A framework for and empirical study of algorithms for traffic assignment

Abstract

Traffic congestion is an issue in most cities worldwide. Transportation engineers and urban planners develop various traffic management projects in order to solve this issue. One way to evaluate such projects is traffic assignment (TA). The goal of TA is to predict the behaviour of road users for a given period of time (morning and evening peaks, for example). Once such a model is created, it can be used to analyse the usage of a road network and to predict the impact of implementing a potential project. The most commonly used TA model is known as user equilibrium, which is based on the assumption that all drivers minimise their travel time or generalised cost. In this study, we consider the static deterministic user equilibrium TA model.The constant growth of road networks and the need of highly precise solutions (required for select link analysis, network design, etc) motivate researchers to propose numerous methods to solve this problem. Our study aims to provide a recommendation on what methods are more suitable depending on available computational resources, time and requirements on the solution. In order to achieve this goal, we implement a flexible software framework that maximises usage of common code and, hence, ensures comparison of algorithms on common ground. In order to identify similarities and differences of the methods, we analyse groups of algorithms that are based on common principles. In addition, we implement and compare several different methods for solving sub-problems and discuss issues related to accumulated numerical errors that might occur when highly accurate solutions are required.

Network Reconfiguration for Increasing Transportation System Resilience Under Extreme Events

“…Given the contraflow configuration and the crossing elimination strategies, the lower‐level optimization problem can be formulated as a TAP. Many algorithms have been proposed for solving this problem (Perederieieva, Ehrgott, Raith, & Wang, ; Zhang & Mahadevan, ). In this article, we choose the gradient projection method (Perederieieva et al., ) due to its efficiency and simplicity.…”

“…Many algorithms have been proposed for solving this problem (Perederieieva, Ehrgott, Raith, & Wang, ; Zhang & Mahadevan, ). In this article, we choose the gradient projection method (Perederieieva et al., ) due to its efficiency and simplicity. The gradient projection method exploits the separability of the origin–destination pairs, and it operates on the path space to shift the flow from costlier paths to the shortest path for each origin–destination pair during the iterations.…”

Numerical stability of path-based algorithms for traffic assignment

“…While studying various algorithms for solving the traffic assignment problem, we noticed that one of the methods from our study (projected gradient) is not able to reach the required level of precision Perederieieva et al (2013Perederieieva et al ( , 2014. In this paper we investigate reasons of this behaviour and propose a way to amend the algorithm in such a way that it is able to converge to high precision.…”

Stochastic user equilibrium with equilibrated choice sets: Part II – Solving the restricted SUE for the logit family

“…Linkbased formulations are attractive in avoiding path enumeration, which is potentially computationally demanding. In the case of DUE, while several path-based algorithms have been proposed (see Perederieieva et al, 2015, for a recent paper testing several variants), link-based formulations retain an attraction due to the fact that we can only hope at best for DUE uniqueness in the space of link flows, not path flows. On the other hand, SUE solutions are unique in path and link flows under mild conditions (Cantarella, 1997).…”