB, 2010)] 0 fails, 21 optimum, avg comp time (algo) best sol 11.6 sec N.B. Specific information on disruption resolution scenarios is not yet included in the solver... 34

CPLEX vs AGLIBRARY (scheduling & routing) small instances medium instances large instances 35

CPLEX vs AGLIBRARY (scheduling & routing) Time solver to compute the best solution (in seconds) BB+TS 7000 CPLEX 6000 FAIL FAIL FAIL FAIL FAIL FAIL 5691,7 best solution time 5000 4000 3000 2000 4358,7 2426,7 2190,6 1000 0 Instance ID 877,0 518,8 376,3 318,7337,9 10,4 13,1 39,0 4,5 15,5 14,8 27,0 25,7 120,7 21,0 116,7 207,1 236,7 80,6 1,1 1,1 4,1 3,1 0,8 1,4 1,3 1,1 4,8 8,5 5,5 13,9 8,4 3,5 1,3 9,1 6,0 5,9 9,0 23,5 2,3 2,6 18,4 24,2 19,1 29,0 24,5 79,3 23,1 0ID 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 small instances medium instances large instances 36

Demo at Alstom Ferroviaria S.P.A.

Presentation contents Introduction Traffic management models AGLIBRARY solver Alstom case study ROMA dispatching system 38

ROMA* system (1) [Networks & Spat. Economics 2009] AGLIBRARY Data Loading: Actual speed and position of all trains at their entrance in the studied area; Infrastructure status (such as track layout, signals, switches and speed limits); Timetable data; Rolling stock characteristics; Any additional significant real-time information. RailXML *Railway traffic Optimization by Means of Alternative graphs 39

ROMA system (2) [Transp. Science 2008] AGLIBRARY Disruption Recovery: Discards infeasible routes from a list of prioritized routes; Assigns the feasible route with highest priority to each train; Emergency timetable to be adopted when dealing with situations of strong disorder. 40

ROMA system (3) [Transp. Science 2008] AGLIBRARY Real-Time Railway Traffic Optimization: Solves the conflict detection and resolution problem by means of alternative graphs and with strict time limits of computation; Modifies train routes & orders; Reduces delay propagation; Improves use of infrastructure capacity at network scale. 41

ROMA system (4) [Comprail 2006] [IEEE Trans. ITS 2007] AGLIBRARY Train Speed Coordination: Adjusts the speed profiles of the running trains (safe headway distances for any pair of trains); Checks feasibility according to the blocking time theory (i.e., UIC norm 406); Uses single/iterative scheduling strategies (in combination with the Real-Time Railway Traffic Optimization module). 42

Inputs Train Speed Coordination [Comprail 2006] [IEEE Trans. ITS 2007] Infrastructure Stations, signals, switches Speed limits Track layouts Signalling rules Rolling Stock Train length Standard acceleration & braking tables Initial speeds & positions Timetable Scheduled arrival/departure times Scheduled paths Stochastic disturbances Iterative rescheduling (Re)Calculation of Train Dynamics Running times Train trajectories No Overlap Detection Any overlaps of blocking times? Outputs Optimal orders Optimal routes New arrival/ departure times Yes Fixed speed CDR Minimizing consecutive delays 43

A list of recent railway-related publications: Corman, F., D Ariano, A. (2013). Assessment of advanced dispatching measures for recovering disrupted railway traffic situations, Transportation Research Record, Journal of the Transportation Research Board, 2289, 1 9. Kecman, P., Corman, F., D Ariano, A., Goverde, R.M.P. (2013). Rescheduling models for railway traffic management in large-scale networks. Public Transport: Planning and Operations. Larsen, R., Pranzo, M., D Ariano, A., Corman, F., Pacciarelli, D. (2013). Susceptibility of Optimal Train Schedules to Stochastic Disturbances of Process Times, Flexible Services and Manufacturing Journal. Corman, F., D Ariano, A., Hansen, I.A. (2013). Evaluating disturbance robustness of railway schedules, Journal of Intelligent Transport Systems: Technology, Planning, and Operations. Giacco, G.L., D Ariano, A., Pacciarelli, D. (2013). Rolling stock rostering optimization under maintenance constraints, Journal of Intelligent Transport Systems: Technology, Planning, and Operations. Corman, F., D'Ariano, A., Pacciarelli, D., Pranzo, M. (2012). Optimal inter-area coordination of train rescheduling decisions, Transportation Research Part E, 48(1), 71 88. Corman, F., D'Ariano, A., Pacciarelli, D., Pranzo, M. (2012). Bi-objective conflict detection and resolution in railway traffic management. Transportation Research Part C, 20 (1), 79 94. Corman, F, D'Ariano, A, Hansen, I.A., Pacciarelli, D. (2011). Optimal multi-class rescheduling of railway traffic, Journal of Rail Transport Planning & Management, 1 (1), 14 24. Corman, F., D'Ariano, A, Pranzo, M, Hansen, I.A. (2011). Effectiveness of dynamic reordering and rerouting of trains in a complicated and densely occupied station area. Transportation Planning and Technology, 34 (4), 341 362. Corman, F., D'Ariano, A, Pacciarelli, D, Pranzo, M. (2011). Centralized versus distributed systems to reschedule trains in two dispatching areas. Public Transport: Planning and Operations, 2 (3), 219 247. Corman, F., D'Ariano, A., Pacciarelli, D., Pranzo (2010). M. A tabu search algorithm for rerouting trains during rail operations. Transportation Research Part B, 44 (1), 175 192. Corman, F., D Ariano, A., Hansen, I.A. (2010). Disruption handling in large railway networks, In: B. Ning, C.A. Brebbia, N. Tomii (Eds.), Computers in Railways XII, WIT Transactions on The Built Environment 114 629 640. D Ariano, A. (2010). Improving real-time train dispatching performance: Optimization models and algorithms for re-timing, re-ordering and local re-routing, 4OR: A Quarterly Journal of Operations Research, 8 (4), 429 432. 44

D'ArianoA., PranzoM., (2009). An advanced real-time train dispatching system for minimizing the propagation of delays in a dispatching area under severe disturbances, Networks and Spatial Economics, 9 (1), 63 84. Corman, F, D'Ariano, A, Pacciarelli, D, Pranzo, M (2009). Evaluation of green wave policy in real-time railway traffic management. Transportation Research Part C, 17 (6), 607 616. Corman, F., Goverde, R.M.P., D Ariano, A. (2009) Rescheduling dense train traffic over complex station interlocking areas, Robust and Online Large-Scale Optimization, Lecture Notes in Computer Science 5868, 369-386. D Ariano, A. (2009). Innovative decision support system for railway traffic control, IEEE Intelligent Transportation Systems Magazine, 1 (4), 8 16. A. D Ariano (2008). Improving Real-Time Train Dispatching: Models, Algorithms and Applications, TRAIL Thesis Series T2008/6, pages 1 240, TRAIL Research School, 2008, Delft, The Netherlands. D'Ariano A., Pacciarelli D. and Pranzo M. (2008). Assessment of flexible timetables in real-time traffic management of a railway bottleneck, Transportation Research Part C, 16 (2), 232 245. D'Ariano, A, Corman, F, Pacciarelli, D., Pranzo, M (2008). A Reordering and local rerouting strategies to manage train traffic in real-time. Transportation Science, 42 (4), 1 15. Flamini, M. and Pacciarelli, D. (2008). Real time management of a metro rail terminus. European Journal of Operational Research, 189 (3), 746-761. Mascis, A., D. Pacciarelli, M. Pranzo. (2008). Scheduling Models for Short-term Railway Traffic Optimisation. In M. Hickman, P. Mirchandani and S. Voß (Eds.), Lecture Notes in Economics and Mathematical Systems 600: Computer-aided Systems in Public Transport. Springer. 71-90. D'Ariano A., Pranzo M., Hansen, I.A. (2007). Conflict Resolution and Train Speed Coordination for Solving Real- Time Timetable Perturbations, IEEE Transactions on Intelligent Transportation Systems, 8 (2), 208 222. D'Ariano A., Pacciarelli D., Pranzo M. (2007). A branch and bound algorithm for scheduling trains in a railway network, European Journal of Operational Research, 183 (2), 643 657. D Ariano A., Albrecht, T. (2006). Running time re-optimization during real-time timetable perturbations, In: J. Allan, C.A. Brebbia, A.F. Rumsey, G. Sciutto, S. Sone and C.J. Goodman(Eds.), Computers in Railways IX, WIT Transactions on The Built Environment, 88, 531 540. Mascis, A. and Pacciarelli, D. (2002). Job-shop scheduling with blocking and no-wait constraints. European Journal of Operational Research, 143(3):498 517. 45