Structural properties and graphical implications of Webster's delay formula

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 such 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.