A methodology to estimate travel time using dynamic traffic assignment (DTA) under incident conditions

This paper presents results from a research case study that examined the distribution of travel time of origin–destination (OD) pairs on a transportation network under incident conditions. Using a transportation simulation dynamic traffic assignment (DTA) model, incident on a transportation network is executed under normal conditions, incident conditions without traveler information availability, and incident conditions assuming that users had perfect knowledge of the incident conditions and could select paths to avoid the incident location. The results suggest that incidents have a different impact on different OD pairs. The results confirm that an effective traveler information system has the potential to ease the impacts of incident conditions network wide. Yet it is also important to note that the use of information may detriment some OD pairs while benefiting other OD pairs. The methodology demonstrated in this paper provides insights into the usefulness of embedding a fully calibrated DTA model into the analysis tools of a traffic management and information center.     

A link-node complementarity model and solution algorithm for dynamic user equilibria with exact flow propagations

In this paper, we propose a link-node complementarity model for the basic deterministic dynamic user equilibrium (DUE) problem with single-user-class and fixed demands. The model complements link-path formulations that have been widely studied for dynamic user equilibria. Under various dynamic network constraints, especially the exact flow propagation constraints, we show that the continuous-time dynamic user equilibrium problem can be formulated as an infinite dimensional mixed complementarity model. The continuous-time model can be further discretized as a finite dimensional non-linear complementarity problem (NCP). The proposed discrete-time model captures the exact flow propagation constraints that were usually approximated in previous studies. By associating link inflow at the beginning of a time interval to travel times at the end of the interval, the resulting discrete-time model is predictive rather than reactive. The solution existence and compactness condition for the proposed model is established under mild assumptions. The model is solved by an iterative algorithm with a relaxed NCP solved at each iteration. Numerical examples are provided to illustrate the proposed model and solution approach. We particularly show why predictive DUE is preferable to reactive DUE from an algorithmic perspective.     

A distributed origin–destination demand estimation approach for real-time traffic network management

Abstract

This paper describes a distributed recursive heuristic approach for the origin–destination demand estimation problem for real-time traffic network management applications. The distributed nature of the heuristic enables its parallelization and hence reduces significantly its processing time. Furthermore, the heuristic reduces dependency on historical data that are typically used to map the observed link flows to their corresponding origin–destination pairs. In addition, the heuristic allows the incorporation of any available partial information on the demand distribution in the study area to improve the overall estimation accuracy. The heuristic is implemented following a hierarchal multi-threading mechanism. Dividing the study area into a set of subareas, the demand of every two adjacent subareas is merged in a separate thread. The merging operations continue until the demand for the entire study area is estimated. Experiments are conducted to examine the performance of the heuristic using hypothetical and real networks. The obtained results illustrate that the heuristic can achieve reasonable demand estimation accuracy while maintaining superiority in terms of processing time.     

The treatment of uncertainty in the dynamic origin–destination estimation problem using a fuzzy approach

Regardless of existing types of transportation and traffic model and their applications, the essential input to these models is travel demand, which is usually described using origin–destination (OD) matrices. Due to the high cost and time required for the direct development of such matrices, they are sometimes estimated indirectly from traffic measurements recorded from the transportation network. Based on an assumed demand profile, OD estimation problems can be categorized into static or dynamic groups. Dynamic OD demand provides valuable information on the within-day fluctuation of traffic, which can be employed to analyse congestion dissipation. In addition, OD estimates are essential inputs to dynamic traffic assignment (DTA) models. This study presents a fuzzy approach to dynamic OD estimation problems. The problems are approached using a two-level model in which demand is estimated in the upper level and the lower level performs DTA via traffic simulation. Using fuzzy rules and the fuzzy C-Mean clustering approach, the proposed method treats uncertainty in historical OD demand and observed link counts. The approach employs expert knowledge to model fitted link counts and to set boundaries for the optimization problem by defining functions in the fuzzification process. The same operation is performed on the simulation outputs, and the entire process enables different types of optimization algorithm to be employed. The Box-complex method is utilized as an optimization algorithm in the implementation of the approach. Empirical case studies are performed on two networks to evaluate the validity and accuracy of the approach. The study results for a synthetic network and a real network demonstrate the robust performance of the proposed method even when using low-quality historical demand data.     

Dynamic user equilibrium with side constraints for a traffic network: Theoretical development and numerical solution algorithm

This paper investigates a traffic volume control scheme for a dynamic traffic network model which aims to ensure that traffic volumes on specified links do not exceed preferred levels. The problem is formulated as a dynamic user equilibrium problem with side constraints (DUE-SC) in which the side constraints represent the restrictions on the traffic volumes. Travelers choose their departure times and routes to minimize their generalized travel costs, which include early/late arrival penalties. An infinite-dimensional variational inequality (VI) is formulated to model the DUE-SC. Based on this VI formulation, we establish an existence result for the DUE-SC by showing that the VI admits at least one solution. To analyze the necessary condition for the DUE-SC, we restate the VI as an equivalent optimal control problem. The Lagrange multipliers associated with the side constraints as derived from the optimality condition of the DUE-SC provide the traffic volume control scheme. The control scheme can be interpreted as additional travel delays (either tolls or access delays) imposed upon drivers for using the controlled links. This additional delay term derived from the Lagrange multiplier is compared with its counterpart in a static user equilibrium assignment model. If the side constraint is chosen as the storage capacity of a link, the additional delay can be viewed as the effort needed to prevent the link from spillback. Under this circumstance, it is found that the flow is incompressible when the link traffic volume is equal to its storage capacity. An algorithm based on Euler’s discretization scheme and nonlinear programming is proposed to solve the DUE-SC. Numerical examples are presented to illustrate the mechanism of the proposed traffic volume control scheme.     

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.     

Implementing first-in–first-out in the cell transmission model for networks

In traffic assignment models with time-varying flows (dynamic network loading or dynamic traffic assignment), overtaking behaviour is normally not included in the model and, in that case, it is important that the model at least approximates first-in–first-out (FIFO), to prevent deviations from FIFO that are arbitrary or unrealistic or not physically possible. For the cell transmission model (CTM) it has recently been shown that the usual recommended method for preserving FIFO will ensure FIFO for each cell taken separately but does not fully ensure FIFO in the transition between cells and hence does not fully ensure FIFO for sequences of cells or for links or for routes. As a result, deviations from FIFO can easily occur and cumulate along the links or routes. In view of that, we define and analyse three different levels of satisfaction or approximation of FIFO, together with corresponding methods for achieving them. Two of these are existing methods and one is new. We develop, analyse and compare the three methods and the extent to which each of them adheres to FIFO for sequences of cells and links or routes. Also, for two of the methods we present a more detailed algorithm for applying them within the CTM. The paper is concerned with how to implement FIFO in the CTM and not with testing for FIFO or measuring deviations from FIFO.     

Route swapping in dynamic traffic networks

A dynamic traffic assignment (DTA) model typically consists of a traffic performance model and a route choice model. The traffic performance model describes how traffic propagates (over time) along routes connecting origin-destination (OD) pairs, examples being the cell transmission model, the vertical queueing model and the travel time model. This is implemented in a dynamic network loading (DNL) algorithm, which uses the given route inflows to compute the link inflows (and hence link costs), which are then used to compute the route travel times (and hence route costs). A route swap process specifies the route inflows for tomorrow (at the next iteration) based on the route inflows today (at the current iteration). A dynamic user equilibrium (DUE), where each traveller on the network cannot reduce his or her cost of travel by switching to another route, can be sought by iterating between the DNL algorithm and the route swap process. The route swap process itself takes up very little computational time (although route set generation can be very computationally intensive for large networks). However, the choice of route swap process dramatically affects convergence and the speed of convergence. The paper details several route swap processes and considers whether they lead to a convergent system, assuming that the route cost vector is a monotone function of the route inflow vector.     

Algorithms for logit-based stochastic user equilibrium assignment

The paper proposes an efficient algorithm for determining the stochastic user equilibrium solution for logit-based loading. The commonly used Method of Successive Averages typically has a very slow convergence rate. The new algorithm described here uses Williams’ result [ Williams, (1977) On the formation of travel demand models and economic evaluation measures of user benefit. Environment and Planning 9A(3), 285–344] which enables the expected value of the perceived travel costs S_rs to be readily calculated for any flow vector x. This enables the value of the Sheffi and Powell, 1982 objective function [Sheffi, Y. and Powell, W. B. (1982) An algorithm for the equilibrium assignment problem with random link times. Networks 12(2), 191–207], and its gradient in any specified search direction, to be calculated. It is then shown how, at each iteration, an optimal step length along the search direction can be easily estimated, rather than using the pre-set step lengths, thus giving much faster convergence. The basic algorithm uses the standard search direction (towards the auxiliary solution). In addition the performance of two further versions of the algorithm are investigated, both of which use an optimal step length but alternative search directions, based on the Davidon–Fletcher–Powell function minimisation method. The first is an unconstrained and the second a constrained version. Comparisons are made of all three versions of the algorithm, using a number of test networks ranging from a simple three-link network to one with almost 3000 links. It is found that for all but the smallest network the version using the standard search direction gives the fastest rate of convergence. Extensions to allow for multiple user classes and elastic demand are also possible.