# Algorithms for the Solution of the Combined Traffic Signal Optimisation and Equilibrium Assignment Problem

## Abstract

The combined traffic signal optimisation and equilibrium assignment problem is one in which a traffic engineer tries to optimise the performance of traffic signals while road users choose their routes so as to minimises their travel costs. Two types of solutions can be defined in the combined problem: the *mutually consistent solution* and the *global optimal solution*. The former is a solution at which the two sub-problems are solved simultaneously while the latter is a solution to the bi-level programming formulation of the combined problem. In this paper, we consider the combined signal optimisation and stochastic user equilibrium assignment problem. We present two types of algorithms for the mutually consistent solution and one type of algorithm for the bi-level solution to the problem. The algorithms are tested on a small network to examine their convergence and efficiency.

## Key words

Traffic signal optimization Stochastic assignment Bi-level programming problem## Preview

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