Multi-commodity traffic assignment by continuum approximation of network flow with variable demand

Consider a city with several highly compact central business districts (CBD), and the commuters’ destinations from each of them are dispersed over the whole city. Since at a particular location inside the city the traffic movements from different CBDs share the same space and do not cancel out each other as in conventional fluid flow problems albeit travelling in different directions, the traffic flows from a CBD to the destinations over the city are considered as one commodity. The interaction of the traffic flows among different commodities is governed by a cost–flow relationship. The case of variable demand is considered. The primal formulation of the continuum equilibrium model is given and proved to satisfy the user optimal conditions, and the dual formulation of the problem and its complementary conditions are also discussed. A finite element method is then employed to solve the continuum problem. A numerical example is given to illustrate the effectiveness of the proposed method.     

A note on traffic assignment and signal timings in a signal-controlled road network

This paper discusses the problems of using signal timings in a signal-controlled road network to influence equilibrium flows in such a way that some network performance index, e.g. total travel time, is optimised, given that at equilibrium each driver is using a minimum-time route. By means of a simple example, we show that an intuitively acceptable approach explored in other articles does not work and may, in fact, lead to a decline in network performance rather than an improvement.     

Network representation,continuum approximations and a solution to the spatial aggregation problem of traffic assignment

This paper complements the preceding one, which showed how one could modify equilibrium traffic assignment algorithms for networks with many centroids. In this one it is shown how one can substitute centroids by zones with continuous population densities. The technique, which is mathematically guaranteed to approximate a flow pattern in accordance with Wardrop's user equilibrium criterion, requires some geometrical calculations which can be handled off-line. With the suggested approach, it is possible to represent the spatial distribution of trip ends more realistically and this allows traffic assignment models to capture the effects of short and intrazonal trips in a way previously impossible. The method is shown to be computationally feasible.     

An improved Dial's algorithm for logit-based traffic assignment within a directed acyclic network

Abstract

Dial's algorithm is one of the most effective and popular procedures for a logit-type stochastic traffic assignment, as it does not require path enumeration over a network. However, a fundamental problem associated with the algorithm is its simple definition of ‘efficient paths’, which sometimes produces unrealistic flow patterns. In this paper, an improved algorithm based on the route extension coefficient is proposed in order to circumvent this problem, in which ‘efficient paths’ simultaneously consider link travel cost and minimum travel cost. Path enumeration is still not required and a similar computing efficiency with the original algorithm is guaranteed. A limitation of the algorithm is that it can only be applied to a directed acyclic network because a topological sorting algorithm is used to decide the order of the sequential calculation. A numerical example based on the Beijing subway network illustrates the effectiveness of the proposed algorithm. It is found that it is able to exclude most unrealistic paths, but include all reasonable paths when compared with path enumeration and the original Dial's algorithm.     

A comparison of user-optimum versus system-optimum traffic assignment in transportation network design

In this report, we compare the computational efficiency and results of solving two alternative models for the problem of determining improvements to an urban road network. Using a 1462 link, 584 node test network of the north Dallas area, we compare a model which assumes user-optimum behavior of travelers with a model which assumes system-optimum flows. Both of these models allow improvements to the road network to take on any nonnegative value, rather than requiring discrete improvement values. Investment costs are modeled by functions with decreasing marginal costs. Unfortunately, the user-optimum model, which is much more realistic than the system-optimum one, normally cannot be solved optimally. However, the simpler system-optimum model can be optimally solved, provided that investment costs are approximated by linear functions. Thus, for this network design problem we compare an accurate representation which can be solved only approximately with an approximate representation which can be solved optimally. Our computational testing showed that the system-optimum model produces solutions as good as those from the user-optimum model, and thus seems justified when favored by other considerations, such as ease of coding, availability of “canned” programs, etc.     

On a link-based day-to-day traffic assignment model

In this paper, we perform a rigorous analysis on a link-based day-to-day traffic assignment model recently proposed in He et al. (2010). Several properties, including the invariance set and the constrained stability, of this dynamical process are established. An extension of the model to the asymmetric case is investigated and the stability result is also established under slightly more restrictive assumptions. Numerical experiments are conducted to demonstrate the findings.     

Traffic noise abatement: How different pavements, vehicle speeds and traffic densities affect annoyance levels

In this paper, annoyance ratings from traffic noise recorded on cobblestones, dense asphalt, and open asphalt rubber pavements are assessed with regard to car speeds and traffic densities. It was found that cobblestones pavements are the most annoying; also while open asphalt rubber pavement imposes less annoyance than dense asphalt it is not significantly different. Higher car speeds always lead to greater annoyance, as does higher traffic densities. LAeq and LAmax correlate well with annoyance, but loudness is the best predictor. Roughness and sharpness exhibit inconsistent interactions.     

Some developments in equilibrium traffic assignment

A network optimization problem is formulated which yields a probabilistic equilibrated traffic assignment incorporating congestion effects and which as a special case, reduces to a user optimized equilibrium solution. In the resulting model, path choice is determined by a logit formula in which path costs are functions of the assigned flows. The article also demonstrates the similarity between some fixed demand incremental methods of traffic assignment and the minimization problem associated with computing the user equilibrium assignment.     

Junction interactions and monotonicity in traffic assignment

We consider the traffic equilibrium problem when the travel demand is inelastic and stationary in time. Junction interactions, which abound in urban road networks, are permitted. We prove that the set of equilibria (solutions to the assignment problem) is convex when certain monotonicity and continuity conditions are statisfied at each junction.     

Dynamic system-optimal traffic assignment using a state space model

We propose a new mathematical formulation for the problem of optimal traffic assignment in dynamic networks with multiple origins and destinations. This problem is motivated by route guidance issues that arise in an Intelligent Vehicle-Highway Systems (IVHS) environment. We assume that the network is subject to known time-varying demands for travel between its origins and destinations during a given time horizon. The objective is to assign the vehicles to links over time so as to minimize the total travel time experienced by all the vehicles using the network. We model the traffic network over the time horizon as a discrete-time dynamical system. The system state at each time instant is defined in a way that, without loss of optimality, avoids complete microscopic detail by grouping vehicles into platoons irrespective of origin node and time of entry to network. Moreover, the formulation contains no explicit path enumeration. The state transition function can model link travel times by either impedance functions, link outflow functions, or by a combination of both. Two versions (with different boundary conditions) of the problem of optimal traffic assignment are studied in the context of this model. These optimization problems are optimal control problems for nonlinear discrete-time dynamical systems, and thus they are amenable to algorithmic solutions based on dynamic programming. The computational challenges associated with the exact solution of these problems are discussed and some heuristics are proposed.     

Multiple equilibria in a dynamic traffic network

This study provides an example in which the dynamic user equilibrium (DUE) assignment of a congested road network with bottlenecks is non-unique. In previous studies, the uniqueness of DUE assignments with the bottleneck model has been shown in limited cases such as single-origin and single-destination networks. Consequently, it is still an important issue whether or not uniqueness is a general property of DUE assignments. The present study describes a network in which multiple patterns of link travel time are found, thus providing a negative answer to this question. The network has a loopy structure with multiple bottlenecks and multiple origin-destination (OD) pairs. Given a certain demand pattern of departure times for vehicles leaving their origins, a non-convex set of equilibria with a non-unique pattern of link travel times is shown to exist.     

多方式多类型交通分配模型(MMA)在收费型公路网中的应用研究

在对收费型公路运营模式进行研究的基础上,利用交通规划软件建立了基于广义费用的交通流量分配模型即多方式多类型交通分配模型,通过对模型参数的科学标定和网络的合理设置,得到各类车型在特定网络上的流量分配、路段饱和率以及通行费用,并对此模型的应用效果进行分析,最终为区域高速公路网规划、路段交通量预测提供依据。     

The dual of the traffic assignment problem with elastic demands

This article is concerned with the dual of the traffic assignment problem, and of the combined generation, distribution, and assignment problem. The duals, and duality relations, for the arc-chain and node-arc formulations of the problem are derived using only the Kuhn-Tucker conditions for convex programs. This has the advantage of being more familiar to most readers than the conjugate function presentation which has been used elsewhere.     

A dynamic traffic assignment model for a continuum transportation system

A predictive continuum dynamic user-optimal (PDUO-C) model is formulated in this study to investigate the dynamic characteristics of traffic flow and the corresponding route-choice behavior of travelers within a region with a dense urban road network. The modeled region is arbitrary in shape with a single central business district (CBD) and travelers continuously distributed over the region. Within this region, the road network is represented as a continuum and travelers patronize a two-dimensional continuum transportation system to travel to the CBD. The PDUO-C model is solved by a promising solution algorithm that includes elements of the finite volume method (FVM), the finite element method (FEM), and the explicit total variation diminishing Runge-Kutta (TVD-RK) time-stepping method. A numerical example is given to demonstrate the utility of the proposed model and the effectiveness of the solution algorithm in solving this PDUO-C problem.     

Optimal traffic assignment to urban streets with air pollution consideration

Traffic assignment is usually determined solely on the basis of minimum travel time through the network. The present study on traffic assignment has taken into account not only traffic performance but also air quality over the street. A simple model of highway air pollution is developed by considering macroscopic material balance of polluted air mass over a segment of a highway that passes through an urban area, A new traffic assignment scheme has been developed based on the air pollution model. The optimal traffic assignment obtained by the new scheme is affected significantly by meteorological conditions.     

Eco-system optimal time-dependent flow assignment in a congested network

This research addresses the eco-system optimal dynamic traffic assignment (ESODTA) problem which aims to find system optimal eco-routing or green routing flows that minimize total vehicular emission in a congested network. We propose a generic agent-based ESODTA model and a simplified queueing model (SQM) that is able to clearly distinguish vehicles’ speed in free-flow and congested conditions for multi-scale emission analysis, and facilitates analyzing the relationship between link emission and delay. Based on the SQM, an expanded space-time network is constructed to formulate the ESODTA with constant bottleneck discharge capacities. The resulting integer linear model of the ESODTA is solved by a Lagrangian relaxation-based algorithm. For the simulation-based ESODTA, we present the column-generation-based heuristic, which requires link and path marginal emissions in the embedded time-dependent least-cost path algorithm and the gradient-projection-based descent direction method. We derive a formula of marginal emission which encompasses the marginal travel time as a special case, and develop an algorithm for evaluating path marginal emissions in a congested network. Numerical experiments are conducted to demonstrate that the proposed algorithm is able to effectively obtain coordinated route flows that minimize the system-wide vehicular emission for large-scale networks.     

The dynamics of traffic assignment and traffic control: A theoretical study

The paper considers traffic assignment, with traffic controls, in an increasingly dynamic way. First, a natural way of introducing the responsive policy, P_o, into steady state traffic assignment is presented. Then it is shown that natural stability results follow within a dynamical version of this static equilibrium model (still with a constant demand). We are able to obtain similar stability results when queues are explicitly allowed for, provided demand is constant. Finally we allow demand to vary with time; we consider the dynamic assignment problem with signal-settings now fixed. Here we assume that vehicles are very short and that deterministic queueing theory applies, and show that the time-dependent queueing delay at the bottleneck at the end of a link is a monotone function of the time-dependent input profile to the bottleneck. We have been unable to obtain results when dynamic demand and responsive signal control are combined.     

Simplical decomposition of the asymmetric traffic assignment problem

This paper presents a convergent simplicial decomposition algorithm for the variational inequality formulation of the asymmetric traffic assignment problem. It alternates between generating minimum path trees based on the cost function evaluated at the current iterate and the approximate solving of a master variational inequality subject to simple convexity constraints. Thus it generalizes the popular Frank-Wolfe method (where the master problem is a line search) to the asymmetric problem. Rules are given for dropping flow patterns which are not needed to express the current iterate as a convex combination of previous patterns. The results of some computational testing are reported.