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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 Assessment Of An Optimal Bus Stop Optimal Bus Stop Spacing Model Using Spacing Model Using High Resolution High Resolution Archived Stop-level DataArchived Stop-level Data
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
TriMet’s Bus Dispatch System
Schedule deviation
Control HeadControl Head
PCMIA CardPCMIA Card
Infrared APCInfrared APC
Operator InputOperator Input
DispatchingDispatching Arrival PredictionArrival Prediction
TRB 88th Annual Meeting, Washington DC January, 2009
TriMet’s Bus Dispatch System
TRB 88th Annual Meeting, Washington DC January, 2009
One Year Stop-Level Data (2007)
Ro
ute
No
.
Serv
ice
Date
Leave T
ime
Sto
p T
ime
Arr
ive T
ime
Bad
ge
Dir
ecti
on
Tri
p N
o.
Lo
cati
on
ID
Dw
ell
Do
or
Lif
t
On
s
Off
s
Est.
Lo
ad
Max S
peed
Patt
ern
D
ista
nce
X C
oo
r.
Y C
oo
r.
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
TRB 88th Annual Meeting, Washington DC January, 2009
2007 AM Boardings
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
Access Cost
Riding and Stopping Cost
TRB 88th Annual Meeting, Washington DC January, 2009
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]
4
s ps
va
TRB 88th Annual Meeting, Washington DC January, 2009
Access Cost
Riding and Stopping Cost
TRB 88th Annual Meeting, Washington DC January, 2009
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]
s
V+Pr
r
=NsrV
+Nr(1 e ps )
TRB 88th Annual Meeting, Washington DC January, 2009
[ ] / s
Average Cost Per Unit Length
Given that
[access]
= 4ravpN
Average cost per unit length
+ [riding] + [stopping]
= ps2a
4v
NsrV
+Nr(1 e ps)
Average cost per unit length =
V
NpN r
r
Independent of s !
Choice of s is independent of V, depends solely on
ps
eps ps )1(
TRB 88th Annual Meeting, Washington DC January, 2009
Objective Function
ps
epsC
ps )1(0
Coverage for >2
If β > 2:ps
e ps )1( ps
1
TRB 88th Annual Meeting, Washington DC January, 2009
ps
psC
10
p
N
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
ps
psC
10
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
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
179
31,
187
782
565
974
726 81
42,
768
1,95
072
81,
579
528
2,10
889
02,
479
952
460
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)
Bu
s S
top
Sp
acin
g (
ft)
0
2
4
6
8
10
12
14
Nu
mb
er
of
Passen
gers
Route 19 Inbound Spacing Status
TRB 88th Annual Meeting, Washington DC January, 2009
Optimized Spacing Calculation• No. of passengers on vehicle • Passenger ons and offs• Lost time
N = 7.9 pax/stop
ps = 33.2 pax/trip =33.6sec
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
Route 19 Inbound Optimized Spacing
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
AM Peak AnalysisFree Trip
TimeAcc&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
TRB 88th Annual Meeting, Washington DC January, 2009
AM Peak Analysis
Optimal
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
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
TRB 88th Annual Meeting, Washington DC January, 2009
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 huanl@pdx.edu
www.its.pdx.edu
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