Path-Constrained Traffic Assignment (original) (raw)
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Path-Constrained Traffic Assignment: Model and Algorithm
Transportation Research Record, 2012
This paper presents a mathematical programming model and solution method for the path-constrained traffic assignment problem, in which route choices simultaneously follow the Wardropian equilibrium principle and yield the distance constraint imposed on the path. This problem is motivated by the need for modeling distance-restrained electric vehicles in congested networks, but the resulting modeling and solution method can be applied to various conditions with similar path-based constraints. The equilibrium conditions of the problem reveal that any path cost in the network is the sum of corresponding link costs and a path-specific out-of-range penalty term. The suggested method, based on the classic Frank-Wolfe algorithm, incorporates an efficient constrained shortest path algorithm as its subroutine. This algorithm fully exploits the underlying network structure of the problem and is relatively easy to implement. Numerical results from the provided example problems clearly show how the equilibrium conditions are reshaped by the path constraint and how the traffic flow patterns are impacted by different constraint tightness levels.
Transportation Research Record Journal of the Transportation Research Board, 2009
The paper reports on the algorithmic treatment and computer implementation of a macroscopic dynamic traffic assignment model called LADTA. The modelling assumptions and the mathematical analysis founding the model are first stated. Detailed descriptions of the main algorithms are given, together with the principles of the computer implementation. It is shown how the design of the software architecture allows for distributed computation of a traffic assignment. The practical ability of this implementation to tackle with large size networks is illustrated by an application to the Paris road network, which comprises around 1,300 zones and 39,000 links.
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.
Dynamic penalty function method for the side constrained traffic assignment problem
Applied Mathematics and Computation, 2008
The traffic assignment problem (TAP) is traditionally defined without side constraints. Although introducing side constraints into the TAP is used as a way of refining applied assignment models, it brings some computational difficulties that prevent the refined model from being applicable in real-case problems. In this paper an iterative solution algorithm is developed for TAP with linear side constraints. This method is based on implicitly considering the side constraints by means of adding a dynamic penalty function (DPF) to the link travel times. Each of the iterations of the algorithm is reduced to an unconstrained assignment followed by updating the penalty functions. The unconstrained assignment is carried out using the linearization method that has been derived from the complementarity formulation of TAP. The implementation of the algorithm and computational experiments on some well-known networks are also presented for two types of side constraint, i.e. link and node capacity constraints. For the link-type side constraint, compared to the reported results of the existing alternative approaches, a DPF algorithm finds feasible solutions with better Beckmann's objective functions in less number of iterations. For the node-type constraints, the algorithm also shows good performance.
Computational Study of Traffic Assignment Algorithms
2013
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.
Path-Constrained Traffic Assignment: A Trip Chain Analysis under Range Anxiety
Transportation Research Part C, 2016
This paper proposes and analyzes a distance-constrained traffic assignment problem with trip chains embedded in equilibrium network flows. The purpose of studying this problem is to develop an appropriate modeling tool for characterizing traffic flow patterns in emerging transportation networks that serve a massive adoption of plug-in electric vehicles. This need arises from the facts that electric vehicles suffer from the “range anxiety” issue caused by the unavailability or insufficiency of public electricity-charging infrastructures and the far-below-expectation battery capacity. It is suggested that if range anxiety makes any impact on travel behaviors, it more likely occurs on the trip chain level rather than the trip level, where a trip chain here is defined as a series of trips between two possible charging opportunities (Tamor et al., 2013). The focus of this paper is thus given to the development of the modeling and solution methods for the proposed traffic assignment problem. In this modeling paradigm, given that trip chains are the basic modeling unit for individual decision making, any traveler’s combined travel route and activity location choices under the distance limit results in a distance-constrained, node-sequenced shortest path problem. A cascading labeling algorithm is developed for this shortest path problem and embedded into a linear approximation framework for equilibrium network solutions. The numerical result derived from an illustrative example clearly shows the mechanism and magnitude of the distance limit and trip chain settings in reshaping network flows from the simple case characterized merely by user equilibrium.
2009
The paper reports on the algorithmic treatment and computer implementation of a macroscopic dynamic traffic assignment model called LADTA. The modelling assumptions and the mathematical analysis founding the model are first stated. Detailed descriptions of the main algorithms are given, together with the principles of the computer implementation. It is shown how the design of the software architecture allows for distributed computation of a traffic assignment. The practical ability of this implementation to tackle with large size networks is illustrated by an application to the Paris road network, which comprises around 1,300 zones and 39,000 links.
Models and algorithms for the traffic assignment problem with link capacity constraints
2004
This paper explores the models as well as solution techniques for the link capacitated traffic assignment problem (CTAP) that is capable of offering more realistic traffic assignment results. CTAP can be approximated by the uncapacitated TAP using different dual/penalty strategies. Two important and distinctive approaches in this category are studied and implemented efficiently. The inner penalty function (IPF) approach establishes a barrier on the boundary of the feasible set so that constraints are not violated in the solution process, and the augmented Lagrangian multiplier (ALM) approach combines the exterior penalty with primal-dual and Lagrangian multipliers concepts. In both implementations, a gradient projection (GP) algorithm was adopted as the uniform subproblem solver for its excellent convergence property and reoptimization capability. Numerous numerical results demonstrated through efficient implementations of either the IPF or the ALM approach that CTAP is computationally tractable even for large-scale problems. Moreover, the relative efficiency of IPF and ALM was explored and their sensitivity to different algorithmic issues was investigated.
A dual scheme for traffic assignment problems
Optimization, 1997
A solution method based on Lagrangean dualization and subgradient optimization for the symmetric traffic equilibrium assignment problem is presented. Its interesting feature is that it includes a simple and computationally cheap procedure for calculating a sequence of feasible flow assignments which tend to equilibrium ones. The Lagrangean subproblem essentially consists of shortest route searches, and it is shown that one may compute an equilibrium flow by taking the simple average of all the shortest route flows obtained during the subgradient optimization scheme, provided that its step lengths are chosen according to a modified harmonic series. The new method is compared to the Frank-Wolfe algorithm and the method of successive averages on a medium-scale problem; its computational performance is at least comparable to that of the two other methods.
PROJECTION AND FUKUSHIMA'S GAP BASED METHODS FOR THE ASYMMETRIC TRAFFIC ASSIGNMENT PROBLEM
Traffic Assignment is the problem of assigning an Origin to Destination, OD matrix onto a network, under given conditions of using the links of the network, to determine the resulting traffic flows in the network. The underlying hypothesis is that travelers travel from origins to destinations in the network along the available routes connecting them. The characteristics of a traffic assignment procedure are determined by the hypothesis on how travelers use the routes. The main modelling hypothesis is based on the concept of user equilibrium which assumes that travelers try to minimize their individual travel times, that is, travelers chose the routes that they perceive as the shortest under the prevailing traffic conditions. The translation of these modelling hypotheses in terms of a mathematical model leads in the general case to a formulation in terms of a system of variational inequalities that has an equivalent convex optimization model when volume-delay functions are separable. However, the separability assumptions on the volume delay functions may lead quite frequently to modelling inaccuracies due to the over simplifications that they represent when dealing with generalized cost in complex multiclass-multimode planning models, or accounting for priorities at intersections, then the problems become asymmetric in terms of the Jacobian of the cost functions and the associated system of variational inequalities must be solved. Projection and Gap Function methods are among the most computationally efficient algorithms to solve the models. This paper explores a combination of a variant of Fukushima's projection algorithm and gap Functions. The new algorithm is computationally tested for several large networks and the computational results are presented and discussed.