New Approach to Bottleneck Capacity Analysis

1. New Approach to Bottleneck Capacity Analysis James H. Banks San Diego State University

2. Basic Concepts

3. Basic concepts • HCM method • Alternative approach • Some behavioral hypotheses

4. HCM methods • Bottleneck types • Basic freeway segments • Ramps and ramp junctions • Weaving sections • Factors affecting capacity • Free-flow speed (FFS) • Relationship between hourly volume (mixed vehicles) and peak 15-min flow rate in PCE • For weaving, length and configuration of section

5. Equations c = 1,800 + 5FFS FFS = BFFS – fLW – fLC – fN – fID

6. Factors affecting capacity • Lane width (FFS) • Right shoulder clearance (FFS) • Number of lanes (FFS) • Interchange density (FFS) • Heavy vehicle presence • Length and steepness of grade • Driver population

7. Limitations of HCM • Does not distinguish pre-queue flow (PQF) from queue discharge flow (QDF) – not clear which is meant • Comparatively little insight into behavioral basis of capacity – driver population factor applies to non-commute traffic and no method for calculating it • Will not explain full range of variation in capacity flows among bottlenecks

8. Alternative approach • Make distinction between • Pre-queue flow (PQF) • Queue discharge flow (QDF) • Use two-stage models: • Flow function of • Headway components • Lane flow distribution • Headway components and lane flow distribution function of • Geometry • Vehicle population • Driver population

9. Headway components and lane flow distributions • Headway composed of • Passage time (time it takes vehicle to pass a point) • Time gap (time between rear of lad vehicle and front of following one) • Lane flow distribution characterized by • Critical lane flow ratio (flow in highest flow lane divided by flow per lane)

10. Mathematical relationships

11. One-stage vs. two-stage models • One-stage simpler • Possible two-stage advantages • Might provide better understanding of driver behavior • Time gaps and lane flow distributions vary among bottlenecks • Appears to be result of driver behavior – can differences be explained? • Might be more accurate

12. Behavioral assumptions • Differences in time gaps and CLFRs depend on • Geometric characteristics of sites • Vehicle mix • Driver characteristics (aggressiveness) – what identifiable characteristics correlate with this? • Some combination of the above

13. Behavioral hypotheses • Gaps will be related negatively to the proportions of young people, males, and wealthy people in the traffic stream. • CLFR will be related positively to the proportions of young people, males, and wealthy people in the driver population. • From the two preceding hypotheses, CLFR and gaps will be negatively correlated.

14. Behavioral hypotheses (cont.) • Gaps will be related negatively to metropolitan area population and the population density in the vicinity of the site. • CLFR will be related positively to metropolitan area population and population density in the vicinity of the site. • Gaps will be smaller during work trip peaks than at other times of day.

15. Behavioral hypotheses (cont.) • Gaps will be larger where there are complicated traffic situations (weaving, high levels of lane changing, closely-spaced ramps, left hand entrances or exits, etc.) than where traffic situations are simple. • Gaps will be related positively to roadway grade, especially in QDF.

16. Behavioral hypotheses (cont.) • CLFR will be related positively to the proportion of heavy vehicles and the length and steepness of grade. • CLFR in critical sections will be related negatively to the ratios of entering and exiting flow to overall flow.

17. Sites and Data

18. Proposed traffic data specifications •  20 bottleneck sites •  50 workdays at each • Data available • Count • Lane occupancy • Available for all lanes • Time base  1 min • Outside San Diego area, detectors must be located in bottleneck section

19. Practical limitations on sample of sites • Lack of definite relationship between time gaps upstream and in bottlenecks sections meant most San Diego sites used for verification of models only • Data problems (usually missing counts) ruled out many sites • Some bottlenecks only rarely active

20. Final sample of sites • 21 total sites • 3 metro areas • Minneapolis-St. Paul • Seattle • San Diego • 15 used for model calibration • One subsequently rejected as outlier • 6 used for model verification

21. Final sample of sites (cont.) • Several types • Merge (15) • Weave exit leg (3) • Weave (1) • Lane drop (1) • Diverge (1) • 15 PM sites, 6 AM sites • Number of directional lanes varied • Two lanes (7) • Three lanes (5) • Four lanes (8) – 3 for calibration, 5 for verification • Five lanes (1) used for verification

22. Traffic data • Counts and occupancies • By lane • Time bases: • Minnesota: 30 s • Seattle: 20 s • San Diego: 30 s

23. Data collection periods • Summer 2004 for all sites • For purposes of comparison, also used data from Minnesota sites for September 16 – December 1, 2000 (taken during experimental shutdown of ramp meters)

24. Other data • Rainfall – National Climatic Data Center • Incidents – PeMS (for San Diego) • Geometrics – MinnDOT, WSDOT, Caltrans • Vehicle classification – MinnDOT, WSDOT, Caltrans • Peak period available for Seattle only • Data available for trucks only • Used 24 hour data • Census data – U. S. Census Bureau

25. Data reduction • Data screening • Transformation of flow, occupancy data • Identification of flow periods • Calculation of site mean averages

26. Data screening • Screening for obviously corrupt data • Missing data • Volume/occupancy ratio out of range • Speed inconsistent with other lanes • Bad data flag set • Identical data for 2 or more consecutive intervals • Identification of relative biases • Compared total flow for adjacent detectors • Discrepancies from <0.1% to 6.5% noted

27. Data transformations Time gaps Speeds

28. Identification of flow periods • Used plots of • Time series of speed • Rotated cumulative speed • Rotated cumulative flow • QDF identified from rotated cumulative speed • Beginning of PQF from rotated cumulative flow • Time series used to confirm beginning and end of flow periods

29. Time series of speed

30. Rotated Cumulative Speed

31. Rotated cumulative flow

32. Identification of QDF

33. Identification of PQF

34. Limitations of method • Requires analysts judgment, especially in determining beginning of PQF • Consequently, may be inconsistent • Tedious, where large number of sites and days are involved

35. Calculation of site-mean averages • Calculated for each site: • Weighted mean over all count intervals • Bottleneck flow/lane (PQF and QDF) • Critical lane flow (PQF and QDF) • Critical lane passage time • Critical lane flow ratio

36. Flow characteristics

37. Site-mean PQF and QDF • Ranges • PQF: 1,686 veh/h/lane – 2,419 veh/h/lane • QDF: 1,647 veh/h/lane – 2,184 veh/h/lane • Relationship of PQF to QDF • PQF exceeded QDF by 1.8% - 15.4% • Difference significant at 0.01 in all but one case • Confirms past research

38. Relationships among flow characteristics • Relationships with flow/lane • Flow/lane vs. critical lane gap • PQF: R = -0.596 (significant at 0.01) • QDF: R = -0.695 (significant at 0.01) • Flow/lane vs. CLFR • PQF: R = -0.336 (not significant) • QDF: R = -0.585 (significant at 0.05) • Flow/lane vs. passage time • PQF: R = +0.009 (not significant) • QDF: R = +0.167 (not significant)

39. Relationships with critical lane flow • Critical lane flow vs. critical lane gap • PQF: R = -0.909 (significant at 0.01) • QDF: R = -0.904 (significant at 0.01) • Critical lane headway vs. critical lane gap • PQF: R = +0.884 (significant at 0.01) • QDF: R = +0.823 (significant at 0.01)

40. Gap vs. flow and headway

41. Implications • Either relationship might be linear (too much scatter to tell) • Might be result of correlation between gap and passage time • PQF: R = -0.472 (significant at 0.05) • QDF: R = -0.564 (significant at 0.05) • Relationship with flow slightly stronger

42. Relationships for use in 2-stage models • PQF: qP,c = 3,731 – 1,071.2gc • QDF: qD,c = 3,249 – 831.1gc

43. Site characteristics

44. Site characteristic variables • Geometric • Roadway grade (GRD) • Vehicle population • Percent heavy vehicles (PHV) • Driver population • Median age (AGE) • Median income (INC) • Percent males aged 18 to 24 (YML) • Percent college graduates (PCG) • Population density (PDN)

45. Site characteristics (cont.) • Also calculated HCM heavy vehicle factor from grade and percent heavy vehicles • Because sites were relatively flat, almost perfectly correlated with percent heavy vehicles • Did use it to calculate HCM capacity estimates

46. Driver population characteristics • Estimated from census data from assumed commuter shed zones • AM zones upstream of bottleneck, PM zones downstream • Approximately 15 km long x 6 km wide • If another freeway within 12 km, boundary halfway between • Limited by major traffic barriers and edge of urbanized area • Terminated at CBD if within 15 km • Census tracts included if > ½ in zone boundaries

47. Correlations among site characteristics • Significant positive correlations (at 0.05) • AGE and INC • LNS and PDN • YML and PDN • Significant negative correlations (at 0.05) • LNS and INC • AGE and YML • AGE and PDN • PHV and YML • INC and YML

48. Initial models – basic forms One-stage q = f1(x1, x2, …) Two-stage qc = a + bgc rc = f3(x1, x2, …) gc = f2(x1, x2, …) or rc = f4(qon, qoff)

49. Initial models • Separate models for PQF and QDF • Total of 6 models • One one-stage model each • Two two-stage models each • CLFR model based on site characteristics • CLFR model based on ramp flow

50. Selection of variables • Stepwise regression to identify most significant relationships • Level of significance (F-value) for entering or removing variable = 0.15 • Variables retained for use in final models: • Flow per lane and gaps: INC, YML • CLFR: YML, PCG • Also models of CLFR based on qon, qoff