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11October 19, 2011
Comparison of Queue Estimation Models at Traffic Signals
Jingcheng Wu
October 19, 2011
Presented at the 18th World Congress on ITS
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Queueing at Traffic Signals
• Traffic flow on urban arterials is periodically interrupted by traffic signals.– Free flow– Decelerate to join the queue– Stop and wait in the queue– Accelerate to leave the queue– Free flow
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How long is the queue?
• Queue Length, number of feet
• Queue Size, number of vehicles
• Conversion from one to the other requires assuming– Average physical vehicle length– Average space headway between vehicles
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What are the benefits?
• Queue lengths in real-time operations– 20 seconds vs. 15 minutes
• Traffic signal control– Adaptive traffic signal control
• Traffic management
• Traveler information
• Incident management
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State of the Practice
• Physically directly measure queues through detection technologies
• Estimate queues through various models based on detector data
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Measure Queues
• Video image detection– What you see is what you get.– High cost
• Install many detectors at close spacings– Higher cost– More does not mean better.
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Queue Estimation Models
• Simple input-output model
• Kalman filter model
• Shock wave model
• Probabilistic model
• Other models
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Simple Input-Output Model
•
• Difference between volumes entering and exiting
• Assuming– Vehicles do not change lanes.– First-in-first-out principle applies.
• Cannot handle long queues
• Accumulate errors over time
outinnn NNQQ 1
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Kalman Filter Model
•
• Time update term and measurement update term
• Covert time occupancy to space occupancy
• Kalman filter gain parameter
• Simplified exponential smoothing model
• Volume balancing ratio
)()( 111 nnoutinnn QqKVVTQQ
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Shock Wave Model
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An Example of Probabilistic Model
𝑃𝑄ሺ𝑖,𝑡ሻ= ൣ�𝑃𝑄ሺ𝑗,𝑡−∆𝑡ሻ∙𝑃𝑎ሺ𝑖 − 𝑗,∆𝑡ሻ൧𝑖𝑗=0
𝑃𝑄ሺ𝑖,𝑡ሻ= �ൣ𝑃𝑄ሺ𝑖 − 𝑙+ 𝑠∙∆𝑡,𝑡−∆𝑡ሻ∙𝑃𝑎ሺ𝑙,∆𝑡ሻ൧ሾ𝑖+𝑠∙∆𝑡ሿ𝑙=0
𝑃𝑄ሺ𝑖,𝑡ሻ= 𝑃𝑄ሺ𝑗,𝑡− ∆𝑡ሻ∙ 𝑃𝑎ሺ𝑙,∆𝑡ሻሾ𝑠∙∆𝑡ሿ𝑙=0 ሾ𝑠∙∆𝑡−𝑙ሿ
𝑗=0
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Other Models
• Cell Transmission Model
• Use data collected by probe-based monitoring techniques to estimate queue length
• Implement fuzzy logic based models
• Base on a Gaussian process model
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Field Data
• New York City Department of Transportation urban arterial performance measurement, proof of concept
• Midblock RTMS volume and occupancy
• Stop bar Citilog Video Image Detector (VID) volume
• Queue length manually collected at stop bar
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Vehicle Queue Length @ Lafayette Street
Field Data
Kalman FilterKalman Filter Model
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Input-Output Model
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Field Data
Input-Output
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Conclusion
• Kalman filter tends to provide better results when volumes are unbalanced.
• The simple input-out model is easier to implement with a little sacrifice in accuracy.
• Very few studies targeting real-time queuing at traffic signals
• Very few queue models suitable for real-time operations
• Improved real-time queue models are needed.
