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TPAC, Columbus, OH, May 5-9, 2013 1
Incorporation of Capacity Constraints, Crowding, and Reliability in Transit Forecasting
Peter Vovsha, Bill Davidson, Gaurav Vyas, PBMarcelo Oliveira, Michael Mitchell, GeoStatsChaushie Chu, Robert Farley, LACMTA
Capacity Constraint & Crowding Effects Intertwined Capacity constraint (demand exceeds total capacity)
Riders cannot board the vehicle and have to wait for the next one
Modeled as effective line-stop-specific headway greater than the actual one
Similar to shadow pricing in location choices or VDF when V/C>1
Crowding inconvenience and discomfort (demand exceeds seated capacity):
Some riders have to stand Seating passengers experience inconvenience in finding a
seat and getting off the vehicle Modeled as perceived weight factor on segment IVT
TPAC, Columbus, OH, May 5-9, 2013 2
Effective Headway Calculation (Line & Stop Specific)
TPAC, Columbus, OH, May 5-9, 2013 3
Stop StopVolume
Alig
ht
Board
Δ Capacity=Total capacity-Volume+Alight
Board/ΔCap
Eff.Hdwy Factor
0 1
1
Critical Points of Crowding Function
TPAC, Columbus, OH, May 5-9, 2013 4
Crowding Factor
Voltr
1.00
0 Seat Cap
Fcap
Fseat
MaxCon
Transit Reliability Measures
1. Schedule adherence at boarding stop (extra wait time)
2. Impact of congestion (extra IVT)3. Combined lateness at destination versus planned
arrival time (similar to auto) TPAC, Columbus, OH, May 5-9, 2013 5
12
3
SP Design & Implementation Survey Platform: GeoStats’ Web GeoSurvey
Supports complex skip logic, computed questions, recalls and rosters Unlimited questionnaire size Fully translatable Can be customized and integrated with other technologies to fit project needs
Survey Design Combined RP survey and SP games into a single self-complete WEB instrument
First collected single one way trip information and then generated scenarios based on it Integrated geocoding of OD using Google Maps Obtained itinerary alternatives directly from Metro’s trip planner Complex logic for game generation also made use of pre-computed LOS skims
Survey Fielding Metro placed placards in vehicles inviting riders to participate Social media and email distribution lists used to drive participants to survey Participant feedback motivated design revisions and simplification of SP games Cash incentive ($250) paid once a week using a random draw
TPAC, Columbus, OH, May 5-9, 2013 6
Web GeoSurvey
7TPAC, Columbus, OH, May 5-9, 2013
Web GeoSurvey
8TPAC, Columbus, OH, May 5-9, 2013
Web GeoSurvey
9TPAC, Columbus, OH, May 5-9, 2013
Crowding LevelsCrowding level Probability of
having a seatVerbal description
1 100% (5 out of 5 trips)
Not crowded
2 80% (4 out of 5 trips)
Slightly crowded
3 60% (3 out of 5 trips)
Somewhat crowded
4 40% (2 out of 5 trips)
Crowded
5 20% (1 out of 5 trips)
Very crowded
6 0% (0 out of 5 trips) Extremely crowded
7 0% (0 out of 5 trips)1 out of 5 trips unable to board
Extremely crowdedTPAC, Columbus, OH, May 5-9, 2013 10
SP Stats 2,500 usable responses 6-9 games per respondent 2 observed choices per game:
1st ranked Alt over 2nd and 3rd 2nd ranked Alt over 3rd
30,000 usable observations
TPAC, Columbus, OH, May 5-9, 2013 11
Person Distribution
TPAC, Columbus, OH, May 5-9, 2013 12
Male Female Missing -
200
400
600
800
1,000
1,200
1,400
Gender
12 -
17
18 -
25
26 -
35
36 -
45
46 -
55
56 -
65
66 -
75
76 o
r abo
ve
Missin
g -
200
400
600
Age
-
200
400
600
800
1,000
Income
Yes No -
200 400 600 800
1,000 1,200 1,400 1,600 1,800 2,000
Student
Observed Trip Distribution
TPAC, Columbus, OH, May 5-9, 2013 13
Home
Wor
k
Scho
ol
Shop
Pers
onal
Medica
l
Leisur
e
Visitin
g -
200 400 600 800
1,000 1,200 1,400 1,600
Destination Trip Purpose
Loca
l Bus
Rapid
Bus
Expr
ess B
us
Tran
sit W
ay BRT
LRT/
Red/P
urpl
e
Metro
Link
-
200
400
600
800
1,000
Transit Mode
In-Vehicle Time
Destination Purpose
Home activities
Work activities
School activities Shopping Personal
businessVisiting doctor or dentist
Leisure, entertainment, or dining out
Visiting others Other Total
Less than 10 min 32 104 31 14 14 4 27 10 15 251
Between 10 to 19 mins 58 237 75 32 41 15 30 21 37 546
Between 20 to 29 mins 49 261 56 17 33 12 45 19 35 527
Between 30 to39 mins 56 223 56 14 25 5 26 6 20 431Between 40 to49 mins 36 172 33 8 17 9 22 6 24 327More than 49 mins 42 239 56 22 35 15 58 24 36 527Total 273 1236 307 107 165 60 208 86 167 2609
Reported Crowding & Reliability
TPAC, Columbus, OH, May 5-9, 2013 14
< 5min5-10 min
10-15 min 15+ min
-
200
400
600
800
1,000
1,200
1,400
Frequency & Amount of Delay
0%20%40%60%80%100%
Not Crowded (100%)
Slightly Crowded
(80%)
Somewhat Crowded
(60%)
Crowded (40%)
Very Crowded
(20%)
Extremely Crowded
(0%)
Unable to board (0%)
-
100
200
300
400
500
600
700
Crowding Level (% Having a Seat)
Crowding Effects Summary Hypotheses confirmed:
Crowding perceived as extra IVT weight Crowding is more onerous for commuters Crowding more onerous for older riders Crowding perceived differentially by
mode Hypotheses not confirmed:
Crowding more onerous for high incomes Crowding weight grows with trip length
TPAC, Columbus, OH, May 5-9, 2013 15
Trip Length Effect It might look counter-intuitive that crowding IVT
weight does not grow with trip length However, even if the weight is constant the
resulted crowding penalty does grow with trip length:
IVT weight 1.5 10 min in crowded vehicle equivalent to 5 extra min 60 min in crowded vehicle equivalent to 30 extra min Logit models are sensitive to differences, thus trip
length manifests itself in crowding-averse behavior
TPAC, Columbus, OH, May 5-9, 2013 16
General Functional Form for Crowding IVT Weight
TPAC, Columbus, OH, May 5-9, 2013 17
1=Not
cro
wded
(100
% se
at)
2=Sl
ight
ly cr
owde
d (8
0% se
at)
3=So
mew
hat c
rowde
d (6
0% sea
t)
4=Cro
wded
(40%
seat
)
5-Ver
y cr
owde
d (2
0% sea
t)
6=Ex
trem
ely
crow
ded
(0%
seat
)
7=Una
blae
to b
oard
(0%
seat
)0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
Estimated IVT weightFunction
Weight=1+(1-SeatProb)3.4×1.58
Segmentation of Crowding IVT Weight – Trip Purpose
TPAC, Columbus, OH, May 5-9, 2013 18
1 2 3 4 5 6 70
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Crowding Weight by Trip Purpose
Commuting TripsNon-Commuting Trips
Crowding Levels Unable to BoardSeat alwaysavailable
Rho-squared w.r.t zero = 0.1124
Segmentation of Crowding IVT Weight – Person Age
TPAC, Columbus, OH, May 5-9, 2013 19
1 2 3 4 5 6 70
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Crowding Weight by Age
Age less than 46 yearsAge more than 45 years
Crowding Levels Unable to BoardSeating alwaysavailable
Rho-squared w.r.t zero = 0.1129
Segmentation of Crowding IVT Weight – Household Income
TPAC, Columbus, OH, May 5-9, 2013 20
1 2 3 4 5 6 70
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Crowding Weight by Income Level
Income Less Than $60,000Income more than $60,000Missing Income
Crowding Levels Unable to BoardSeating alwaysavailable
Rho-squared w.r.t zero = 0.1100
Segmentation of Crowding IVT Weight – Transit Mode
TPAC, Columbus, OH, May 5-9, 2013 21
1 2 3 4 5 6 70
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Crowding Weight by Mode
BusLRTCRT
Crowding Levels Unable to BoardSeating alwaysavailable
Rho-squared w.r.t zero = 0.1135
Reliability Impact: Expected Delay (Linear Formulation)
Calculated as Amount×Frequency Weight vs. non-crowded IVT is 1.76 Confirms negative perception
beyond just extension of IVT
TPAC, Columbus, OH, May 5-9, 2013 22
Illustration of Linear Formulation
TPAC, Columbus, OH, May 5-9, 2013 23
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
35
40
Linear
Delay = 5 minsDelay = 10 minsDelay = 20 mins
Frequency
Disu
tility
as c
ompa
red
to IV
TT (m
in)
Rho-squared w.r.t zero = 0.1119
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70
80
90
100
Linear
Frequency = 0.1Frequency = 0.5Frequency = 0.9
Delay (min)
Disu
tility
as c
ompa
red
to IV
TT (m
in)
Rho-squared w.r.t zero = 0.1119
Possible Non-Linear Effects Amount of delay:
Discarding small delays, avoiding big delays (convexity)
Adaptation to big delays (concavity) Frequency of delay:
Discarding infrequent delays, avoiding frequent delays (convexity)
Adaptation to frequent delays (concavity)
TPAC, Columbus, OH, May 5-9, 2013 24
Best Statistical Form
-0.142×Delay×Freq (base linear)+0.091×Delay×Freq2 (freq convex)+0.161×Delay0.5×Freq (delay
concave)
TPAC, Columbus, OH, May 5-9, 2013 25
Amount of Delay Effect
TPAC, Columbus, OH, May 5-9, 2013 26
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70
80
90
100
Linear
Frequency = 0.1Frequency = 0.5Frequency = 0.9
Delay (min)
Disu
tility
as c
ompa
red
to IV
TT (m
in)
Rho-squared w.r.t zero = 0.1119
0 10 20 30 40 50 60 70-10
0
10
20
30
40
50
60
70
80
90
Linear + Delay*(Freq)^2+Freq*sqrt(Delay)
Frequency = 0.1Frequency = 0.5Frequency = 0.9
Delay (min)
Disu
tility
as c
ompa
red
to IV
TT (m
in)
Rho-squared w.r.t zero = 0.1135
Convexity, discarding very small
delays
Frequency of Delay Effect
TPAC, Columbus, OH, May 5-9, 2013 27
Concavity, adaptation
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
5
10
15
20
25
30
35
40
Linear
Delay = 5 minsDelay = 10 minsDelay = 20 mins
Frequency
Disu
tility
as c
ompa
red
to IV
TT (m
in)
Rho-squared w.r.t zero = 0.1119
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-5
0
5
10
15
20
25Linear + delay*(Frequency)^2+freq*sqrt(delay)
Delay = 5 minsDelay = 10 minsDelay = 20 mins
Frequency
Disu
tility
as c
ompa
red
to IV
TT (m
in)
Rho-squared w.r.t zero = 0.1135
6 Travel Time Components
TPAC, Columbus, OH, May 5-9, 2013 28
Component Wait IVT Weight Calculated for each line
Combined for strategy & skimming
Scheduled wait X 2.0-2.5 calibrated
0.5 Headway
Combined headway
Extra wait due capacity restraint
X 2.0-3.0 calibrated
0.5 Effective headway
Combined headway
Unreliability extra wait
X 2.0-3.0 SP Regression Weighted average
Physical scheduled IVT
X 0.85-1.00Calibrated
Transit time function
Weighted average
Perceived crowding inconvenience
X Entire component SP
Crowding function SP
Weighted average
Unreliability IVT delay
X 2.0-3.0 SP Regression Weighted average
Passenger Split between Attractive Lines
TPAC, Columbus, OH, May 5-9, 2013 29
Line share Effective Frequency Discount ×~S
ched
ule
wait
Cap
aci
ty w
ait
Un
relia
bili
ty w
ait
Ph
ysi
cal IV
T
Cro
wd
ing
IV
T
Un
relia
bili
ty IV
T
Standard combined frequency approach
Logit discrete choice
Conclusions Capacity constraints, crowding, and
reliability can be effectively incorporated in travel model: Transit assignment Model choice
Essential for evaluation of transit projects: Capacity relief Real attractiveness for the user Explanation of weird observed choices (driving
backward to catch a seat)
TPAC, Columbus, OH, May 5-9, 2013 30