User-optimal Traffic Assignment Research Articles

Efficient Computation of User Optimal Traffic Assignment via Second-Order Cone and Linear Programming Techniques

Static traffic assignment aims to disclose the spatial distribution of vehicular flow over a transportation network subject to given traffic demands, and plays an essential role in transportation engineering. User-optimal pattern adheres the individual rationality of motorists, in which everyone chooses a route that minimizes his own travel cost, while considering congestion effects influenced by the aggregated movement of vehicles. User optimal traffic assignment, which is also known as the user equilibrium, entails solving an optimization problem with a strictly convex objective function and linear constraints. However, the performances of general-purpose solvers are quite disappointing. This paper proposes two highly efficient computation models for the user equilibrium problem. The first one exploits the second-order cone reformulation of a convex power function, resulting in a second-order cone program, and no approximation is incurred. The second one approximates the convex objective function using a piece-wise linear function, and comes down to a linear program. An adaptive path generation oracle is devised in order to circumvent path enumeration in problem setup. Case studies demonstrate that the proposed method can deal with large-scale transportation systems, and outperforms the most popular iterative algorithm in the literature.

A Multiclass User Equilibrium Model Considering Overtaking Across Classes

In this paper, we deal with the traffic assignment problem solving a multiclass equilibrium problem. In particular, we focus our analysis on when the overtaking of vehicles is permitted. A new family of link travel time functions is presented, which allows us to reproduce the same asymptotic congestion behavior of several overtaking classes to mimic the fact that high congestion impedes overtaking and that all classes must have identical link travel times. This family is generated based on local linear convex combinations of travel time Bureau of Public Roads (BPR) functions. A nonlinear complementary problem (NCP), which does not require path enumeration, is used to solve the user-optimal traffic assignment. An example is used to show the proposed methods and techniques. In particular, a case in which cars and motorcycles share the network is analyzed under congested and uncongested conditions.

A computational model for the probit‐based dynamic stochastic user optimal traffic assignment problem

AbstractThis paper focuses on computational model development for the probit‐based dynamic stochastic user optimal (P‐DSUO) traffic assignment problem. We first examine a general fixed‐point formulation for the P‐DSUO traffic assignment problem, and subsequently propose a computational model that can find an approximated solution of the interest problem. The computational model includes four components: a strategy to determine a set of the prevailing routes between each origin–destination pair, a method to estimate the covariance of perceived travel time for any two prevailing routes, a cell transmission model‐based traffic performance model to calculate the actual route travel time used by the probit‐based dynamic stochastic network loading procedure, and an iterative solution algorithm solving the customized fixed‐point model. The Ishikawa algorithm is proposed to solve the computational model. A comparison study is carried out to investigate the efficiency and accuracy of the proposed algorithm with the method of successive averages. Two numerical examples are used to assess the computational model and the algorithm proposed. Results show that Ishikawa algorithm has better accuracy for smaller network despite requiring longer computational time. Nevertheless, it could not converge for larger network. Copyright © 2010 John Wiley & Sons, Ltd.

Formulation and Estimation of Combined Network Equilibrium Models with Applications to Stockholm

Combined network equilibrium models of trip distribution, modal split, and route choice are formulated and estimated for the Stockholm region. These models take into account the feedback effects among three stages of the classical four-step model. A simultaneous structure of the mode and destination choices is studied together with nested combined models reflecting conditional choice probabilities. In the traditional combined model, mode choice is assumed conditional on destination choice. The reverse combined model, in contrast, considers destination choice conditional on mode choice. User-optimal traffic assignment is integrated with these approaches to modeling travel demand in network equilibrium models. The three combined models are estimated using the full-information maximum likelihood technique implying that all preference parameters are estimated simultaneously. The models are estimated on medium-size travel and network data for the Stockholm region in 1986. The results suggest a rejection of the traditional nested model because of incorrect relative values of the estimated cost-sensitivity parameters. The reverse nested model is preferred, even if the overall goodness-of-fit is better for the traditional nested model. An application to a future scenario for the year 2020 is included.

Dynamic user optimal traffic assignment model for many to one travel demand

A freeway or expressway corridor where all vehicles travel to the same destination such as the city centre is considered in this article, similar to the morning commute problem. A continuous time optimal control model that deals with the dynamic user optimal assignment for multiple origins and single destination is proposed. The splitting rates of traffic flows at each network node are defined as the control variables in this model. The optimality conditions are proved to be equivalent to the dynamic user optimal principle or user equilibrium of instantaneous travel cost. In order not to solve the complicated two-point boundary-value problem with substantial computational times for obtaining the optimal control solution, a steady state-costate solution algorithm is developed that generates an approximate solution to the network optimal control problem. This algorithm exploits advantage of the embedded network structure of the problem and would be computationally efficient. A numerical example with two peak period traffic demands which was drawn from the road network problem between Hong Kong and several adjacent cities of inland China is used to demonstrate the performance of the proposed algorithm.

PREDICTIVE AND DYNAMIC USER OPTIMAL TRAFFIC ASSIGNMENT AS A TIME-DELAY OPTIMAL CONTROL PROBLEM

This paper presents a look at dynamic user optimal traffic assignment as a time-delay optimal control problem. The approach proposed here allows us to develop a model for solving the predictive and dynamic user optimal assignment problem which is capable for considering both time-delay effects in the dynamic of link traffic flow and the information providing process to travelers.

A New Class of Instantaneous Dynamic User-Optimal Traffic Assignment Models

The instantaneous dynamic user-optimal (DUO) traffic assignment problem is to determine vehicle flows on each link at each instant of time resulting from drivers using instantaneous minimal-time routes. Instantaneous route time is the travel time incurred if traffic conditions remain unchanged while driving along the route. In this paper, we introduce a different definition of an instantaneous DUO state. Using the optimal control theory approach, we formulate two new DUO traffic assignment models for a congested transportation network. These models include new formulations of the objective function and flow propagation constraints, and are dynamic generalizations of the static user-optimal model. The equivalence of the solutions of the two optimal control programs with DUO traffic flows is demonstrated by proving the equivalence of the first-order necessary conditions of the two programs with the instantaneous DUO conditions. Since these optimal control problems are convex programs with linear constraints, they have unique solutions. A numerical example is presented indicating that this class of models yields realistic results.

Dynamic user optimal traffic assignment on congested multidestination networks

An equivalent continuous time optimal control problem is formulated to predict the temporal evolution of traffic flow pattern on a congested multiple origin-destination network, corresponding to a dynamic generalization of Wardropian user equilibrium. Optimality conditions are derived using the Pontryagin minimum principle and given economic interpretations, which are generalizations of similar results previously reported for single-destination networks. Analyses of sufficient conditions for optimality and of singular controls are also given. Under the steady-state assumptions, the model is shown to be a proper dynamic extension of Beckmann's mathematical programming problem for a static user equilibrium traffic assignment.