# FORMATION AND DISSIPATION OF TRAFFIC QUEUES: SOME MACROSCOPIC CONSIDERATIONS (ABRIDGEMENT)

In this paper, a rigorous mathematical model shows the evolution of queue length in time at any approach to the intersection as a function of the demands, the intersection capacity, and the signal control policy. Due to space limitations, the results of the simplest possible model are given here. More detailed (therefore, more realistic) models, along with stability analysis and numerical examples, can be found in Michalopoulous and Stephanopoulos. The mathematics of queue dynamics discussed here can be used for optimal control of traffic signals. It is believed that, in light of these results, the traffic signal control problem can be placed on a new, more realistic, and rigorous framework of analysis. The approach taken here to a new and rigorous mathematical model and analysis that show the formation and dissipation of traffic queues at signalized intersections is macroscopic in nature in the sense that automobiles are treated as platoons rather than as single units. The shock wave analysis is fairly realistic for moderate to high demands where the shock waves can be clearly realized. In fact, it is this volume range in which the traffic signal control problem is more pronounced. The analytical results given here have been used for the derivation of a real-time control policy that minimizes total intersection delays subject to queue length constraints at isolated critical intersections. It is important to note that the traffic queue dynamics noted here are valid for isolated intersections at which the assumption of constant average flow rates is fairly realistic. If traffic arrivals are affected by an upstream signal, the analysis becomes more complex. Extension of the basic theory to a system of two or more intersections in succession is not trivial due to the side streets and sinks or sources between the intersections. The fact that the input flows to the downstream intersection is a function of the output of the upstream intersection for any pair of intersections further complicates the analysis. We have also studied the queue dynamics for a system of intersections as well as the related optimal traffic signal control problems. (Author)

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• Supplemental Notes:
• Publication of this paper sponsored by Committee on Traffic Flow Theory and Characteristics. Distribution, posting, or copying of this PDF is strictly prohibited without written permission of the Transportation Research Board of the National Academy of Sciences. Unless otherwise indicated, all materials in this PDF are copyrighted by the National Academy of Sciences. Copyright © National Academy of Sciences. All rights reserved
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• Authors:
• Michalopoulos, Panos G
• Pisharody, Vijay B
• Stephanopoulos, Gregory
• Publication Date: 1979

## Media Info

• Media Type: Print
• Features: Figures; References;
• Pagination: pp 81-84
• Monograph Title: TRAFFIC CONTROL DEVICES, GEOMETRICS, VISIBILITY, AND ROUTE GUIDANCE
• Serial:

## Filing Info

• Accession Number: 00315071
• Record Type: Publication
• ISBN: 0309029929
• Report/Paper Numbers: HS-029 511
• Files: TRIS, TRB
• Created Date: Oct 8 1980 12:00AM