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A Brief COURSE on DEMAND MODELLING in RAILWAY MODE

Francisco G. Benitez. A Brief COURSE on DEMAND MODELLING in RAILWAY MODE. Contents. Demand Modelling on rail Lines, Stations and Trains Motivation for modelling of passengers demand Determining passengers demand. The main goal in Rail Network Design is:

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A Brief COURSE on DEMAND MODELLING in RAILWAY MODE

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  1. Francisco G. Benitez A Brief COURSE on DEMAND MODELLING in RAILWAY MODE

  2. Contents • Demand Modelling on rail Lines, Stations and Trains • Motivation for modelling of passengers demand • Determining passengers demand

  3. The main goal in Rail Network Design is: To satisfy the transport needs of people. Demand Modelling on rail Lines, Stations and Trains Motivation

  4. The main goal in Rail Network Design is: To satisfy the transport needs of people. To satisfy the transport needs of people, efficiently. Demand Modelling on rail Lines, Stations and Trains Motivation

  5. 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. Demand Modelling on rail Lines, Stations and Trains Motivation

  6. 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. Demand Modelling on rail Lines, Stations and Trains Motivation FUNCTIONAL Rail Network FUNCTIONAL Rail services

  7. 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). Demand Modelling on rail Lines, Stations and Trains Motivation

  8. Demand Modelling on rail Lines, Stations and Trains 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)

  9. Demand Modelling on rail Lines, Stations and Trains Time period: t Station: e Line: l Train Router Determining passengers demand

  10. Demand Modelling on rail Lines, Stations and Trains Time period: t Station: e Line: l Train Pathr Determining passengers demand (by measuring) (by estimating)

  11. Demand Modelling on rail Lines, Stations and Trains Practical Case: Metropolitan rail lines BARCELONA VALENCIA MADRID BILBAO

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

  13. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand To estimate a variable, statistics is used, through data corresponding to: • same Station • same Line • same day Type (labor day, holiday, saturday, holiday eve, friday,…) • same time Period Direct estimate n measures x x x x x x x x x x x x x x x x x Service time h

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

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

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

  17. Demand Modelling on rail Lines, Stations and Trains • Data getting-on • Data getting-off • ___ Curve fitting getting-on • ___Curve fitting getting-off • Data getting-on • Data getting-off • ___ Curve fitting getting-on • ___Curve fitting getting-off Travellers Travellers Time period Time period • Data getting-on • Data getting-off • ___ Curve fitting getting-on • ___Curve fitting getting-off • Data getting-on • Data getting-off • ___ Curve fitting getting-on • ___Curve fitting getting-off Travellers Travellers Time period Time period Determining passengers demand • same Station, same Line (Madrid, C1, path 0), same day Type (L) Polynomial O(5) Polynomial O(4) • same Station, same Line (Madrid, C1, path 0), same day Type (L) Polynomial O(5) Polynomial O(4)

  18. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand 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)- passengers

  19. Demand Modelling on rail Lines, Stations and Trains Polynomial O(5) r2=0.83 Chebyshev O(5) r2=0.85 Chebyshev O(20) r2=0.87 Getting-on Time period Determining passengers demand Other curve fitting • R. Kelly (2007). “The generation of profiles by formulae”. Traffic Engineering & Control, Vol. 48, No.8, 368-371, 2007.

  20. Variable estimates: By Station: Getting-on Getting-off Remaining By Service: Occupancy Variables are estimated independently, with different methodologies and error level. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand Independent Variable Estimates

  21. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand

  22. 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”. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand

  23. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand “Station” variables

  24. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand Balance equilibrium for “stations” Balance for stations NE equations

  25. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand Balance equilibrium for “train-service” 2 equations

  26. 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. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand Objective function to minimize:

  27. Demand Modelling on rail Lines, Stations and Trains Mathematical scheme of the optimization problem : Determining passengers demand

  28. Demand Modelling on rail Lines, Stations and Trains Determining passengers demand

  29. 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. Demand Modelling on rail Lines, Stations and Trains Conclusions

  30. Demand Modelling on rail Lines, Stations and Trains That’s over ! Thanks for your attention

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