Evolving application of mathematical optimisation in design and operation of individual signal-controlled road junctions

A mathematical framework for optimisation of the sequencing and timing of traffic signals at an individual junction is set out, distinguishing between discrete and continuous aspects of the problem and indicating how various practically important features of the effects of signal control upon traffic conditions are represented in mathematically tractable forms. Objective functions for optimisation are defined and constraints are set. Progress in formulating and solving the resulting optimisation problems in progressively less simplified forms, and in implementing the solutions in procedures that are usable by practising engineers, is outlined.