incorporation of capacity constraints, crowding, and reliability in transit forecasting

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


Effective Headway Calculation (Line & Stop Specific)


Stop StopVolume

Alight

Board

Δ Capacity=Total capacity-Volume+Alight

Board/ΔCap

Eff.Hdwy Factor

0 1

1

Critical Points of Crowding Function


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)


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


Web GeoSurvey

7TPAC, Columbus, OH, May 5-9, 2013

Web GeoSurvey


Crowding LevelsCrowding level Probability of

having a seatVerbal description

1 100% (5 out of 5 trips)

Not crowded


Slightly crowded


Somewhat crowded


Crowded


Very crowded

6 0% (0 out of 5 trips) Extremely crowded7 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


Person Distribution


Male Female Missing -

200 400 600 800

1,000 1,200 1,400

Gender

12 - 1

718

- 25

26 - 3

536

- 45

46 - 5

556

- 65

66 - 7

5

76 or

above

Missing

-

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


Home

WorkSch

ool

Shop

Person

al

Medica

l

Leisur

e

Visitin

g -

200 400 600 800

1,000 1,200 1,400 1,600

Destination Trip Purpose

Local

Bus

Rapid

Bus

Expres

s Bus

Transi

t Way BR

T

LRT/Red

/Purpl

e

MetroLi

nk -

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


< 5min 5-10 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


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


General Functional Form for Crowding IVT Weight


1=Not

crowde

d (10

0% se

at)

2=Slig

htly c

rowde

d (80

% seat)

3=Som

ewha

t crow

ded (

60% se

at)

4=Crow

ded (4

0% se

at)

5-Very

crowde

d (20%

seat)

6=Ext

remely

crowded

(0% se

at)

7=Una

blae t

o boa

rd (0%

seat)

0.000.200.400.600.801.001.201.401.601.80

Estimated IVT weightFunction

Weight=1+(1-SeatProb)3.4×1.58

Segmentation of Crowding IVT Weight – Trip Purpose


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


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


Segmentation of Crowding IVT Weight – Household Income


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



Segmentation of Crowding IVT Weight – Transit Mode


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



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


Illustration of Linear Formulation


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)


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)


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)


Best Statistical Form-0.142×Delay×Freq (base linear)+0.091×Delay×Freq2 (freq convex)+0.161×Delay0.5×Freq (delay

concave)


Amount of Delay Effect


0 10 20 30 40 50 60 700

102030405060708090

100

Linear


Delay (min)

Disu

tility

as c

ompa

red

to IV

TT (m

in)


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)


Delay (min)

Disu

tility

as c

ompa

red

to IV

TT (m

in)


Convexity, discarding very small

delays

Frequency of Delay Effect


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


Frequency

Disu

tility

as c

ompa

red

to IV

TT (m

in)


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)


Frequency

Disu

tility

as c

ompa

red

to IV

TT (m

in)


6 Travel Time Components


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


Line share Effective Frequency Discount ×~Sc

hedu

le w

ait

Capa

city

wait

Unre

liabi

lity

wait

Phys

ical I

VT

Crow

ding

IVT

Unre

liabi

lity

IVT

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)


incorporation of capacity constraints, crowding, and reliability in transit forecasting

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