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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

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## 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 • “Conventional” (time-space) Approach • Proposed (input-output) Approach • Extensions to Approach • Automation, varying capacity, traffic signal • Conclusions**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**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)**Assumptions**• Constant free-flow speed, vf • speed is constant, regardless of flow • Congested speed, vm • speed is dependent on bottleneck capacity • Typical time-space diagram assumptions • e.g., instantaneous speed changes**Other Applications**• Automation on a spreadsheet • required: upstream arrival times, m, vf, vm • provides same measures • Bottleneck whose capacity changes once • simple extension to above approach • Undersaturated Traffic Signal • “limiting” case**Conclusions**• Simplicity • modifies widely used and understood tool • much less tedious than t-x; automation**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**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

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