New Approach to Bottleneck Capacity Analysis

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New Approach to Bottleneck Capacity Analysis

• James H. Banks
• San Diego State University

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Basic Concepts
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Basic concepts

• HCM method
• Alternative approach
• Some behavioral hypotheses

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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

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Equations
c 1,800 5FFS
FFS BFFS fLW fLC fN fID
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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

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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

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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

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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)

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Mathematical relationships
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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

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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

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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.

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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.

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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.

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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.

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Sites and Data
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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

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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

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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

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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

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Traffic data

• Counts and occupancies
• By lane
• Time bases
• Minnesota 30 s
• Seattle 20 s
• San Diego 30 s

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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)

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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

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Data reduction

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

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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 lt0.1 to 6.5 noted

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Data transformations
Time gaps
Speeds
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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

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Time series of speed
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Rotated Cumulative Speed
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Rotated cumulative flow
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Identification of QDF
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Identification of PQF
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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

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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

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Flow characteristics
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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

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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)

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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)

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Gap vs. flow and headway
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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

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Relationships for use in 2-stage models

• PQF
• qP,c 3,731 1,071.2gc
• QDF
• qD,c 3,249 831.1gc

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Site characteristics
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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)

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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

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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 gt ½ in zone boundaries

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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

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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)
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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

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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

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Evaluation of models

• Regression statistics
• Ability to predict PQF and QDF for individual
  sites
• Compared with each other and HCM
• Compared for calibration sites and verification
  sites

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Results for calibration sites

• Performance of all models developed similar
• R-values significant at 0.01 for all models
• All unbiased (guaranteed by calibration)
• Maximum errors for individual sites
• PQF about 150 veh/h/lane
• QDF about 225 veh/h/lane
• Conclusion two-stage models do not increase
  accuracy significantly
• HCM seriously inaccurate
• Overestimated both PQF and QDF at all sites
• Estimated flow negatively correlated with actual
  flow

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Results for verification sites

• None of the models developed were satisfactory
• Negative correlations (not significant) between
  estimated and measured flow for all models
• Tend to underestimate PQF, better for QDF
• HCM inaccurate, but less so than at calibration
  sites
• Still overestimates QDF
• On average, relatively accurate for PQF
• Correlations still negative

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Suspected problem

• Distortion of model by outlier
• Site MN-14
• Lowest PQF and QDF (by far)
• Highest percentage of young males (zone contains
  dorms at University of Minnesota)

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Effect on models
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Development of revised models

• Repeated stepwise regression analysis for
  one-stage model, omitting MN-14 data
• Only significant variable was number of lanes
• Calibrated models for PQF and QDF

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Revised models
PQF

QDF
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Possible alternative to regression models

• Relationship betweens number of lanes and
  capacity flows not necessarily linear
• Mean of PQF and QDF for sites with different
  numbers of lanes could be predicted capacity
• Standard deviations could be used to give an idea
  of the uncertainty of the estimate
• Might not be valid for sites with steep grades

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Recommended ranges for PQF and QDF
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Conclusions
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Behavioral hypotheses

• Gaps will be related negatively to the
  proportions of young people, males, and wealthy
  people in the traffic stream.
• Not supported

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Behavioral hypotheses (cont.)

• CLFR will be related positively to the
  proportions of young people, males, and wealthy
  people in the driver population.
• Not supported, unless site MN-14 included

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Behavioral hypotheses (cont.)

• From the two preceding hypotheses, CLFR and gaps
  will be negatively correlated.
• Not supported. No significant correlations

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Behavioral hypotheses (cont.)

• Gaps will be related negatively to metropolitan
  area population and the population density in the
  vicinity of the site.
• Metro area population could not test
• Population density not supported

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Behavioral hypotheses

• CLFR will be related positively to metropolitan
  area population and population density in the
  vicinity of the site.
• Metro area population could not test
• Population density not supported

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Behavioral hypotheses (cont.)

• Gaps will be smaller during work trip peaks than
  at other times of day.
• Not tested

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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.
• Not fully tested, but appears to be false

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Behavioral hypotheses (cont.)

• Gaps will be related positively to roadway grade,
  especially in QDF.
• Not supported

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Behavioral hypotheses (cont.)

• CLFR will be related positively to the proportion
  of heavy vehicles and the length and steepness of
  grade.
• Not supported

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Behavioral hypotheses (cont.)

• CLFR in critical sections will be related
  negatively to the ratios of entering and exiting
  flow to overall flow.
• Apparently half true
• Negatively correlated with exiting flow
• Positively correlated with entering flow

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Other conclusions

• HCM methods do not explain variations in capacity
  among bottlenecks
• Do not properly distinguish PQF and QDF
• Estimated flows negatively correlated with
  measured flows
• Overestimate PQF at most sites
• Overestimate QDF at all sites

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Other conclusions

• Differences in PQF and QDF among sites are
  primarily related to critical lane time gaps.
  Differences in CLFR do play a role but they are
  less important

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Other conclusions

• No relationships between flow characteristics and
  socioeconomic characteristics could be
  identified. The only site characteristic with
  significant influence on capacity flow is the
  number of lanes

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Other conclusions

• One-stage and two-stage models perform similarly.
  For predictive purposes, one-stage models are
  preferred because of their simplicity

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Other conclusions

• Lack of data and data quality remain major
  barriers to understanding variations in PQF and
  QDF among bottlenecks
• Poorly located detectors and long-term detector
  failures limited sample of sites
• Lack of detail in vehicle classification data
• Lack of data about driver population and trip
  purpose characteristics of specific traffic
  streams

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Recommendations
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Recommendation

• Use results of this study to supplement HCM
  analyses. Table of recommended ranges and
  standard deviations may be used to modify HCM
  results and get an idea of the level of
  uncertainty

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Recommendation

• Sponsor further research to expand and refine
  table of ranges of PQF and QDF, by providing a
  larger sample of bottlenecks

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Recommendation

• To facilitate such research, develop automated
  method to identify periods of PQF and QDF

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Recommendation

• Upgrade freeway surveillance systems, especially
  in and around bottlenecks
• More detector stations
• Locate stations in bottleneck sections
• Better maintenance of surveillance systems

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Recommendation

• Continue to pursue issue of relationship between
  flow characteristics and driver population
  characteristics, but with better data
• Ask MPOs to include route on travel diary surveys
• If this does not result in sufficient sample
  sizes, consider special surveys

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Recommendation

• Conduct as many intensive studies of bottlenecks
  as possible
• This study was extensive statistical analysis of
  data from many bottlenecks
• Intensive studies aim to understand performance
  of individual bottlenecks in detail
• If there were enough intensive studies, we might
  be able to generalize their results

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Questions?