TRB 88th Annual Meeting, Washington DC January, 2009 Huan Li and Robert L. Bertini Transportation Research Board 88th Annual Meeting Washington, DC January 11-15, 2009 Assessment Of An Optimal Bus Stop Spacing Model Using High Resolution Archived 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- Board Computer Radio Doors Lift APC (Automatic Passenger Counter) Overhead Signs Odometer Signal Priority Emitters Stop Annunciation Memory Card Radio System Garage PC’s Radio Antenna GPS Antenna Navstar GPS Satellites Control Head

TRB 88th Annual Meeting, Washington DC January, 2009 TriMet’s Bus Dispatch System Schedule deviation Control Head PCMIA Card Infrared APC Operator Input Dispatching Arrival 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)  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, 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: ft  units/acre: ft  4-22 units/acre: 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 Derivation Trade 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) in interval of length s C a = [avg. no. of pax] [avg. dist traveled] [cost/unit dist]

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 Cost Value 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 P r =1-e -p s = probability that vehicle actually stops (from Poisson for number of ons and offs) γ r = average cost per unit time per person for riding in interval length s C r = [avg. no. of pax] [riding time + lost time] [cost/unit time]

TRB 88th Annual Meeting, Washington DC January, 2009 [ ] / s Average Cost Per Unit Length Given that [access]  Average cost per unit length + [riding] + [stopping] Average cost per unit length = Independent of s ! Choice of s is independent of V, depends solely on     ps e )1( 

TRB 88th Annual Meeting, Washington DC January, 2009 Objective Function Coverage for  >2 If β > 2:

TRB 88th Annual Meeting, Washington DC January, 2009 p s = expected number of passengers to board or alight per stop

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 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, Time Space Passenger Load Plot Route 19 Time (hour) Distance (mi)

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 AM Passenger Ons&Offs Plot Route 19

TRB 88th Annual Meeting, Washington DC January, 2009 AM Peak Analysis Free Trip TimeAcc&Dec TimePassenger OnPassenger Off All Day22.2 min17.0 sec3.0 sec4.1 sec AM Peak23.9 min18.4 sec0.8 sec3.0 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