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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License
Article
Structural Properties and Graphical Implications of Webster’s Delay Formula
Author(s)
Thorsten Neumann and Robert Oertel
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DOI:10.17265/2328-2142/2015.05.003
Affiliation(s)
German Aerospace Center (DLR), Institute of Transportation Systems, Berlin 12489, Germany
ABSTRACT
Stochastic queuing models
have been and still are an essential topic in the field of traffic flow theory
at signalized intersections. The present article enhances the existing
theoretical knowledge by a systematic review of the mutual relationship between
traffic demand, green time split and average delay in context of a coupled
system of Webster equations for a simple intersection scenario. Formally proved
conditions for the existence and uniqueness of valid fixed time control
strategies are derived so that these are able to simultaneously handle given traffic
flows at the four approaches of the considered intersection. At that,
consistency with measured or planned (maximum) average delays, for instance, is
ensured. The strictly mathematical analysis finally leads to a new way of
illustrating the dependencies of the three above named variables in terms of
level curve diagrams that become an easy-to-understand graphical tool for
answering a number of practical questions in context of traffic signal
planning. Several theoretic examples are discussed.
KEYWORDS
Traffic flow theory, queuing model, average delay, signal control, fixed time control, level function.
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