1. Transportation Engineering Higher Technical School of Engineering, University of Sevilla, Spain Fall School on Robust Network Design and Delay Management, Sevilla, November 2007 1/30 A Brief COURSE on DEMAND MODELLING in RAILWAY MODE Francisco G. Benitez

2. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 2/30 Demand Modelling on rail Lines, Stations and Trains Motivation for modelling of passengers demand Determining passengers demand Contents

3. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 3/30 The main goal in Rail Network Design is: To satisfy the transport needs of people. Motivation Demand Modelling on rail Lines, Stations and Trains

4. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 4/30 The main goal in Rail Network Design is: To satisfy the transport needs of people. To satisfy the transport needs of people, efficiently. Motivation Demand Modelling on rail Lines, Stations and Trains

5. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 5/30 The main goal in Rail Network Design is: To satisfy the transport needs of people. To satisfy the transport needs of people, efficiently. To satisfy the transport needs of people, efficiently, complying with economical constraints. Motivation Demand Modelling on rail Lines, Stations and Trains

6. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 6/30 The main goal in Rail Network Design is: To satisfy the transport needs of people. To satisfy the transport needs of people, efficiently. To satisfy the transport needs of people, efficiently, complying with economical constraints. Motivation FUNCTIONAL Rail NetworkFUNCTIONAL Rail services Demand Modelling on rail Lines, Stations and Trains

7. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 7/30 In order to reach a Functional design of Rail (transport) Services the following tasks are needed: Determining passenger demand (travellers demand): -actual (by measuring, by estimating) -prospective (by estimating) Planning lines in function of demand and available budget (optimizing lines layout). Designing services in function of demand, lines and available budget (trains, vehicles). Motivation Demand Modelling on rail Lines, Stations and Trains

8. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 8/30 Determining passengers demand Determining actual passengers demand by measuring: -Indirect measures -Ticketing (aggregated values, passes, travelcards). -Direct measures -travellers counting by manual survey (reduced sample, expensive, distorting) -travellers counting by automatic counters (some are aggregated) Demand Modelling on rail Lines, Stations and Trains

9. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 9/30 Train Route r Time period: t Station: e Line: l Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

10. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 10/30 Train Path r Time period: t Station: e Line: l (by measuring) (by estimating) Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

11. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 11/30 MADRID BILBAO VALENCIA BARCELONA Practical Case: Metropolitan rail lines Demand Modelling on rail Lines, Stations and Trains

12. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 12/30 same Station same Line same day Type (labor day, holiday, saturday, holiday eve, friday,…) same time Period To estimate a variable, statistics is used, through data corresponding to: x x x x x x x Service time n measures h Direct estimate x x x x x x x x x x Determining passengers demand Demand Modelling on rail Lines, Stations and Trains Methodology

13. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 13/30 same Station same Line same day Type (labor day, holiday, saturday, holiday eve, friday,…) same time Period To estimate a variable, statistics is used, through data corresponding to: x x x x x x x Service time n measures h Direct estimate x x x x x x x x x x Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

14. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 14/30 same Station same Line same day Type (labor day, holiday, saturday, holiday eve, friday,…) same time Period adjacent time Period To estimate a variable, statistics is used, through data corresponding to: x x x x x x x Service time n measures h Direct estimate x x x x x x x x x x Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

15. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 15/30 same Station same Line same day Type (labor day, holiday, saturday, holiday eve, friday,…) same time Period adjacent time Period To estimate a variable, statistics is used, through data corresponding to: x x x x x x x Service time n measures h Direct estimate x x x x x x x x x x ? ? ?? ? ? Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

16. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 16/30 Curve fitting same Station same Line same day Type (labor day, holiday, saturday, holiday eve, friday,…) same time Period adjacent time Period To estimate a variable, statistics is used, through data corresponding to: x x x x x x x Service time h x x x x x x x x x x ? ? ?? ? ? Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

17. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 17/30 Time period Travellers Data getting-on Data getting-off ___ Curve fitting getting-on ___ Curve fitting getting-off Time period Travellers Data getting-on Data getting-off ___ Curve fitting getting-on ___ Curve fitting getting-off Time period Travellers Data getting-on Data getting-off ___ Curve fitting getting-on ___ Curve fitting getting-off Time period Travellers Data getting-on Data getting-off ___ Curve fitting getting-on ___ Curve fitting getting-off same Station, same Line (Madrid, C1, path 0), same day Type (L) Polynomial O(4) Polynomial O(5) Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

18. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 18/30 Determining passengers demand Demand Modelling on rail Lines, Stations and Trains passengers Curve fitting with variable time interval length Variable: Getting-off -polynomial O(5)- passengers Curve fitting with variable time interval length Variable: Getting-off -polynomial O(10)-

19. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 19/30 Getting-on Time period Polynomial O(5) r 2 =0.83 Chebyshev O(5) r 2 =0.85 Chebyshev O(20) r 2 =0.87 Other curve fitting R. Kelly (2007). “The generation of profiles by formulae”. Traffic Engineering & Control, Vol. 48, No.8, 368-371, 2007. Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

20. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 20/30 Variable estimates: –By Station: Getting-on Getting-off Remaining –By Service: Occupancy Variables are estimated independently, with different methodologies and error level. Determining passengers demand Demand Modelling on rail Lines, Stations and Trains Independent Variable Estimates

21. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 21/30 Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

22. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 22/30 The approach does not complete the estimates for all time period. Some “mismatching” might arise in the independent estimating of variables “getting-on”, “getting-off” and “remains”. Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

23. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 23/30 “Station” variables Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

24. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 24/30 Balance for stations NE equations Balance equilibrium for “stations” Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

25. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 25/30 2 equations Balance equilibrium for “train-service” Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

26. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 26/30 A weighting function is applied to each variable attending to its reliability (error level): We look for the minimum deviation w.r.t. estimates, in particular for most reliable variables. Objective function to minimize: Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

27. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 27/30 Mathematical scheme of the optimization problem : Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

28. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 28/30 % Trains monitorizedEstimate scheme ON OFFRem.Occ. 20%VOID0000 20%+/- 1 time interval429 52 20%Chebyshev0000 20%Direct1181 178 15%VOID3400 15%+/- 1 time interval705 71 15%Chebyshev1211153 15%Direct883 156 10%VOID441500 10%+/- 1 time interval1023 0 10%Chebyshev83112127100 10%Direct453 130 5%VOID16018300 5%+/- 1 time interval736 111 5%Chebyshev64662380653 5%Direct61 66 Determining passengers demand Demand Modelling on rail Lines, Stations and Trains

29. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 29/30 Optimum prediction with a 20 % of train-services monitorized. Maximum explotation of the available data. An error minimazing scheme (Quadratic optimization) consistent among independent variable w.r.t the variable reliability. Conclusions Demand Modelling on rail Lines, Stations and Trains

30. F. G. Benitez Transportation Engineering. University of Sevilla, Spain 30/30 Demand Modelling on rail Lines, Stations and Trains That’s over ! Thanks for your attention