Transcript Using the Input-Output Diagram to Determine the Spatial

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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Outline
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Background
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Bottleneck with constant departure rate
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“Conventional” (time-space) Approach
Proposed (input-output) Approach
Extensions to Approach
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Purpose and objective
Automation, varying capacity, traffic signal
Conclusions
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Background
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Concepts of “Delay” and “Time in Queue”
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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
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Value of time
Energy and emissions
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Motivation
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Time-Space Diagram Approach
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clear distinction: Delay & Time in Queue
(often) well understood
difficult to construct
Objective
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clear up some of the confusion
provide a simple approach based on
familiar tools (input-output diagram)
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Assumptions
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Constant free-flow speed, vf
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Congested speed, vm
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speed is constant, regardless of flow
speed is dependent on bottleneck capacity
Typical time-space diagram assumptions
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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
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1
w =  v - v dQ
 m
f 
w
dQ = 1
1
v
v
m
tQ =
f
w
vm
1- v
f
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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
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Automation on a spreadsheet
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Bottleneck whose capacity changes once
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required: upstream arrival times, m, vf, vm
provides same measures
simple extension to above approach
Undersaturated Traffic Signal
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“limiting” case
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Conclusions
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Simplicity
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modifies widely used and understood tool
much less tedious than t-x; automation
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Conclusions
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Simplicity
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

modifies widely used and understood tool
much less tedious than t-x; automation
Utility
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estimates of wait times, etc.; impacts
queue lengths; time of maximum queue
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Conclusions
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Simplicity
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
Utility
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
modifies widely used and understood tool
much less tedious than t-x; automation
estimates of wait times, etc.; impacts
queue lengths; time of maximum queue
Superiority
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corrects significant misunderstanding
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