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Trip Generationand Mode Choice
CEE 320Steve Muench
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Outline
1. Trip Generation
2. Mode Choicea. Survey
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Trip Generation
• Purpose– Predict how many trips will be made– Predict exactly when a trip will be made
• Approach– Aggregate decision-making units – Categorized trip types– Aggregate trip times (e.g., AM, PM, rush hour)– Generate Model
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Motivations for Making Trips
• Lifestyle– Residential choice– Work choice– Recreational choice– Kids, marriage– Money
• Life stage• Technology
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Reporting of Trips - Issues
• Under-reporting trivial trips• Trip chaining• Other reasons (passenger in a car for
example)
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Trip Generation Models
• Linear (simple)
• Poisson (a bit better)
nnxxxT ...22110
nni xxx ...ln 22110
! tripsofnumber
x
xexP
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Poisson Distribution
• Count distribution– Uses discrete values– Different than a continuous distribution
!n
etnP
tn
P(n) = probability of exactly n trips being generated over time t
n = number of trips generated over time t
λ = average number of trips over time, t
t = duration of time over which trips are counted (1 day is typical)
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Poisson Ideas
• Probability of exactly 4 trips being generated– P(n=4)
• Probability of less than 4 trips generated– P(n<4) = P(0) + P(1) + P(2) + P(3)
• Probability of 4 or more trips generated– P(n≥4) = 1 – P(n<4) = 1 – (P(0) + P(1) + P(2) + P(3))
• Amount of time between successive trips
tt
eet
thPP
!0
00
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Poisson Distribution Example
Trip generation from my house is assumed Poisson distributed with an average trip generation per day of 2.8 trips. What is the probability of the following:
1. Exactly 2 trips in a day?2. Less than 2 trips in a day?3. More than 2 trips in a day?
!
trips/day8.2trips/day8.2
n
etnP
tn
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Example Calculations
%84.232384.0
!2
18.22
18.22
e
PExactly 2:
Less than 2:
More than 2:
102 PPnP
21012 PPPnP
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Example Graph
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trips in a Day
Pro
bab
ility
of
Occ
ura
nce
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Example Graph
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trips in a Day
Pro
bab
ility
of
Occ
ura
nce
Mean = 2.8 trips/day
Mean = 5.6 trips/day
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Example: Time Between Trips
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Time Between Trips (Days)
Pro
bab
ility
of
Exc
edan
ce
Mean = 2.8 trips/day
Mean = 5.6 trips/day
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Example
kidsmarriedinternetagegender
autosbus
bicyclesedanvansportssuv
incomeeducationi
*8
*7
*6
*5*4
*#37*36
*35*34*33*32*31
*2*10ln
Recreational or pleasure trips measured by λi (Poisson model):
Variable Coefficient Value Product
Constant 0 1 0
Education (undergraduate degree or higher) 0.15 1 0.15
Income 0.00002 45,000 0.9
Whether or not individual owns an SUV 0.1 1 0.1
Whether or not individual owns a sports car 0.05 0 0
Whether or not individual owns a van 0.1 1 0.1
Whether or not individual owns a sedan 0.08 0 0
Whether or not individual uses a bicycle to work 0.02 0 0
Whether or not individual uses the bus to work all the time -0.12 0 0
Number of autos owned in the last ten years 0.06 6 0.36
Gender (female) -0.15 0 0
Age -0.025 40 -1
Internet connection at home -0.06 1 -0.06
Married -0.12 1 -0.12
Number of kids 0.03 2 0.06
Sum = 0.49
λi = 1.632 trips/day
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Example
• Probability of exactly “n” trips using the Poisson model:
• Cumulative probability – Probability of one trip or less: P(0) + P(1) = 0.52– Probability of at least two trips: 1 – (P(0) + P(1)) = 0.48
• Confidence level– We are 52% confident that no more than one recreational or
pleasure trip will be made by the average individual in a day
20.0
!0
0632.10 632.1
eP
32.0!1
1632.11 632.1
eP
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Mode Choice
• Purpose– Predict the mode of travel for each trip
• Approach– Categorized modes (SOV, HOV, bus, bike, etc.) – Generate Model
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Dilemma
Explanatory Variables
Qu
alit
ativ
e D
epe
nd
ent V
ari
able
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Dilemma
Home to School Distance (miles)
Wa
lk to
Sch
ool
(ye
s/n
o v
ari
able
)
0
1
0 10
1 =
no,
0 =
yes
= observation
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A Mode Choice Model
• Logit Model
• Final form
mkn
kmnmnmk zV
s
U
U
mk sk
mk
e
eP
Specifiable part Unspecifiable part
n
kmnmnmk zU
s = all available alternativesm = alternative being consideredn = traveler characteristick = traveler
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Discrete Choice Example
Regarding the TV sitcom Gilligan’s Island, whom do you prefer?
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Ginger Model
UGinger = 0.0699728 – 0.82331(carg) + 0.90671(mang) + 0.64341(pierceg) – 1.08095(genxg)
carg = Number of working vehicles in household
mang = Male indicator (1 if male, 0 if female)
pierceg = Pierce Brosnan indicator for question #11 (1 if Brosnan chosen, 0 if not)
genxg = generation X indicator (1 if respondent is part of generation X, 0 if not)
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Mary Anne Model
UMary Anne = 1.83275 – 0.11039(privatem) – 0.0483453(agem) – 0.85400(sinm) – 0.16781(housem) + 0.67812(seanm) + 0.64508(collegem) – 0.71374(llm) + 0.65457(boomm)
privatem = number of years spent in a private school (K – 12)
agem = age in years
sinm = single marital status indicator (1 if single, 0 if not)
housem = number of people in household
seanm = Sean Connery indicator for question #11 (1 if Connery chosen, 0 if not)
collegem = college education indicator (1 if college degree, 0 if not)
llm = long & luxurious hair indicator for question #7 (1 if long, 0 if not)
boomm = baby boom indicator (1 if respondent is a baby boomer, 0 if not)
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No Preference Model
Uno preference = – 9.02430x10-6(incn) – 0.53362(gunsn) + 1.13655(nojames) + 0.66619(cafn) + 0.96145(ohairn)
incn = household income
gunsn = gun ownership indicator (1 if any guns owned, 0 if no guns owned)
nojames = No preference indicator for question #11 (1 if no preference, 0 if preference for a particular Bond)
cafn = Caffeinated drink indicator for question #5 (1 if tea/coffee/soft drink, 0 if any other)
ohairn = Other hair style indicator for question #7 (1 if other style indicated, 0 if any style indicated)
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Results10. Regarding the TV sitcom “Gilligan’s Island” whom do
your prefer?
29
9085
30
88 89
7
112
87
0
20
40
60
80
100
120
Ginger Mary Ann No Preference
# o
f R
es
po
nd
an
ts
Survey
average
Model
Average probabilities of selection for each choice are shown in yellow. These average percentages were converted to a hypothetical number of respondents out of a total of 207.
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My Results
s
U
U
mk sk
mk
e
eP
8201.13265.02636.01075.1 eeees
U sk
1815.08201.1
1075.1
e
e
eP
s
U
U
ginger sk
mk
4221.08201.1
2636.0
e
e
eP
s
U
U
annemary sk
mk
3964.08201.1
3265.0
e
e
eP
s
U
U
preferenceno sk
mk
Uginger = – 1.1075
Umary anne = – 0.2636
Uno preference = – 0.3265
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Primary References
• Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition. Chapter 8
• Transportation Research Board. (2000). Highway Capacity Manual 2000. National Research Council, Washington, D.C.