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Estimating Reliability Indices and Confidence Intervals for Transit and Traffic at the Corridor Level

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Travis Glick, Portland State University

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Estimating Reliability Indices and Confidence Intervals for Transit and Traffic at the Corridor Level

  1. 1. Estimating Reliability Indices and Confidence Intervals for Transit and Traffic at the Corridor Level Miguel A. Figliozzi, PhD, Professor Travis B. Glick, EI, GRA (Presenter) TRB 96th Annual Meeting — Washington, DC Session: 595 — Tuesday, 10 January 2017 — 10:15am–12:00pm
  2. 2. Presentation Overview •High Resolution (HR) Data •Methodology •Speed and Travel Time with Confidence Intervals •Space-Time-Speed Diagrams •Other Applications •Conclusions
  3. 3. Powell Blvd. in Portland, OR
  4. 4. Powell Blvd
  5. 5. High-Resolution Data Visualizing Collection and Analysis
  6. 6. 5-SR Data Analysis 450 ft.50 ft. 100 ft. 150 ft. 200 ft. 250 ft. 300 ft. 350 ft. 400 ft. Time 1 Time 2 Time 3
  7. 7. 5-SR Data Analysis 450 ft.50 ft. 100 ft. 150 ft. 200 ft. 250 ft. 300 ft. 350 ft. 400 ft. Time 2 Time 3 Speed 1 Speed 2 Speed 3 C = Centerness Factor Time 1
  8. 8. 5-SR Data Analysis 450 ft.50 ft. 100 ft. 150 ft. 200 ft. 250 ft. 300 ft. 350 ft. 400 ft. Time 2 Time 3 Speed 1 Speed 3 Speed 2 C = Centerness Factor Time 1
  9. 9. 5-SR Data Analysis 450 ft.50 ft. 100 ft. 150 ft. 200 ft. 250 ft. 300 ft. 350 ft. 400 ft. Time 2 Time 3 Speed 1 Speed 2 Speed 3 C = Centerness Factor Time 1
  10. 10. Methodology
  11. 11. Equations for Speed • If there is a set of 𝐽𝐽 bus trips passing segment 𝑠𝑠𝑖𝑖, for each bus trip 𝑗𝑗, • ∀𝑗𝑗 ∈ 𝐽𝐽𝑖𝑖, 𝐽𝐽𝑖𝑖 = 1,2,3, … , 𝑛𝑛𝐽𝐽𝐽𝐽 • Find the pair of consecutive GPS coordinates immediately before and after the center points of 𝑠𝑠𝑖𝑖 • Speed can be calculated between those sets of point-pairs • Calculate Speed for the segment using harmonic mean of speed • ̅𝑣𝑣𝑖𝑖 = 𝑛𝑛𝐽𝐽𝐽𝐽 ∑𝐽𝐽𝑖𝑖 1 𝑣𝑣𝑖𝑖𝑖𝑖 • Harmonic mean is used in transportation to better estimate speeds within a segment
  12. 12. Equations for Confidence • Large Sample Size • (𝑛𝑛𝐽𝐽𝐽𝐽 > 50 ∀𝑖𝑖) • Using the confidence level 𝛼𝛼, and the 𝑧𝑧(𝛼𝛼) score, • Standard Deviation is calculated for a given percentile • 𝜎𝜎𝑖𝑖 𝑖𝑖 2 = 𝑛𝑛𝐽𝐽𝐽𝐽 𝑝𝑝 1 − 𝑝𝑝 • And, the range of that confidence interval for a given percentile • [𝑝𝑝 𝑛𝑛𝐽𝐽𝐽𝐽−𝜎𝜎𝑖𝑖 𝑖𝑖 𝑧𝑧 𝛼𝛼 , 𝑝𝑝 𝑛𝑛𝐽𝐽𝐽𝐽 +𝜎𝜎𝑖𝑖 𝑖𝑖 𝑧𝑧 𝛼𝛼 ]
  13. 13. Removal of Points Around Bus Stops • Using High-Resolution and Stop Level Data, we compared, • Bus Number • Date • Route • Time • From this combined set, we determined GPS coordinates immediately surrounding bus stops • Then removed them from the data set. • The same calculations for speed and percentiles were then run. • For the remaining data
  14. 14. Speed Percentiles with Confidence Intervals
  15. 15. Speed and Travel Time
  16. 16. Speed and Travel Time
  17. 17. Speed and Travel Time
  18. 18. Speed and Travel Time
  19. 19. Speed and Travel Time
  20. 20. Speed and Travel Time
  21. 21. Time-Space-Speed Diagrams Westbound Data
  22. 22. Westbound
  23. 23. Westbound
  24. 24. Time-Space-Speed Diagrams Eastbound Data
  25. 25. Eastbound
  26. 26. Eastbound
  27. 27. Other Applications
  28. 28. Other Applications •Difference Between 85th and 15th percentiles (All Data) Westbound
  29. 29. Other Applications •Difference Between 85th and 15th percentiles (No Bus Stops) Westbound
  30. 30. ∆𝒗𝒗𝒊𝒊= 𝒗𝒗𝒊𝒊,𝟖𝟖𝟖𝟖 − 𝒗𝒗𝒊𝒊,𝟏𝟏𝟏𝟏
  31. 31. Other Applications •Speed Variability Index (All Data) Westbound
  32. 32. Other Applications •Speed Variability Index (No Bus Stops) Westbound
  33. 33. Speed Variability Index 𝝁𝝁𝒊𝒊
  34. 34. Conclusions •High Resolution Data can be used: • To estimate travel-speed percentiles and associated confidence intervals • For Time-Space-Speed Plots • To Identify Congestion Hotspots •Can provide insights into • Travel Time Variability • The best locations for infrastructure Improvements
  35. 35. Acknowledgements NITC for funding this Research Steve Callas and Miles Crumley of TriMet for providing the data and definitions used in analysis And to the researchers who lay the groundwork for this analysis.
  36. 36. Thank you for listening. Any Questions?

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