1. 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

2. 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

3. 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

4. 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)

5. 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

6. “Conventional” Approach

7. Conventional Approach

8. Lessons From t-x Diagram

9. Basic Input-Output Diagram

10. Proposed Approach

11. Interpretation

12. Interpretation

13. 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

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

15. 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

16. 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