Phase-based optimisation of isolated signal-controlled junctions: Sensitivity analysis and a treatment of double green phases

This paper describes a phase-based approach to optimisation of fixed time traffic signl control that can be naturally extended to deal with various special types of traffic streams. The general case is discussed briefly where optimisation techniques are used to solve a linear programming problem in a finite number of variables. The problem of maximising the junction practical reserve capacity is used as an example. Due to the choice of programming variables, the particular methods used for the general problem can be naturally extended to represent sequences containing phases with more than one green period, in which each separate green period may have a different saturation flow. This allows a number of features to be modelled explicitly for a signal-controlled junction, in a way that is not possible with other methods. These features include phases that contain opposed turning traffic either in the form of early cut-offs or late starts. The extensions required to model a phase with more than one green period in one cycle are described and also how these can be manipulated to treat opposed turning traffic. The treatment of opposed turning traffic introduces non-linear constraints into the optimisation, but this problem may be overcome using an iterative procedure where the actual constraints are replaced by linear approximations and an optimum value of the objective function is obtained for each iteration. The practicality of this approach is discussed, and in particular whether the sequence of solutions to the linearly constrained sub-problems will converge. The linear programming techniques used allow an extensive sensitivity analysis to be carried out whereby the change in the optimum value of the objective function due to small changes in any of the parameters of the problem can be assessed. As an example, the formulae for these changes are given for the capacity maximising problem.