Transportation and Spatial Modelling: Lecture 4
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Transcript of Transportation and Spatial Modelling: Lecture 4
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
3 CIE4801: Mode choice
1.
Mode choice: what’s it about?
4 CIE4801: Mode choice
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.
5 CIE4801: Mode choice
What do we want to know?
6 CIE4801: Mode choice
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
7 CIE4801: Mode choice
Selection of modes trips and trip kilometres
8 CIE4801: Mode choice
2.1
Method 1: Descriptive
9 CIE4801: Mode choice
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
− ⋅ − ⋅ − += +
10 CIE4801: Mode choice
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
11 CIE4801: Mode choice
2.2
Method 2: Choice modelling
12 CIE4801: Mode choice
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= + + +
13 CIE4801: Mode choice
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.)
14 CIE4801: Mode choice
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
15 CIE4801: Mode choice
3.
Trip distribution revisited
16 CIE4801: Mode choice
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
17 CIE4801: Mode choice
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
18 CIE4801: Mode choice
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
19 CIE4801: Mode choice
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
20 CIE4801: Mode choice
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?
21 CIE4801: Mode choice
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
22 CIE4801: Mode choice
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
23 CIE4801: Mode choice
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= − −∑
24 CIE4801: Mode choice
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= = =∑
25 CIE4801: Mode choice
4.
Special topics
26 CIE4801: Mode choice
Special topics
• Role of constraints: Car ownership
• Car passenger
• Parking
• What comes first: destination choice or mode choice?
27 CIE4801: 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
28 CIE4801: Mode choice
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
29 CIE4801: Mode choice
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)?
30 CIE4801: Mode choice
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