Traffic Assignment

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.

... established. Zeleny (8) and Steuer (9) provide a thorough introduction to the theory of multiple-criteria decision making. ... decisions. List and Mirchandani (12) have done multiple-objective routing and siting for hazardous materials and waste. Turnquist ...

This paper describes a two-stage equilibrium travel demand model. The unique feature of this model is that it takes time-of-day traffic counts instead of land use and demographic data as inputs to derive spatial and temporal travel demand patterns. The first stage of the model is a trip matrix estimator based on traffic count; the second stage is an elastic-demand network flow estimator, which recognizes latent demand shifts while performing mode split, time-of-day split, and traffic assignment in a multilevel equilibration. The main purpose of this paper is to describe model development, algorithm design, and software implementation experiences. An example application illustrates how the model is used to evaluate multiclass, multimode, and multiperiod network flow patterns for sketch planning purposes.

The recent literature observes that the development of advanced algorithms for the traffic assignment problem (TAP) heavily relies on the proper use of some specific topological structures. This paper focuses on discussing a particular topological structure named paired alternative segment (PAS), which consists of two path segments sharing the same starting and ending nodes but no other common nodes. We first present two alternative conditions that establish an equivalency relationship between user equilibrium (UE) flows and PAS structures. Starting from the traffic assignment method by paired alternative segments (TAPAS), we then examine the utilization of PASs for TAP and explore some algorithmic and implementation issues, which leads to the birth of an improved TAPAS procedure (termed iTAPAS in this paper). Compared to the original TAPAS, iTAPAS enhances the algorithmic efficiency in two aspects: (1) a more effective PAS identification method is used; (2) each PAS is set as being associated with only one origin in the UE-finding process. Some analytical results based on the new PAS identification method are presented to justify the convergence and efficiency of iTAPAS. A simplified post-process procedure is also presented to achieve the proportionality for iTAPAS. Numerical results obtained from applying the new and original algorithms for several large networks reveal that iTAPAS is nearly two times faster than TAPAS in achieving highly precise link flow solutions while it is practically identical to TAPAS in finding stable path flow solutions that meet consistency and proportionality.

The aim of this paper is to explore a new approach to obtain better traffic demand (Origin-Destination, OD matrices) for dense urban networks using traffic simulation data. From reviewing existing methods, from static to dynamic OD matrix evaluation, possible deficiencies in the approach could be identified. To improve the global process of traffic demand estimation, this paper is focusing on a new methodology to determine dynamic OD matrices for urban areas characterized by complex route choice situation and high level of traffic controls. An iterative bi- level approach will be used to perform the OD estimation. The Lower Level (traffic assignment) problem will determine, dynamically, the utilization of the network by vehicles using heuristic data from mesoscopic traffic simulator particularly adapted for urban context. The Upper Level (matrix adjustment) problem will proceed to an OD estimation using optimization least square techniques. In this way, a full dynamic and continuous...

This paper presents an extensive analytical and numerical investigation on a class of origin-based algorithms for the user equilibrium-based traffic assignment problem. A total of nine known algorithms in this class are first clustered into four algorithmic structures, based on their structural differences and similarities in algorithm design. We further conduct a complexity analysis on these different algorithmic structures by calculating the frequency of executing node and link operations, which provides a simple analytical way to estimate their per-iteration computational costs. To deliver a comprehensive and fair comparison on their convergence performance, all these nine algorithms are then implemented on the same programming platform and run to solve a few representative large-scale traffic networks with different sizes and congestion levels. A close look on the convergence performance statistics further justifies the consistency of the complexity analysis and numerical evaluation results on the computational efficiency of these algorithms. Discussions on the degeneration of algorithm convergence efficiency with respect to network size and congestion level provide useful insights for the potential improvement of current origin-based algorithms or the proposition of new algorithms.

This paper formulates two dynamic network traffic assignment models in which O-D desires for the planning horizon are assumed known a priori: the system optimal (SO) and the user equilibrium (UE) time-dependent traffic assignment formulations. Solution algorithms developed and implemented for these models incorporate a traffic simulation model within an overall iterative search framework. Experiments conducted on a test network provide the basis for a comparative analysis of system performance under the SO and UE models.

Abstract We present a method for estimating intra-metropolitan freight flows on a highway network. The work is part of a larger project aimed at developing an automated, integrated system for freight flow analysis and planning. To overcome the limitations of current ...

It is notoriously known that range anxiety is one of the major barriers that hinder a wide adoption of plug-in electric vehicles, especially battery electric vehicles.  Recent studies suggested that if the caused driving range limit makes any impact on travel behaviors, it more likely occurs on the tour or trip chain level rather than the trip level.  To properly assess its impacts on travel choices and network congestion, this research is devoted to studying a new network equilibrium problem that implies activity location and travel path choices on the trip chain level subject to stochastic driving ranges.  Convex optimization and variational inequality models are respectively constructed for characterizing the equilibrium conditions under both discretely and continuously distributed driving ranges.  For deriving the equilibrium flow solutions defined by these different problem cases, we suggested different adaptations of a well-known path-based algorithm for the prime traffic assignment problem—the projected gradient method.  While the problem instance with a discrete number of driving ranges can be simply treated as a multi-class version extended from its deterministic counterpart, the one with continuous driving ranges poses a much more complicated situation.  To overcome this arising modeling and algorithmic difficulty, we introduce new variables with reference to path lengths, namely, path-referred travel subdemand rate and traffic subflow rate, by which the demand and flow rates as well as their corresponding feasible path sets are then dynamically classified in the solution process.  An illustrative example with various types and forms of driving range distributions demonstrates the applicability of the proposed modeling and solution methods and various impacts of the heterogeneity of range anxiety on network flows and computational costs.  The numerical analysis results from this example show that stochastic driving ranges shape network flows in a different way from deterministic or no driving ranges and the projected gradient procedure based on dynamically classified subdemand and subflow rates is generally preferable for both the discrete and continuous driving range cases.

... Secondly, many problems of practical interest are non-monotone, due to interactions at uncontrolled intersections, responsive signals, or mixed-mode interactions (see Watling, 1996, for examples). In such cases, multiple equilibria may exist, some of which may be unstable (ie ...

A joint optimization problem for solving area traffic control and network flow is investigated. A bilevel programming is used to formulate this joint optimization problem where the network flow following Wardrop's principles can be obtained by solving traffic assignment problems. In ...

To support the evaluation of dynamic road pricing strategies in a network context, this study develops a bi-criterion dynamic user equilibrium (BDUE) model, which aims to capture users' path choices in response to time-varying toll charges, and hence explicitly considers heterogeneous users with different value of time (VOT) preferences in the underlying path choice decision framework. The VOT is represented as a continuously distributed random variable across the population of trips, and an infinite dimensional variational inequality ...