A Brief COURSE on

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

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

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Demand Modelling on rail Lines, Stations and
Trains
Motivation

• The main goal in Rail Network Design is
• To satisfy the transport needs of people.

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Demand Modelling on rail Lines, Stations and
Trains
Motivation

• The main goal in Rail Network Design is
• To satisfy the transport needs of people.
• To satisfy the transport needs of people,
  efficiently.

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Demand Modelling on rail Lines, Stations and
Trains
Motivation

• 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.

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Demand Modelling on rail Lines, Stations and
Trains
Motivation

• 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.

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

• 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).

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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)

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Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
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Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
(by measuring)
(by estimating)
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Demand Modelling on rail Lines, Stations and
Trains
Practical Case Metropolitan rail lines
VALENCIA
BARCELONA
MADRID
BILBAO
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Demand Modelling on rail Lines, Stations and
Trains
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

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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
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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
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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

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

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Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
Independent Variable Estimates

• Variable estimates
• By Station
• Getting-on
• Getting-off
• Remaining
• By Service
• Occupancy
• Variables are estimated independently,
• with different methodologies and error level.

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

• 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.

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Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
Station variables
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Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
Balance equilibrium for stations
Balance for stations
NE equations
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Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
Balance equilibrium for train-service
2 equations
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Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
Objective function to minimize

• 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.

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Mathematical scheme of the optimization problem
Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
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Demand Modelling on rail Lines, Stations and
Trains
Determining passengers demand
Trains monitorized Estimate scheme ON OFF Rem. Occ.
20 VOID 0 0 0 0
20 /- 1 time interval 429 429 429 52
20 Chebyshev 0 0 0 0
20 Direct 1181 1181 1181 178
15 VOID 3 4 0 0
15 /- 1 time interval 705 705 705 71
15 Chebyshev 12 11 15 3
15 Direct 883 883 883 156
10 VOID 44 15 0 0
10 /- 1 time interval 1023 1023 1023 0
10 Chebyshev 83 112 127 100
10 Direct 453 453 453 130
5 VOID 160 183 0 0
5 /- 1 time interval 736 736 736 111
5 Chebyshev 646 623 806 53
5 Direct 61 61 61 66
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Demand Modelling on rail Lines, Stations and
Trains
Conclusions

• 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.

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Demand Modelling on rail Lines, Stations and
Trains
Thats over !
Thanks for your attention