Tim W. Lawson David J. Lovell Carlos F. Daganzo University of California at Berkeley
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1 Using the Input-Output Diagram to Determine the Spatial and Temporal Extents of a Queue Upstream of a Bottleneck Tim W. Lawson David J. Lovell Carlos F. Daganzo University of California at Berkeley
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Using the Input-Output Diagram to Determine the Spatial and Temporal Extents of a Queue Upstream of a Bottleneck. Tim W. Lawson David J. Lovell Carlos F. Daganzo University of California at Berkeley. Outline. Background Purpose and objective Bottleneck with constant departure rate - PowerPoint PPT Presentation
Transcript of Tim W. Lawson David J. Lovell Carlos F. Daganzo University of California at Berkeley
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Using the Input-Output Diagram to Determine the
Spatial and Temporal Extents of a Queue
Upstream of a BottleneckTim W. Lawson
David J. Lovell
Carlos F. Daganzo
University of California at Berkeley
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Outline
Background Purpose and objective
Bottleneck with constant departure rate “Conventional” (time-space) Approach Proposed (input-output) Approach
Extensions to Approach Automation, varying capacity, traffic signal
Conclusions
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Background
Concepts of “Delay” and “Time in Queue” Delay actual time free flow time Time in Queue Delay for “point” queues Time in Queue Delay for traffic queues Concepts confused in the literature
Evaluation and MOEs Value of time Energy and emissions
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Motivation
Time-Space Diagram Approach clear distinction: Delay & Time in Queue (often) well understood difficult to construct
Objective clear up some of the confusion provide a simple approach based on
familiar tools (input-output diagram)
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Assumptions
Constant free-flow speed, vf
speed is constant, regardless of flow
Congested speed, v
speed is dependent on bottleneck capacity Typical time-space diagram assumptions
e.g., instantaneous speed changes
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“Conventional” Approach
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Conventional Approach
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Lessons From t-x Diagram
w dv v Qf
1 1
dw
Qv v f
1 1
tw
Q v
v f
1
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Basic Input-Output Diagram
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Proposed Approach
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Interpretation
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Interpretation
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Other Applications
Automation on a spreadsheet required: upstream arrival times, , vf, v
provides same measures Bottleneck whose capacity changes once
simple extension to above approach Undersaturated Traffic Signal
“limiting” case
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Conclusions
Simplicity modifies widely used and understood tool much less tedious than t-x; automation
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Conclusions
Simplicity modifies widely used and understood tool much less tedious than t-x; automation
Utility estimates of wait times, etc.; impacts queue lengths; time of maximum queue
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Conclusions
Simplicity modifies widely used and understood tool much less tedious than t-x; automation
Utility estimates of wait times, etc.; impacts queue lengths; time of maximum queue
Superiority corrects significant misunderstanding
