Project B5 03/2003–05/2006 Line planning and periodic timetabling in railway traffic

DFG Research Center MATHEON Christian Liebchen Rolf H. Möhring Elmar Swarat Technische Universität mathematics for Berlin key technologies www.math.tu-berlin.de/coga/projects/matheon/B5/ www.tu-berlin.de www.matheon.de4u Sonntag 15 20 10 U 2.01Q 3.46 4.01 4.16 4.35Q 7.15 . 7.35Q 23.35 23.46 0.01 0.16 0.31 U Zwickauer Damm 2.03Technology 3.48 4.03 4.18transfer 4.36 7.16 . 7.36 23.36 23.48 0.03 0.18 0.33 U Wutzkyallee 2.04 3.49 4.04 4.19 4.37 7.17 . 7.37 23.37 23.49 0.04 0.19 0.34 U Lipschitzallee 2.05We established 3.50 4.05 a4.20 cooperation 4.39 with 7.19 the underground . 7.39 division 23.39of 23.50Berliner 0.05 Verkehrsbe- 0.20 0.35 U Johannisthaler Chaussee 2.07triebe 3.52 (BVG). 4.07 Our 4.22 computations 4.40 lead 7.20 to the .2005 7.40 timetable 23.40 of Berlin 23.52 Undergound 0.07 0.22 0.37. Objectives U Britz-Süd 2.09To the 3.54 best 4.09 of our 4.24 knowledge, 4.42 this 7.22 is the 7.32 first timetable 7.42 that 23.42 has 23.54 been computed 0.09 0.24 with 0.39 mathematical optimization techniques, and finally got into daily operation. U Parchimer Allee 2.10 3.55 4.10 4.25 4.43 7.23 7.33 7.43 23.43 23.55 0.10 0.25 0.40 U Blaschkoallee• short transfer times 2.11 3.56 4.11 4.26 4.45 7.25 7.35 7.45 23.45 23.56 0.11 0.26 0.41 U Grenzallee• balanced service 2.13 3.58 4.13 4.28 4.47 7.27 7.37 7.47 23.47 23.58 0.13 0.28 0.43 S+U Neukölln 2.15 4.00 4.15 4.30 4.48 7.28 7.38 7.48 23.48 0.00 0.15 0.30 0.45 04.5 Sn Sn U Karl-Marx-Str.• few trains 2.16 4.01 4.16 4.31 4.50 7.30 7.40 7.50 23.50 0.01 0.16 0.31 0.46 U Rathaus Neukölln 2.17 4.02Fp 4.17 4.32 4.51 7.31 7.41 7.51Fp 23.51 0.02 0.17 0.32 0.47 • safety requirements 02.0 U Hermannplatzheadways, single tracks. . . 2.19 4.04 4.19 4.34 4.52 7.32 7.42 7.52 23.5208.5 0.04 0.19 06.0 0.34 0.49 U Südstern 2.21 4.06 4.21 4.36Be 4.54 7.34 7.44 7.54 23.54 0.06Be 0.21 0.36 0.51 • robustness U Gneisenaustr. 2.22 4.07 4.22 4.37 4.56 7.36 7.46 7.56 23.56 0.07 0.22 0.37 0.52 U Mehringdamm an 2.24 4.09 4.24 4.39 4.58 7.38 7.48 7.58 23.58 0.09 0.24 0.39 0.54 U Mehringdamm ab 2.25An important 4.10 4.25 step 4.40 is 4.58the visualization 7.38 of 7.48 results. 7.58 To that 23.58 end, 0.10 we developed 0.25 0.40 the 0.54 U Möckernbrücke 2.26network 4.11 waiting 4.26 4.41 time chart4.59. Important 7.39 7.49transfers 7.59 are represented 23.59 0.11 by 0.26bold 0.41transfer 0.56 S+U Yorckstr. 2.28arcs. 4.13 In our 4.28 example, 4.43 5.01 long waiting 7.41 times 7.51 (> 5 8.01min) are highlighted 0.01 0.13 by 0.28red 0.43transfer 0.57 arcs. One can observe easily that the number of (bold) red arcs decreased after U Kleistpark 2.29 4.14 4.29 4.44 5.02 7.42 7.52 8.02 0.02 0.14 0.29 0.44 0.59 mathematical optimization has been involved (right chart). U Eisenacher Str. 2.31 4.16 4.31 4.46 5.04 7.44 7.54 8.04 0.04 0.16 0.31 0.46 1.00 U Bayerischer Platz 2.32 4.17 4.32 4.47 5.05 7.45 7.55 8.05 0.05 0.17 0.32 0.47 1.01 USelected Berliner Str. publications an 2.33 4.18 4.33 4.48 5.06 7.46 7.56 8.06 0.06 0.18 0.33 0.48 1.03 U Berliner Str. ab 2.33 4.18 4.33 4.48 5.08 7.48 7.58 8.08 0.08 0.18 0.33 0.48 1.03 C. Liebchen, Finding Short Integral Cycle Bases for Cyclic Timetabling, In: Algorithms (ESA) 2003, Springer LNCS 2832 UC. Blissestr. Liebchen and R.H. Möhring, The Modeling 2.34 Power of the 4.19Periodic 4.34 Event 4.49 Scheduling 5.09 Problem: Railway7.49 7.59 Timetables 8.09 - and Beyond 0.09, 0.19 0.34 0.49 1.04 UTo Fehrbelliner appear in: Proceedings Platz of CASPT 2004, Springer 2.36 LNEMS, 4.21 2006 4.36 4.51 5.11 7.51 8.01 8.11 0.11 0.21 0.36 0.51 1.05 UC. Konstanzer Liebchen and Str. R. Rizzi, A Greedy Approach 2.37 to Compute a4.22 Minimum 4.37 Cycle 4.52 Bases 5.12 of a Directed 7.52 Graph 8.02, Information 8.12 Processing 0.12 Letters 0.2294 (3), 0.37 2005 0.52 1.07 U AdenauerplatzSupporting theory 2.38 4.23 4.38 4.53 5.13 7.53 8.03 8.13 0.13 0.23 0.38 0.53 1.08 U Wilmersdorfer Str. 2.40 4.25 4.40 4.55 5.15 7.55 8.05 8.15 0.15 0.25 0.40 0.55 1.09 U Bismarckstr.Our solution algorithms are essentially 2.41 based 4.26 on 4.41integer 4.56 pro- 5.16 7.56 8.06 8.16 0.16 0.26 0.41 0.56 1.11 gramming techniques. We identified short integral cycle bases Cooperation/Visibility U Richard-Wagner-Platz 2.42 4.27 4.42 4.57 5.17 7.57 8.07 8.17 0.17 0.27 0.42 0.57 1.12 of directed graphs to be particularly helpful for finding strong U Mierendorffplatzsuch IP formulations. We succeded 2.44 to draw 4.29 the 4.44 complete 4.59 5.19pic- 7.59• Inside 8.09 M 8.19ATHEON 0.19 0.29 0.44 0.59 . S+U Jungfernheideture of seven subclasses of directed 2.45 cycle 4.30 bases. 4.45 5.00 5.20 8.00B1 8.10adaptation 8.20 of 0.20 interfaces, 0.30 0.45 1.00 . U Jakob-Kaiser-Platz 2.47 4.32 4.47 5.02 5.22 8.02 8.12integration 8.22 line 0.22 planning/timetabling 0.32 0.47 1.02 . ⇒ U . . 4.48 5.03 5.23 8.03 8.13 8.23NEW PROJECT 0.23 0.33 B15 0.48 1.03 . B8 Investigation of cycle bases U Siemensdamm . . 4.50 5.05 5.25 8.05 8.15 8.25 0.25 0.35 0.50 1.05 . F5 MATHEON Video U . . 4.51 5.06 5.26 8.06 8.16 8.26 0.26 0.36 0.51 1.06 . strictly weakly G5 talks in schools TUM integral undirected directed U Paulsternstr.fund. fund. . . 4.53 5.08 5.28 8.08 8.18 8.28 0.28 0.38 0.53 1.08 . • External scientists U HaselhorstSF(3) K .K3,3 Champ. .P11 4.54,4 5.09P7,2 5.29 8.09 8.19 8.29 0.29 0.39 0.54 1.09 . 3 EU research project ARRIVAL, U Zitadelle . . 4.56 5.11 5.31 8.11 8.21 8.31 0.31 0.41 0.56 1.11 . 2-bases Leon Peeters (Zürich), Romeo Rizzi (Trento) U Altstadt Spandau . . 4.57 5.12 5.32 8.12 8.22 8.32 0.32 0.42 0.57 1.12 . S+U Rathaus Spandau . . 4.58 5.13 5.33 8.13• Industry 8.23 8.33 0.33 0.43 0.58 1.13 . 6 ×V 8 Berliner Verkehrsbetriebe (BVG), Deutsche Bahn AG (funded software development), intranetz GmbH, PTV AG

Map of directed cycle bases (Liebchen and Rizzi, 2005) • General Audience two newspaper articles, radio interview, Adventskalender, Lange Nacht der Wiss.