Train Timetabling New Approach

Transcription

1 Tran Tmetablng New Approach Tomáš Robenek CUSO Doctoral Programme n Operatons Research Sprng Semnar January 13, / 27

2 Lberalsaton / 27

3 Lberalsaton Overvew 3 / 27

4 Publc Sector Accessblty/Moblty Fgure : Moblty evoluton n Swtzerland 1 1 source: Entwcklung der MIV und OV Errechbarket n der Schwez: ; Ph. Frohlch, M. Tschopp and K.W. Axhausen

5 Prvate Sector

6 Market Settngs Travel Tme s the same Serve Dfferent Destnatons Better Qualty Better Prce Better Departure Tmes

7 Orgn of a Tmetable? In the ndustry hstorcal Tmetable desgn n the lterature non-cyclc: usng so called "deal tmetables" cyclc: does not take nto account anythng Need to measure qualty of a tmetable! 7 / 27

8 Update of Plannng STRATEGIC - several years TACTICAL - >= 1 year OPERATIONAL - < 1 year Actual Tmetables Tran Platformng Platform Assgnment s Demand Lne Plannng Lnes Ideal Tran Tmetablng Ideal Tmetables Tran Tmetablng Actual Tmetables Rollng Stock Plannng Tran Assgnment s Actual Tmetables Crew Plannng Crew Assgnment s TOC IM 8 / 27

9 TOC Pont of Vew 9 / 27

10 Passenger Pont of Vew Speed (Tme) Beng On Tme Tmetable Watng Tme Transfers

11 Passenger Cost Perceved cost of a gven path usng a gven tmetable (a path s defned as a sequence of tran lnes, n order to get from an orgn to a destnaton): C =argmn α VT + β WT + γ NT + mn (ɛ SD e, η SD l ) I j J I for all possble sets I, where: I set of possble trans n a gven path J I set of transfers n a gven path usng gven trans α value of tme (monetary unts per mnute) β value of watng tme (monetary unts per mnute) γ penalty for havng a transfer (monetary unts) ɛ value of beng early (monetary unts per mnute) η value of beng late (monetary unts per mnute) 11 / 27

12 Routng Model max (revenue cost) D t C t (1) I t T = 1, I, t T, (2) x tp p P y tplv = 1, v V l I, t T, p P, l L p, ( ) (3) dv l dv 1 l = c zv, l l L, v V l : v > 1, (4) C t 0, I, t T, (5) d l v 0, l L, v V l, (6) x tp (0, 1), I, t T, p P, (7) y tplv (0, 1), I, t T, p P, l L p, v V l, (8) z l v N, l L, v V l. (9)

13 Tran Capacty u l 1 v1 = I t T p P l 2 L p :l 2 =l 1 y tpl2v2 v 2 V l 2 :v 2 =v 1 D t, l 1 L, v 1 V l 1, (10) cap b l v u l v, l L, v V l, (11) u l v 0, l L, v V l, (12) b l v N, l L, v V l, (13) 13 / 27

14 Defnng Passenger Cost C t = β w t + γ +α p P p P r pl l L p x tp ( L p 1) x tp + s t, I, t T. (14) 14 / 27

15 Scheduled Delay s t s tp (( s tp η d Lp v + h Lp + r p Lp ( M ( ( s tp ɛ t d Lp v + h Lp M (1 x tp ), I, t T, p P, ) 1 y tp Lp v ) t )) + r p Lp ( M 1 y tp Lp v (15) ), I, t T, p P, v V Lp, (16) ), I, t T, p P, v V Lp, (17) s t 0, I, t T, (18) s tp 0, I, t T, p P. (19)

16 Watng Tme w tpl w tpl (( w t ) d l v + hpl (d l M (1 y tpl v ) d l v + hpl (d l +M (1 y tpl v (( ( w tp M w tp = v + h pl ) M v + h pl ) + M 1 x tp l L p \1 + r pl ( + m 1 y tplv + r pl ( + m 1 y tplv ), I, t T, p P, (20) w tpl, I, t T, p P, (21) )) I, t T, p P, l L p : ), l > 1, l = l 1, v V l, v V l, (22) )) I, t T, p P, l L p : ), l > 1, l = l 1, v V l, v V l, (23) w t 0, I, t T, (24) w tp 0, I, t T, p P, (25) w tpl 0, I, t T, p P, l L p. (26) 16 / 27

17 Breakng the symmetry Cyclc d l v d l v 1 = z l1 v 60 + z l2 v 120, l L, v V : v > 1, z l1 v + z l2 v = 1, l L, v V : v > 1, Non-Cyclc d l v < d l v+1, l L, v V : v < V, 17 / 27

18 Case Study Canton Vaud, Swtzerland 0 source: 18 / 27

19 S-Tran Network Pars Djon Neuchâtel Neuchâtel Benne Ins Kerzers Buttes Trans régonaux Arrêt avec correspondances Murten/Morat Trans régonaux, crculent grandes lgnes Lac de Faoug à certanes heures Arrêt Neuchâtel Avenches Trans grandes lgnes Arrêt sur demande R R Domdder et autres lgnes ferrovares Arrêt à certanes heures Concse Domperre Corcelles-Nord Edton I Sous réserve Ste-Crox Payerne Grandson de modfcatons I CFF SA P-RV-LS Trey Yverdon-les-Bans Granges-Marnand Pontarler S1 Hennez S11 Lucens Ependes Moudon R Romont Essert-Pttet Bressonnaz TER Ecublens-Rue Svrez Chavornay S21 RE Vauderens S2 Bercher Châtllens Oron Echallens RE Palézeux-Vllage R L Isle Cossonay Palézeux Morellon Bussgny Chez-le-Maître Ecoles Vufflens-la-Vlle Pudoux-Chexbres Chez-le-Maître Le Brassus Apples S31 Bère S2 S4 Chexbres-Vllage RE RE Corseaux- Cornalles Vevey-Fun S4 S1 S3 S3 Frasne Le Pont Charbonnères Séchey Le Leu Esserts-de-Rve Le Rocheray Sollat-Golsse Senter-Orent La Cure St-Cergue Vallorbe Nyon Genève RE Gland Le Day Rolle Bretonnères Croy-Romanmôter Orbe Arnex La Sarraz St-Prex Etoy Allaman Lac Léman Eclépens Bavos Denges-Echandens Lonay-Prévrenges Morges-St-Jean Morges Renens VD Prlly-Malley Lausanne Réseau Express Régonal Vaud. Pully-Nord Pully Lutry Vllette VD Cully Epesses Rvaz St-Saphorn Grandvaux La Converson Bossère Evan-les-Bans FRANCE St-Gngolph (Susse) Vevey La Tour-de-Pelz Burer Clarens Montreux Terrtet Veytaux- Chllon Les Pléades Vlleneuve Roche VD R/RE Les Rochersde-Naye Bern Frbourg/Freburg Bulle Broc Zwesmmen Montbovon Leysn Les Dablerets Bretaye Agle Bex St-Maurce Brg 19 / 27

20 Reduced Network Vallorbe 13 Yverdon-Les-Bans 12 Payerne 1 S1 S2 S3 S4 S11 S21 S31 Cossonay 11 2 Palézeux 3 Pudoux-Chexbres Lausanne Renens 8 7 Montreux 9 Morges Vevey Allaman Vlleneuve 4

21 Current Tmetable (Mornng Peak) Lne ID From To Departures S1 S2 S3 S4 S11 S21 S31 1 Yverdon-les-Bans Vlleneuve 6:19 7:19 8:19 2 Vlleneuve Yverdon-les-Bans 5:24 6:24 7:24 8:24 3 Vallorbe Palézeux 5:43 6:43 7:43 8:43 4 Palézeux Vallorbe 6:08 7:08 8:08 5 Allaman Vlleneuve 6:08 7:08 8:08 6 Vlleneuve Allaman 6:53 7:53 8:53 7 Allaman Palézeux 5:41 6:41 7:41 8:41 8 Palézeux Allaman 6:35 7:35 8:35 9 Yverdon-les-Bans Lausanne 5:26* 6:34 7:34 8:34 10 Lausanne Yverdon-les-Bans 5:55 6:55 7:55 8:55 11 Payerne Lausanne 5:39 6:39 7:38* 8:39 12 Lausanne Payerne 5:24 6:24 7:24 8:24 13 Vevey Pudoux-Chexbres 6:09 7:09 8:09 14 Pudoux-Chexbres Vevey 6:31* 7:36 8:36 21 / 27

22 General Inputs α = CHF/hour β = 2.5 α γ = α/6 = CHF ɛ = 0.5 α η = α mnmum transfer = 4 mn 180 seats 200 standng op. expenses per tran/km = 30.4 CHF 22 / 27

23 Demographcs cca 8 mllon nhabtants cca nhabtants 23 / 27

24 Demographcs SBB Facts and Fgures on average 1 mllon passenger journeys per day n 2013 n CH from prevous slde Canton Vaud cca 1/10 of Swtzerland Passenger Journeys 5 to PJ 6 to PJ 7 to PJ 8 to PJ

25 Passenger Flow s a defned OD par wth a desred arrval tme to a destnaton Lausanne gare S-trans : other trans raton = 40:60 % PF multpled by the sze of the demand group PJ 5 to 6 42 PF 6 to PF 7 to PF 8 to PF OD unform dstrbuton F(13, 1, 14) Demand group F(22, 1, 23)

26 Summary New plannng Phase Mult Objectve: Mnmze Passenger Cost Maxmze TOC Proft Pareto Fronter Can Produce Cyclc and Non-Cyclc Tmetables 26 / 27

27 Thank you for your attenton.