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Mathematical Aspects of Public Transportation Networks Niels Lindner July 9, 2018 July 9, 2018 1 / 48 Reminder Dates I July 12: no tutorial (excursion) I July 16: evaluation of Problem Set 10 and Test Exam I July 19: no tutorial I July 19/20: block seminar on shortest paths I August 7 (Tuesday): 1st exam I October 8 (Monday): 2nd exam Exams I location: ZIB seminar room I start time: 10.00am I duration: 60 minutes I permitted aids: one A4 sheet with notes July 9, 2018 2 / 48 Chapter 6 Metro Map Drawing x6.1 Metro Maps July 9, 2018 3 / 48 x6.1 Metro Maps Berlin, 1921 (Pharus-Plan) alt-berlin.info July 9, 2018 4 / 48 x6.1 Metro Maps Berlin, 1913 (Hochbahngesellschaft) Sammlung Mauruszat, u-bahn-archiv.de July 9, 2018 5 / 48 x6.1 Metro Maps Berlin, 1933 (BVG) Sammlung Mauruszat, u-bahn-archiv.de July 9, 2018 6 / 48 x6.1 Metro Maps London, 1926 (London Underground) commons.wikimedia.org July 9, 2018 7 / 48 x6.1 Metro Maps London, 1933 (Harry Beck) July 9, 2018 8 / 48 x6.1 Metro Maps Plaque at Finchley Central station Nick Cooper, commons.wikimedia.org July 9, 2018 9 / 48 x6.1 Metro Maps Berlin, 1968 (BVG-West) Sammlung Mauruszat, u-bahn-archiv.de July 9, 2018 10 / 48 x6.1 Metro Maps Berlin, 2018 (BVG) Wittenberge RE6 RB55 Kremmen Stralsund/Rostock RE5 RB12 Templin Stadt Groß Schönebeck (Schorfheide) RB27 Stralsund/Schwedt (Oder) RE3 RE66 Szczecin (Stettin) RB24 Eberswalde Legende Barrierefrei durch Berlin Key to symbols Step-free access Sachsenhausen (Nordb) RB27 Schmachtenhagen 7 6 S-Bahn-/U-Bahn : Aufzug Oranienburg 1 RB20 : Wandlitzsee urban rail/underground lift Vehlefanz Rüdnitz Berlin Lehnitz RB27 Wensickendorf RE1 Wandlitz RE1 RB22 Bahn-Regionalverkehr Rampe Bärenklau Borgsdorf Bernau 2 : RB22 regional rail ramp Basdorf Birkenwerder 8 : Zühlsdorf : Einige Linien halten nicht überall : nur zur S-Bahn Velten (Mark) Hohen Neuendorf West RB20 RE5.RB12 Bernau-Friedenstal Schönwalde (Barnim) Some trains do not stop at all stations only to urban rail RB2 Zepernick : Flughafen : Hennigsdorf bE RB55 : :Hohen Neuendorf Bergfelde : Schönfließ Mühlenbeck-Mönchmühle 7 Schönerlinde 0A nur zur U-Bahn Röntgental : airport only to underground Heiligensee : :Frohnau Fernbahnhof : bF : Buch : nur zum Bahn-Regionalverkehr : :Hermsdorf Waidmannslust mainline station only to regional rail Schulzendorf Karow RB27 : Wittenau 8 : ZOB Zentraler Omnibusbahnhof :Rathaus Reinickendorf bus terminal : Tegel : : Wilhelmsruh A B C VBB-Tarifteilbereiche Berlin :6 Alt-Tegel Karl-Bonhoeffer- :Blankenburg Nervenklinik VBB fare zones Berlin 0 Borsigwerke . RB2 Eichborndamm : Alt-Reinickendorf Schönholz : Kein Zugverkehr Holzhauser Str. :Pankow-Heinersdorf eE Stand: 7. Mai 2018 RE6 : . RB27 no service © Berliner Verkehrsbetriebe (BVG) :Otisstr. :Lindauer Allee RB1 . RE66 2 . 05.06. - 11.12.2018 600-1-18.1-2 RB24 :Scharnweberstr. :Paracelsus-Bad . RE5 RE3 :Kurt-Schumacher-Platz 128 Residenzstr. :hE 2 Pankow Werneuchen RB25 : Franz-Neumann-Platz Osloer Str. 9 : Wollankstr. : 0A Tegel TXL Afrikanische Str. Am Schäfersee Seefeld (Mark) 28 Blumberg 1 :Rehberge gE Blumberg-Rehhahn TXL 128 Wartenberg Nauen Seestr. Nauener Platz Vinetastr. : Ahrensfelde Nord RB10 Pankstr. RB14 09 7 Ahrensfelde Friedhof 1 Ahrensfelde TXL Brieselang Leopoldplatz : X9 : Bornholmer RE2 Amrumer Str. : Wismar : Str. : Hohenschönhausen : : Siemens- RE6 RE66 RB27 Mehrower Allee Finkenkrug Zitadelle Haselhorst Paulsternstr. Rohrdamm damm Halemweg : : : : Schönhauser Allee : Prenzlauer Allee : < Beusselstr. Westhafen Wedding Gesundbrunnen RE2 5 Strausberg Nord . RE6 Falkensee : 5 . Jakob-Kaiser-Platz . Gehrenseestr. RB2 RB1 RE4 RE6 RB10 RE3 RE5 RE6 : Greifswalder Str. : Raoul-Wallenberg-Str. Strausberg Stadt 0 Altstadt Spandau :Reinicken- Voltastr. 2 > 0 . Seegefeld : 1 Jungfernheide :Humboldthain : RB1 dorfer Str. Eberswalder Str. < RB S4 RB13 : RE3 Bernauer Str. : S42 Hegermühle 4 . Albrechtshof S42 RE4 : S4 Marzahn : : < Birkenstr. Schwartz- :Nordbahnhof :5 Rathenow Dallgow- : 7 : . 1> Hönow Elstal Döberitz : Rathaus Spandau RE5 kopffstr. Senefelderplatz : RE4 . :Oranien- TXL RB1 : . RE4.RE6.RB10.RB13 09 Naturkunde- Rosenthaler Louis-Lewin-Str. Wuster- RE4 RB13 RE2 RE4 RE6 RB10 RB13 RB14 1 :Staaken Spandau 0 burger Poelchaustr. mark 3 9 :museum :Platz Rosa-Luxemburg-Platz : Stresow : X9 Str. Kostrzyn RB13 4 Mierendorffplatz Hellersdorf (Küstrin) RB21 :Turmstr. eE : :Oranien- Weinmeisterstr. 1 RB RB26 :Ruhleben . : Hauptbahnhof burger Tor Hackescher Markt : Strausberg 2 dF :5 : Landsberger Allee : Springpfuhl : RE2 Westend RB25 Cottbusser Platz . Alexanderplatz 4 X9 Petershagen Nord :Pichelsberg :Olympia- Schillingstr. : 2 RB : Richard-Wagner-Platz : RE1.RE2.RE7.RB14 . Kienberg 2 Stadion 09 Bundestag Fried- Gärten der Welt : 1 Fredersdorf : Neu-Westend richstr. Strausberger Platz 1 : : RB Bellevue RB21 RB22 : :Friedrichs- Neuenhagen Weberwiese : Storkower Str. : Kaulsdorf-Nord :Olympiastadion Sophie- : Branden- Jannowitz- felde Ost RB26 Kaiserdamm Charlotte-Platz Bismarckstr. TXL :Tiergarten burger ToreE : Klosterstr. brücke : Frankfurter Tor : Magdalenen- Biesdorf Wuhletal Kaulsdorf Mahlsdorf Birkenstein Hoppegarten : Theodor-Heuss-Platz : Messe Nord/ Deutsche Ernst-Reuter- : : Französische Str. :Märkisches : Samariterstr. : Heerstr. ICC : Hansaplatz Mohrenstr. : Museum str. : Friedrichsfelde : : : : : : Messe ZOB Oper Platz Potsdamer Platz Ostbahnhof Priort Wilmers- : Elsterwerdaer Platz : Frankfurter Lichtenberg Messe :dorfer Str. Savignyplatz Mendelssohn-Bartholdy- :Stadtmitte Hausvogtei-Spittel- Heinrich- 1 3 : : Süd :Park Allee RB26 : : platz markt Heine-Str. Warschauer Str. Biesdorf-Süd Zoologischer Garten : Anhalter Bhf : : Nöldnerplatz :Tierpark Kochstr. : Moritzplatz Westkreuz Charlotten- : Checkpoint Charlie Wittenberg- Kurfürsten- < Rummelsburg : :5 :burg :1 Uhlandstr. platz str. Prinzenstr. : RE1 : . Schlesisches Tor Ostkreuz RE2 :Halensee Adenauer- gE RB12 RB25 . Betriebsbahnhof Rummelsburg : :Kurfürsten- Gleis- Hallesches Tor :Kottbusser Tor Görlitzer Bhf RE7 platz . damm Nollen- Bülow- dreieck Möckern- RB1 2 : : : brücke 4 Karlshorst Grunewald : : Schönleinstr. RB24 . RB2 Augsburger dorfplatz str. A B C 1 RB21 4 . Str. : : Wuhlheide : 0 . RB2 Spichernstr. Mehringdamm : 2 Hermannplatz : Treptower Park . RE7 Viktoria-Luise- RB Konstanzer Str. Hohenzollern- RE1 Platz :platz :Yorckstr. Gneisenaustr. Südstern : Rathaus Köpenick : Güntzelstr. Großgörschenstr. Neukölln : Yorckstr. : : :Fehrbelliner Platz Berliner Str. : :Kleistpark Platz der Boddinstr. > Luftbrücke S42 RB24 Plänterwald : 4 Hirschgarten 5 :Hohenzollerndamm RE 1 . Karl-Marx- 1 Blissestr. Bayerischer Platz Eisenacher S4 RB < < . S4 Paradestr. : : Str. 4 Str. RE Leinestr. RE1 . 1 0 7 S42 Rathaus : RE : Julius- Sonnenallee : . Friedrichshagen RB1 3 > Schöneberg Leber-Brücke RE : : Tempelhof Neukölln RE2 Köllnische Heide : :Heidelberger Platz Baumschulenweg : Rahnsdorf : :Bundesplatz Innsbrucker Schöneberg : Südkreuz : Hermannstr. : Marquardt Rüdesheimer Platz Alt-Tempelhof < : :4 Platz dE RB10 dG 8 Grenzallee Wilhelmshagen Breitenbachplatz Oberspree Spindlersfeld dG Frankfurt :Friedrich-Wilhelm-Platz Kaiserin-Augusta-Str. : :Schöneweide (Oder) Podbielskiallee 3 : Friedenau : Blaschkoallee : Erkner RE1 Ullsteinstr. : Eisen- :Dahlem-Dorf :Walther-Schreiber-Platz hütten- :Betriebsbahnhof Schöneweide stadt :Priesterweg Westphalweg Parchimer Allee Freie Universität Feuerbachstr. : RE1 Thielplatz Schloßstr. 6 : : Fangschleuse Oskar-Helene-Heim Alt-Mariendorf Adlershof : Britz-Süd : : Attilastr. :Onkel Toms Hütte :9 Rathaus Steglitz Südende hE : Johannisthaler Grünau : : Schlachtensee Krumme Lanke Lankwitz Marienfelde Chaussee 3 : :Botanischer Garten Lipschitzallee : :Mexikoplatz :Altglienicke Eichwalde : Golm Lichterfelde West Wutzkyallee : :Nikolassee :Lichterfelde Ost RE2 Zeuthen 8 Frankfurt 2 . 2 Buckower Chaussee Grünbergallee (Oder) RB22 : Niederlehme Zernsdorf Kablow RB Zwickauer Damm Wildau RB36 . 1 RB33 :Wannsee . 1 : : RB2 Branden- 2 Zehlendorf Sundgauer Str. RB36 . RE5 4 burg RB 2 . 0 : : : : . RE4 7 : RE1 2 1 Osdorfer Str. Schichauweg : Rudow . RB2 dF RB22 RB36 : Park Char- : Griebnitz- 4 Königs Wusterhausen RB RB2 RE3 Magde- . 3 burg Sans- lotten- Babelsberg see . RB1 souci hof . RE.7RB3 RE1 2 X7 1 RE7 RE1 Zeesen :Werder Potsdam Hbf : RB2 :Lichterfelde Süd 71 N7 (Havel) 7 RB20 RB21 RB22 Medienstadt Babelsberg Lichtenrade Cottbus RB23 RE2 Pirschheide Rehbrücke RB22 RB24 Teltow Caputh- < :bE bFTeltow Stadt < Mahlow : Flughafen Berlin-Schönefeld dE 9 RB14 Senftenberg Geltow Wilhelmshorst RB22 Großbeeren RE5.RB22 RE7.RB22 0A Schönefeld SXF Caputh Saarmund Ludwigsfelde Struveshof : 2 Blankenfelde Schwielowsee RB23 Michendorf RB23 : > Birkengrund Waßmannsdorf Dahlewitz Ferch- Ludwigsfelde : Lienewitz Seddin Thyrow Rangsdorf Flughafen Berlin Brandenburg Airport Ein Verbund. Ein Tarif. Dessau RE7 RB33 Jüterbog Jüterbog RE4 RE3 Lutherstadt Wittenberg/Falkenberg (Elster) Elsterwerda RE5 RE7 Wünsdorf-Waldstadt Berliner Verkehrsbetriebe, bvg.de July 9, 2018 11 / 48 x6.1 Metro Maps London, 2018 (Transport for London) Tube map 123456789 Special fares apply Special fares Check before you travel 978868 7 57Cheshunt Epping § Brixton Chesham 9 apply Watford Junction No step-free access until September. Chalfont & Enfield Town Theydon Bois Latimer Theobalds Grove --------------------------------------------------------------------------- Watford High Street Bush Hill Debden Shenfield § Watford Heathrow Amersham Cockfosters Park Turkey Street High Barnet Loughton 6 TfL Rail customers should change at A Chorleywood Bushey A Terminals
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