University of California at Berkeley 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 Bottleneck with constant departure rate 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” Evaluation and MOEs 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 Objective 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 Congested speed, vm 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

“Conventional” Approach

Conventional Approach

Lessons From t-x Diagram

Basic Input-Output Diagram

Proposed Approach

Interpretation

Interpretation

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 Get exactly the same statistics (almost) with spreadsheet

Conclusions Simplicity modifies widely used and understood tool much less tedious than t-x; automation

Conclusions Simplicity Utility 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 Utility Superiority 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