huan li and robert l. bertini transportation research board 88th annual meeting washington, dc

TRB 88th Annual Meeting, Washington DC January, 2009

Huan Li and Robert L. Bertini

Transportation Research Board 88th Annual Meeting Washington, DCJanuary 11-15, 2009

Assessment Of An Optimal Bus Stop Spacing Model Using High Resolution Archived Stop-level Data


About TriMet Serves 1.2 M

population 63.9 M annual bus

trips 95 bus routes 655 buses 8100 bus stops Also LRT, Commuter

Rail, Streetcar & Paratransit


TriMet’s Bus Dispatch System

On-BoardComputer

Radio

DoorsLift

APC (Automatic Passenger Counter)Overhead Signs

OdometerSignal Priority Emitters

Stop Annunciation

Memory Card

RadioSystem

Garage PC’s

Radio AntennaGPS Antenna

Navstar GPS Satellites

Control Head



Schedule deviation

Control Head

PCMIA Card

Infrared APC

Operator Input

Dispatching Arrival Prediction


One Year Stop-Level Data (2007)

Rou

te N

o.Se

rvic

e D

ate

Leav

e Ti

me

Stop

Tim

e

Arr

ive

Tim

e

Bad

geD

irect

ion

Trip

No.

Loca

tion

IDD

wel

lD

oor

Lift

Ons

Offs

Est.

Load

Max

Spe

edPa

ttern

D

ista

nce

X C

oor.

Y C

oor.

14 01NOV2001 8:53:32 8:49:15 8:53:28 285 0 1120 4964 0 0 0 0 0 21 41 10558.58 7644468 67600514 01NOV2001 8:55:00 8:51:41 8:54:46 285 0 1120 4701 4 0 0 0 1 20 50 15215.05 7649112 67632814 01NOV2001 8:56:22 8:52:00 8:55:08 285 0 1120 4537 36 3 0 6 0 26 34 15792.35 7649674 676220

Route Number Vehicle Number Service Date Actual Leave Time Scheduled Stop Time Actual Arrive Time Operator ID Direction Trip Number Bus Stop Location

Dwell Time Door Opened Lift Usage Ons & Offs (APCs) Passenger Load Maximum Speed on

Previous Link Distance Longitude Latitude


2007 AM Boardings


Background on Stop Location• Challenges in delivering reliable and timely bus

service • Financial constraints• Public transit operational issues• Transit service generally favors bus stop

accessibility• Sometimes based on past history and tradition

rather than rigorous ongoing analysis at the stop level


Stop Spacing Service Standards

TriMet • Portland >80 units/acre: 400-600 ft 22-80 units/acre: 500-750 ft 4-22 units/acre: 600-1000 ft <4 units/acre: as needed Inner Portland has 200 ft blocks (264 ft street spacing) Route 19 mean stop spacing is 942 ft (3 blocks)

Objective: Develop and test a simple stop spacing model using this rich data


Concept DerivationTrade off: person’s time in parallel access vs. another person’s time in riding.

•Minimize access cost: favors small s•Minimize riding cost: favors large s


Assumptions• Origins & destinations distributed along route

in one dimension (ignore perpendicular access)…

• Average access distance (parallel only) =s/4

• Assume number of passengers boarding or alighting at a stop to be ~Poisson distributed


Access Cost

Riding and Stopping Cost


Access Cost Value of Passenger Travel Distance

p = density of trip origins plus density of trip destinations for passengers who board or alight the same vehicle (units: number/distance)

s/4= average access distance (unit: distance) ν = passenger access speed (unit: distance/time)• a = average cost per unit time per person for access

(unit: cost/time)

ps2a

4vin interval of length s

Ca= [avg. no. of pax] [avg. dist traveled] [cost/unit dist]

4s ps

va


Access Cost

Riding and Stopping Cost


Riding and Stopping CostValue of in-vehicle passenger lost time due to boardings and alightings

• N = expected number of passengers on vehicle• V = vehicle cruise speed• = time lost in stopping to serve passengers• Pr =1-e-ps = probability that vehicle actually stops (from

Poisson for number of ons and offs)• γr= average cost per unit time per person for riding

N= in interval length s

Cr= [avg. no. of pax] [riding time + lost time][cost/unit time]

sV+Pr

r

= NsrV

+Nr(1 e ps )


[ ] / s

Average Cost Per Unit Length

Given that

[access]

= 4 ravpN

Average cost per unit length

+ [riding] + [stopping]

= ps2a

4v

NsrV

+Nr(1 e ps)

Average cost per unit length =

VNpN r

r

Independent of s !

Choice of s is independent of V, depends solely on

pseps ps )1(


Objective Function

psepsC

ps )1(0

Coverage for >2

If β > 2:pse ps )1(

ps1


pspsC 1

0

pN

p

Npv

ps a

r

44

ps = expected number of passengers to board or alight per stop

nsDestinatio and Origins Trip ofDensity Buson Pax No.ofTimeLost 4Spacing Optimal

pspsC 1

0


Case Study: Inbound Route 19 All Day

• 370 days (2/20/07 - 1/5/08) • 19,344 trips• 33.2 ons and offs/trip:• Average passenger load/stop:

7.9

• Route 19 Glisan to Portland• Route Length: 9.27 mi• Number of stops: 52• Mean delay due to stopping:

33.6 s• Use 4ft/s walking speed


343

780

1,26

42,

045

807

1,49

955

179

359

996

6 1,01

783

760

581

971

0 758 80

5 859

762

1,02

464

879

61,

096

623

613

638

660

890

861

505

991

420

704

630 76

1 793

1,18

778

256

597

472

6 814

2,76

81,

950

728

1,57

952

82,

108

890

2,47

995

246

0

0

500

1,000

1,500

2,000

2,500

3,000

0.0

0.1

0.2

0.5

0.8

1.0

1.3

1.4

1.5

1.6

1.8

2.0

2.2

2.3

2.4

2.6

2.7

2.9

3.0

3.2

3.4

3.5

3.7

3.9

4.0

4.1

4.2

4.3

4.5

4.7

4.8

5.0

5.0

5.2

5.3

5.4

5.6

5.8

6.0

6.1

6.2

6.4

6.5

7.1

7.4

7.6

7.9

8.0

8.4

8.5

9.0

9.2

9.3

9.5

Distance Along Route Toward Downtown (miles)

Bus

Sto

p Sp

acin

g (ft

)

0

2

4

6

8

10

12

14

Num

ber o

f Pas

seng

ers

Route 19 Inbound Spacing Status


Optimized Spacing Calculation• No. of passengers on vehicle • Passenger ons and offs• Lost time

Rou

te N

o.

Serv

ice

Dat

e

Leav

e Ti

me

Stop

Tim

e

Arr

ive

Tim

e

Bad

geD

irec

tion

Trip

No.

Loca

tion

IDD

wel

lD

oor

Lift

Ons

Offs

Est.

Load

Max

Spe

edPa

ttern

Dis

tanc

e

X C

oor.

Y C

oor.

14 01NOV2001 8:53:32 8:49:15 8:53:28 285 0 1120 4964 0 0 0 0 0 21 41 10558.58 7644468 67600514 01NOV2001 8:55:00 8:51:41 8:54:46 285 0 1120 4701 4 0 0 0 1 20 50 15215.05 7649112 67632814 01NOV2001 8:56:22 8:52:00 8:55:08 285 0 1120 4537 36 3 0 6 0 26 34 15792.35 7649674 676220

N = 7.9 pax/stopps = 33.2 pax/trip

=33.6sec


2007 Time Space Passenger Load Plot Route 19

Time (hour)

Dis

tanc

e (m

i)9

8

7

6

5

4

3

2

1

05 10 15 20

30

25

20

15

10

5

0


Route 19 Inbound Optimized Spacing

0 10 20 30 400

500

1000

1500

2000

2500

3000

3500

4000

N (number of passengers on bus)

Stop

Spa

cing

(ft)

20 ons/offs

60 ons/offs

40 ons/offs

Feb.20th,2007-Jan.5th,2008consider stop circle delay: Stop circle time - free flow timeFor n=790,392, mean = 33.6 sec, stdev = 22.8 sec (range 1-100)Mean ons/offs=33.2Also show spacing plot for 20 ,40 and 60 ons/offsStep function based on 20 blocks/mile

33.2 ons/offs

Optimal


AM Peak Analysis• Direction: all inbound trips• Analyzed time period: AM

peak hours (6:00-9:00 defined by TriMet) in weekdays

• Number of trips: 3,658 • Mean headway in peak hour:

12 minutes• Mean trip time: 32.6 min

2007 AM Passenger Load Plot Route 19

2007 AM Passenger Ons&Offs Plot Route 19


AM Peak AnalysisFree Trip Time Acc&Dec Time Passenger On Passenger Off

All Day 22.2 min 17.0 sec 3.0 sec 4.1 sec

AM Peak 23.9 min 18.4 sec 0.8 sec 3.0 sec

Passenger Load Ons and Offs Lost Time Opt Spacing

7.9pax

33.2pax 33.6sec

1222ft

12.8pax

48.7pax

37sec

1258ft

All Day AM Peak


AM Peak Analysis

0 10 20 30 400

500

1000

1500

2000

2500

3000

3500

4000

N (number of passengers on bus)

Stop

Spa

cing

(ft)

20 ons/offs

60 ons/offs

40 ons/offs

48.7 ons/offs

Feb.20th,2007-Jan.5th,2008 AM Peak (6:00-9:00)consider stop circle delay: Stop circle time - free flow timeFor n=169,702, mean = 37.03 sec, stdev = 22.8 sec (range 1-100)Mean ons/offs=37.6Also show spacing plot for 20 ,40 and 60 ons/offsStep function based on 20 blocks/mile

Optimal


Conclusions• 12 (14) stops are recommended for consolidation• The trip time would be reduced by 3.4 (4.0) min/trip• The total savings due to consolidation could be up

to 3.7 (4.4) hours of service time per day • Allow the addition of approximately 7.6 (9)

additional trips per weekday • Mean weekday headway would drop from 18.0 min

to 16.1 (15.8) min • Total of 17,076 inbound trips, the time saved would

be 980 (1140) hours during the year • Assuming $60/hr operating cost, about $60,000

($68,000) could be saved by TriMet


Next Steps• Automate process for all routes• Produce quarterly reports for TriMet• Verify “real” cost savings• Check model assumptions (e.g. Poisson) • Consider “real” relationship to demand and equity• Connect to scheduling


Acknowledgements• David Crout of TriMet

for providing the rich data set that facilitated this analysis

• Prof. Gordon Newell• Prof. Michael Cassidy,

University of California at Berkeley, for his assistance in developing the analytical framework for this paper [email protected]

www.its.pdx.edu

huan li and robert l. bertini transportation research board 88th annual meeting washington, dc

Documents

annual meeting washington

washington dcjanuary

optimal bus stop

stop trb

stop level trb

optimal stop

stop locationchallenges

year stoplevel data