A computational study of traffic assignment algorithms

Traffic congestion is an issue in most cities worldwide. One way to model and analyse the effect of congestion and other factors on route choice behaviour and to predict the impact of traffic management projects and transport policies is traffic assignment (TA). The most commonly used TA model is known as user equilibrium (UE), which is based on the assumption that all drivers want to minimise their travel time or generalised cost. As a result, an equilibrium is achieved when no one has an incentive to switch to another route. Although the conventional mathematical model of TA belongs to the convex optimisation domain and, hence, is relatively easy to solve, efficient algorithms are required in order to be able to solve TA in a reasonable amount of time for realistic transport networks. This motivates researchers to propose numerous methods and algorithms to solve this problem in the literature. However, there is no comprehensive empirical study that compares the performance of different approaches on benchmark instances. In this study, our objective is to fill this gap. We provide a literature review of the most promising methods. We classify algorithms according to the way the solution is represented, namely, link-based (solution is represented by link flows), path-based (solution is represented by path flows) and origin-based (solution is represented by link flows corresponding to each origin), and implement the most representative algorithms in each group. We perform numerical tests on benchmark instances of various sizes, compare the algorithms and analyse the impact of their main components on their running time. We also study the convergence behaviour of the methods with respect to different levels of solution accuracy.