Headline

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Estimating Link Travel Time with Explicitly
Considering Vehicle Delay at Intersections
Aichong Sun Email asun_at_pagnet.org Tel (520)
792-1093
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Content Outline

• Current Status of VDF in Travel Demand Model
• VDF Estimation
• VDF Validation
• VDF Implementation
• Conclusions

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Current Status of VDF in Travel Demand Model

• Link-Based VDFs
• The Bureau of Public Roads (BPR) Function

• Conical Volume-Delay Function

Could change
Free-Flow-Travel-Time and Capacity are typically
determined by link-class/area-type lookup table
without considering the intersecting streets
Stay same
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Current Status of VDF in Travel Demand Model

• VDF Considering Intersection Delay
• Logit-based Volume Delay Function
• Israel Institute of Transportation Planning
  Research
• HCM Intersection Delay Function
• Other functions (good discussion on TMIP
  3/6/08-3/17/08)

• Common Issues
• over-sophisticated with the intension of
  thoroughly characterizing traffic dynamics
• Computational Burden Data Requirement
• Function are not convex in nature
• No convergence for traffic assignment procedure

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Current Status of VDF in Travel Demand Model

• PAGs Travel Demand Model
• Use only BPR functions until very recently
• BPR functions are not calibrated with local data
• Travel demand model is not calibrated against
  travel speed/time
• Traffic is not routed appropriately
• Overestimate average travel speed

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VDF Estimation

• Study Design - Foundamental Thoughts
• The VDF should be
• Well Behaved reaction to the changes of travel
  demand, traffic controls and cross-streets
• Simple computation time
• Convex model convergence
• Least Data Demanding - implementation

Data Collected must cover whole range of
congestion
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VDF Estimation

• Study Design Data Collection Method
• Floating-Car method with portable GPS devices
• Two major arterial corridors were selected

Corridor Name Area Type Length (Mile) of Lanes of Signalized Intersections
Broadway Blvd Central Urban 7 6(4) 18
Ina Rd Suburban 4 4 9
Data collected from Broadway Blvd to estimate the
model data collected from Ina Rd to validate the
model

• Survey Duration
• 3 weekdays (Mar. 3 6, 2008), 12 hours a day
  (600AM 600PM)

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VDF Estimation

• Collected Data
• GPS 1(2)-Sec Vehicle Location Data

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VDF Estimation

• Collected Data
• Distance between signalized intersections
• Posted speed limits
• Lane Configuration for each street segment
  between intersections
• 15-min interval traffic counts between major
  intersections
• Collected concurrently at 7 locations on Broadway
  Blvd and 3 locations on Ina Rd
• Signal phasing/timing/coordination information
• Collected from jurisdictions

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VDF Estimation
VDF Model Form
Signal Delay (NCHRP 387)
BPR function
- Percentage of through traffic
Adjustment based on congestion
- Traffic Progression Adjustment Factor
- Coefficients
- Segment capacity
- Intersection Approach Capacity for
through traffic
- signal g/c ratio for through traffic
- midblock free-flow travel time, NCHRP
387
- Signal Cycle Length
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VDF Estimation

• Nature of the function form
• Convex (when Betas gt 1)

Convex
Convex
Convex

• Sensitive to Signal Timing Congestion

Midblock congestion
Intersection congestion
g/c ratio
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VDF Estimation

• Parameters
• Capacity
• Mid-block
• - HCM approach
• - (Linkclass, AreaType) lookup Table
• Intersection
• - Saturation rate 1800/1900 vehicle/hr/lane (HCM)
• - Signal g/c ratio

• Speed
• NCHRP Report 387

High-speed facilities (gt 50 mph)
Low-speed facilities (lt 50 mph)
Or
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VDF Estimation

• Parameters
• Through Traffic Percentage (70-90)
• Traffic Progression Adjustment Factor
• - HCM 2000 (0 2.256)
• - NCHRP Report 387

Condition Progression Adjustment Factor
Uncoordinated Traffic Actuated Signals 0.9
Uncoordinated Fixed Time Signals 1.0
Coordinated Signals with Unfavorable Progression 1.2
Coordinated Signals with Favorable Progression 0.9
Coordinated Signals with Highly Favorable Progression 0.6
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VDF Estimation

• Model Estimation Prepare Dataset
• Identify the floating car locations and arrival
  times immediately after the intersections to
  compute travel time and travel distance for each
  run
• Build the dataset with one record for each pair
  of identified travel distance and travel time
  between two neighboring intersections
• Append the following data to each record in the
  dataset
• Traffic Counts
• Street Segment Capacity
• Free-Flow-Speed
• Signal Cycle Length
• Signal g/c Ratio
• Signal Traffic Progression Adjustment Factor
• Intersection Saturation Rate

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VDF Estimation

• Model Estimation Regression
• Nonlinear regression
• Often no global optimum
• Regression Methods
• - Enumeration Method (Least Square)
• Specify range increment for each parameter
• Enumerate the combinations of possible values
  for each parameter
• Compute MSE for each combination of parameter
  values
• Save 50 combinations of the parameter values
  that result in the least MSE
• - Statistical Analysis Software (SPSS, SAS)
• Verify the parameters estimated from Enumeration
  Method
• Report statistical significance for estimated
  parameters

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VDF Estimation

• Model Estimation Results
• Enumeration Method

Best_Alpha1 Best_Beta1 Best_Alpha2 Best_Beta2 Best_MSE
1.9 1.9 2.1 2.4 464.9736023
1.7 1.8 2.1 2.4 464.97755
1.6 1.7 2.1 2.5 465.0029037
2 2 2.1 2.3 465.0132826
1.8 1.8 2 2.4 465.0143812
2 1.9 2 2.4 465.0149071
1.8 1.8 2.1 2.5 465.0155575
1.8 1.9 2.1 2.3 465.0163662
2.1 2 2.1 2.4 465.0249737
1.9 1.9 2 2.3 465.0272314
2.1 2 2 2.3 465.0363844

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VDF Estimation

• Model Estimation Results
• Statistical Analysis Software (SPSS SAS)

Parameter Estimates R2 0.38
Parameter Estimate Std. Error 95 Confidence Interval 95 Confidence Interval
Parameter Estimate Std. Error Lower Bound Upper Bound
a1 1.835 (1.9) .890 .089 3.581
b1 1.858 (1.9) .535 .809 2.907
a2 2.073 (2.1) .213 1.655 2.491
b2 2.392 (2.4) .475 1.460 3.324

• Both Methods reported very similar parameter
  estimates

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VDF Validation

• Ina Rd Data
• Apply the parameters estimated from Broadway Blvd
  data to Ina Rd

Corridor Name Average I-I Travel Time (Sec) RMSE (Sec) RMSE
Broadway Blvd 53 21.5 40
Ina Rd 67 27.8 (26.9) 41.5 (40.2)
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VDF Validation

• Average Regional Travel Speed

BPR FFS from NCHRP Report 387
  Parkway Major Arterial Minor Arterial Frontage Road Average
SPEED 51.0 45.5 46.8 45.3 46.1
BPR FFS from PAG Model Speed Lookup Table
  Parkway Major Arterial Minor Arterial Frontage Road Average
SPEED 51.0 45.5 46.8 45.3 40.9
New VDF FFS from NCHRP Report 387
  Parkway Major Arterial Minor Arterial Frontage Road Average
SPEED 36.9 32.0 35.7 29.5 33.5
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VDF Validation

• Travel Times of Individual Routes

Route Travel Time (min) Travel Time (min) Travel Time (min) Travel Distance (mile) Actual Number of Signalized Intersections Modeled number of Signalized Intersections
Route Reported Model Estimated (BPR) Model Estimated (New VDF) Travel Distance (mile) Actual Number of Signalized Intersections Modeled number of Signalized Intersections
1 35 17 31 12 26 24
2 11 6 10 4 9 6
3 30 14 25 9 21 25
4 21 13 19.5 9 17 15
5 40 19 31 13 23 22
N
W
E
N
NE
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VDF Implementation

• New VDF is made with C codes and compiled as the
  modeling software DLL
• OUE Assignment is used to replace standard UE
  assignment for faster convergence
• FAQs
• Q Posted Speed Limits for future year network
• A Use the average of the present similar
  facilities in terms of link class and area type
• Q Cycle Length, g/c Ratio, Progression
  Adjustment Factor for future year network
• A Categorize the intersection in terms of the
  facility type of intersecting streets, area type
  and so on

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Conclusions

• Empirical Model
• Provide some insights into the traffic dynamics,
  but not as much as HCM traffic flow/congestion
  models
• Report more precise vehicle travel time/speed
• Reasonably sensitive to intersection
  configuration
• Turning traffic may experience further delay that
  is not captured by the VDF
• Further study with more samples is necessary (in
  plan)
• Other function forms should be investigated

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Questions, Comments Or Suggestions?
Aichong Sun Email asun_at_pagnet.org Kosok
Chae Email kchae_at_pagnet.org Tel [phone]