cie4801 transportation and spatial modelling mode choice

17/4/13

Challenge the future Delft University of Technology

CIE4801 Transportation and spatial modelling

Rob van Nes, Transport & Planning

Mode choice

2 CIE4801: Mode choice

Content

• What’s it about

• Two methods

• Trip distribution revisited

•  Special topics


1.

Mode choice: what’s it about?


Introduction to modal split Trip production / Trip attraction

Trip distribution

Modal split

Period of day

Assignment

Zonal data

Transport networks

Travel resistances

Trip frequency choice

Destination choice

Mode choice

Time choice

Route choice

Travel times network loads

etc.


What do we want to know?


Introduction to modal split

Given: The number of trips of each OD pair Determine: •  The number of trips of each OD pair for each mode

all modes

car

train

bike


Selection of modes trips and trip kilometres


2.1

Method 1: Descriptive


Travel time ratio (VF)

• Ratio between travel time by public transport and travel time by car

• Data used: observed trips where PT might be attractive •  i.e. train service or ‘express’ service available •  Public transport: Access and egress time to main PT mode, waiting

time first stop, in-vehicle time of main PT mode, waiting time transfer •  Car: travel time based on fixed speeds per area and period of day,

parking

• Basic version:

•  Elaborate model: Nt=transfers, F=frequency

20.45 0.02VFptP e− ⋅= +

2 1.350.36 0.17 0.230.03tVF N

FptP e

− ⋅ − ⋅ − += +


Travel time ratio (basic version)

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Per

cent

age

PT

Travel time ratio


2.2

Method 2: Choice modelling


Mode choice model

exp( )exp( )

ijvijv

ijww

VV

µβ

µ=∑

all modes

i

j 1ijβcar share:

train share:

bike share: 2ijβ

3ijβ

0 1 1 2 2 3 3v v v v v v v

ijv ij ij ijV X X Xα α α α= + + +


Mode choice model

0 1 1 2 2 3 3v v v v v v v

ijv ij ij ijV X X Xα α α α= + + + +K

exp( )exp( )

ijvijv

ijww

VV

µβ

µ=∑

mode-specific constant (includes comfort, status, safety, etc.)

variables (e.g. distance, travel time of each mode, etc.)


exp( )exp( )

ijvijv

ijww

VV

β =∑car

train

2

2 3

A B

C

0 200 150 200 0 200 150 200 0

A B C

A B C

0.6car carCA CAV c= − ⋅

0.5 0.8train trainCA CAV c= − − ⋅

exp( 0.6 4)exp( 0.6 4) exp( 0.5 0.8 3)62%

carCAβ

− ⋅=

− ⋅ + − − ⋅

=

car train 93 57

0 200 93 200 0 200 93 200 0

0 0 57 0 0 0 57 0 0

car train

Mode choice model


3.

Trip distribution revisited


Gravity model and distribution functions

• Using distribution functions per mode

• Note that this formula also holds per mode

( )with ij i j ij ij v ijvv

T Q X F F f cρ= =∑

( ) ( )ij i j ij i j v ijv i j v ijv ijvv v v

T Q X F Q X f c Q X f c Tρ ρ ρ= = = =∑ ∑ ∑

50km10kmdistance

f

cartrain

bike


Distribution functions per mode

0

2

4

6

8

10

12

14

16

0 10 20 30 40 50 60

Dis

tribu

tion

func

tion

Travel time (min)

Car PT Bike


Example mode choice

Zoetermeer - TU Delft

•  Car: 30 min •  PT: 50 min •  Bike: 45 min

Function values •  Car: 1.12 •  PT: 0.40 •  Bike: 0.04

Result •  Car: 71% •  PT: 27% •  Bike: 2% Total: 1.59


Doubly constrained simultaneous distribution/modal split model

( )ijv i j i j ijv ijv v ijv

ijv i ijv jj v i v

T a b P A F F f c

T P T A

= =

= =∑∑ ∑∑with

and

… … … … … … … … …

car PT car PT car PT

Σ

Σ

zone 1

zone 2

zone 3

zone 1 zone 2 zone 3

… … … … … … … … … … … … … … … … … …

Can be solved in a similar way as the standard doubly constrained model


Alternative approach: aggregate costs

with ( )ij i j ij ij ijT Q X F F f cρ= =

General gravity model for trip distribution:

Which travel costs do we use? Every mode may have different travel costs

ijc.ijvc

Example A trip from Rotterdam to Delft takes 20 minutes by car and 35 minutes by bus. What is the travel cost between Rotterdam and Delft?


Which costs should be applied?

min{ }ij ijvvc c= 20ijc =

1.  Minimum cost

1 ln exp( )ij ijvv

c cµ µ⎛ ⎞

= − −⎜ ⎟⎝ ⎠∑

18 ( 0.1)

20 ( 1)ij

ij

cc

µ

µ

= =

= =

2.  Logit analogy

1(1/ )ij

ijvv

cc

=∑

12.7ijc =

3.  Electric circuit analogy

1ij ijvV

vc c= ∑ 27.5ijc =

4.  Average costs


Derivation of logit analogy

i j ijvc

k ikc

Probability of choosing alternative j ?

i j ijc

k ikc

⇒ cij = − 1

µ ln exp(−µcijv )v∑

Let’s first look at the mode choice for j

( )( )

exp

expi

i

ijvijv

ijvv

cP

c

µ

µ

−=

−∑Translate attractiveness of all alternatives into costs

Attractiveness of alternative vi

Attractiveness of all alternatives


Derivation of logit analogy

i j ijvc

k ikc

Probability of choosing alternative j :

i j ijc

k ikc

( )( ) ( )

exp( , , )

exp( , , ) exp( , , )d a ja ij

jd a ja ij d a ka ik

k j

V w X cp

V w X c V w X c

µ

µ µ≠

=+∑

1 ln exp( )ij ijvv

c cµ µ= − −∑


Simultaneous distribution/modal split model

Most of the time, destination choice and mode choice are made simultaneously instead of sequentially.

Combined choices (e.g. for going shopping): •  Take the train to the center of Amsterdam •  Take the bike to the center of Delft •  Take the car to the center of Rotterdam

General gravity model for simultaneous trip distribution/modal split:

( ) ( ) with or ij i j ij ij ij ij ijvv

T Q X F F f c F f cρ= = =∑


4.

Special topics


Special topics

• Role of constraints: Car ownership

• Car passenger

•  Parking

• What comes first: destination choice or mode choice?


Car ownership

• How is that accounted for so far?

•  Implicit •  Mode specific constant •  Distribution functions

•  Explicit approach •  Split demand matrix in matrix for people having a car and people not

having a car available and apply appropriate functions


Car passenger

• Why is this relevant?

•  Simple approach •  Exogenous car occupancy rate per trip purpose

• Comprehensive approach •  Car passenger and car driver as separate modes

•  Problem in both cases? No guarantee for consistency in trip patterns car driver and car passenger


Parking

• Would you include it, and if so, how?

• How would you do it in case of tours?

• How would you do it in case of trips?

• What about morning and evening peak? Assign half of parking costs to a trip (origin and destination)?


What comes first: trip distribution or mode choice?

• What is the order we discussed so far?

•  Swiss model:

• Mode preferences appear to be pretty strong

cie4801 transportation and spatial modelling mode choice

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