An equilibrium algorithm for the spatial aggregation problem of traffic assignment

Present traffic assignment methods require that all possible origins and destinations of trips taking place within a study area be represented as if they were taking place to and from a small set of points or centroids. Each centroid is supposed to represent the location of all trip-ends within a given zone, and this necessarily misrepresents points located at the edges of the zone.In order to alleviate this problem (which we refer to as the spatial aggregation problem) one could use smaller zones and more centroids, but existing traffic assignment algorithms cannot efficiently handle many centroids.This paper introduces an algorithm procedure which is designed to handle a substantially larger number of centroids. In the paper that follows, the technique is further developed to take into account a continuous distribution of population.     

General stochastic user equilibrium traffic assignment problem with link capacity constraints

This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path‐specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.     

On the dual approach to the traffic assignment problem

This paper attempts to explore the possibility of solving the traffic assignment problem with elastic demands by way of its dual problem. It is shown that the dual problem can be formulated as a nonsmooth convex optimization problem of which the objective function values and subgradients are conveniently calculated by solving shortest path problems associated with the transportation network. A subgradient algorithm to solve the dual problem is presented and limited computational experience is reported. The computational results are encouraging enough to demonstrate the effectiveness of the proposed approach.     

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.     

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.     

More paradoxes in the equilibrium assignment problem

The sensitivity of travel costs to changes in input flows in the Wardrop equilibrium problem is studied. Examples are given showing that both origin to destination and global travel costs may decrease as a result of an increase in input flows. Other examples show that, in the two-mode equilibrium assignment problem transit origin to destination travel costs may decrease as a result of an increase in automobile input flows.     

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.     

A modified Frank-Wolfe algorithm for solving the traffic assignment problem

This paper presents a very simple modification of the Frank-Wolfe algorithm for the solution of the traffic assignment problem. It is shown that the modified algorithm can be implemented without much increase in computational effort over the original one. Convergence of the algorithm is proved and computational results are reported to demonstrate the validity of the modification.     

Properties of a traffic control policy which ensure the existence of a traffic equilibrium consistent with the policy

We consider a network with interactions and capacity constraints at each junction. We give conditions on the interactions and constraints which, if satisfied at each separate junction, ensure that any feasible assignment problem has an equilibrium solution. Two illustrative examples are provided; the first arises naturally and does not satisfy our conditions, while the second does satisfy our conditions but is somewhat unnatural.     

A cell-based Merchant-Nemhauser model for the system optimum dynamic traffic assignment problem

A cell-based variant of the Merchant-Nemhauser (M-N) model is proposed for the system optimum (SO) dynamic traffic assignment (DTA) problem. Once linearized and augmented with additional constraints to capture cross-cell interactions, the model becomes a linear program that embeds a relaxed cell transmission model (CTM) to propagate traffic. As a result, we show that CTM-type traffic dynamics can be derived from the original M-N model, when the exit-flow function is properly selected and discretized. The proposed cell-based M-N model has a simple constraint structure and cell network representation because all intersections and cells are treated uniformly. Path marginal costs are defined using a recursive formula that involves a subset of multipliers from the linear program. This definition is then employed to interpret the necessary condition, which is a dynamic extension of the Wardrop’s second principle. An algorithm is presented to solve the flow holding back problem that is known to exist in many discrete SO-DTA models. A numerical experiment is conducted to verify the proposed model and algorithm.     

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.     

The existence, uniqueness and computation of an arc-based dynamic network user equilibrium formulation

In this paper, a dynamic user equilibrium traffic assignment model with simultaneous departure time/route choices and elastic demands is formulated as an arc-based nonlinear complementarity problem on congested traffic networks. The four objectives of this paper are (1) to develop an arc-based formulation which obviates the use of path-specific variables, (2) to establish existence of a dynamic user equilibrium solution to the model using Brouwer's fixed-point theorem, (3) to show that the vectors of total arc inflows and associated minimum unit travel costs are unique by imposing strict monotonicity conditions on the arc travel cost and demand functions along with a smoothness condition on the equilibria, and (4) to develop a heuristic algorithm that requires neither a path enumeration nor a storage of path-specific flow and cost information. Computational results are presented for a simple test network with 4 arcs, 3 nodes, and 2 origin–destination pairs over the time interval of 120 periods.     

The existence, uniqueness and stability of traffic equilibria

The paper considers, in a simple case, the interaction between Webster's Method and drivers' route-choice decisions. In the example considered the overall network capacity is severely reduced by using Webster's Method. This shows that Webster's Method does not, in general, maximize the travel capacity of a road network. The analysis of this simple case suggests a signal-setting policy which does maximize the travel capacity of a general network.     

On the modeling and solution algorithm for the reverse logistics recycling flow equilibrium problem

This paper presents a study that characterizes, formulates, and solves the reverse logistic recycling flow equilibrium (RLRFE) problem. The RLRFE problem is concerned with the recycling channel in which recyclable collectors, processors, landfills, and demand markets form a multi-tiered network to process the recycled material flows from sources destined either for landfills or demand markets. Motivated by a government policy making or enterprise conglomerate recycling system design and operation needs, the RLRFE problem is elaborated from a system-optimal perspective using the variational inequality (VI) approach. For each origin–destination (OD) pair, the corresponding equilibrium conditions are established as a variation of the Wardrop second principle. In light of demand and cost function interactions, a nested diagonalization solution (ND) algorithm is proposed that gradually transforms the RLRFE problem into a traffic assignment model. To address multiple landfills in the recycling network and to understand how a variable-demand problem can be analyzed as a fixed-demand problem, we propose a supernetwork representation of the RLRFE problem. A numerical analysis on a test case illustrates the model formulation and the proposed algorithm.     

The corridor problem: Preliminary results on the no-toll equilibrium

Consider a traffic corridor that connects a continuum of residential locations to a point central business district, and that is subject to flow congestion. The population density function along the corridor is exogenous, and except for location vehicles are identical. All vehicles travel along the corridor from home to work in the morning rush hour, and have the same work start-time but may arrive early. The two components of costs are travel time costs and schedule delay (time early) costs. Determining equilibrium and optimum traffic flow patterns for this continuous model, and possible extensions, is termed “The Corridor Problem”. Equilibria must satisfy the trip-timing condition, that at each location no vehicle can experience a lower trip price by departing at a different time. This paper investigates the no-toll equilibrium of the basic Corridor Problem.     

A dynamic traffic assignment model for the assessment of moving bottlenecks

Moving bottlenecks in highway traffic are defined as a situation in which a slow-moving vehicle, be it a truck hauling heavy equipment or an oversized vehicle, or a long convey, disrupts the continuous flow of the general traffic. The effect of moving bottlenecks on traffic flow is an important factor in the evaluation of network performance. This effect, though, cannot be assessed properly by existing transportation tools, especially when the bottleneck travels relatively long distances in the network.This paper develops a dynamic traffic assignment (DTA) model that can evaluate the effects of moving bottlenecks on network performance in terms of both travel times and traveling paths. The model assumes that the characteristics of the moving bottleneck, such as traveling path, physical dimensions, and desired speed, are predefined and, therefore, suitable for planned conveys.The DTA model is based on a mesoscopic simulation network-loading procedure with unique features that allow assessing the special dynamic characteristics of a moving bottleneck. By permitting traffic density and speed to vary along a link, the simulation can capture the queue caused by the moving bottleneck while preserving the causality principles of traffic dynamics.     

Accessibility, entropy and the distribution and assignment of traffic revisited

An optimizing model which minimizes average generalised trip cost subject to constraints on the entropy was given in a previous paper. In this note the model is placed in a planning context.     

Convergence of the Frank-Wolfe method for certain bounded variable traffic assignment problems

In two recent papers published in Transportation Research, Daganzo presented a modification of the Frank-Wolfe algorithm to solve certain link capacitated traffic assignment problems satisfying certain conditions. In order to show convergence of the modified algorithm, the assumption was made that the integral of the volume delay formula for each link tends to infinity as the link flow approaches the link capacity. In this paper we give a Theorem which establishes convergence of the modified algorithm under much weaker conditions. This result is then used to show convergence if the objective function of the assignment model is sufficiently large (not necessarily infinite) when the link flows are at capacity. Thus the modified method is applicable to a broader class of assignment problems. Two numerical examples illustrate (a) when the method converges and when it does not, and (b) that our Theorem provides a weaker condition for convergence of the method.     

段里仁:紧急救援缓解"蝴蝶效应"

段里仁的书房就是资料室,四壁书架上摆着来自各个国家的书籍材料,"我每去一个国家,书架就会多一个资料夹",他笑着对记者说.