Observed Link Flows Research Articles

Sequential experimental approach for congestion pricing with multiple vehicle types and multiple time periods

This paper develops a sequential experimental approach for the optimal congestion pricing problem on a general transportation network with multiple vehicle types and multiple time periods. The approach explicitly considers the interaction among different types of vehicular flow and the interdependence of demand among various origin–destination (O–D) pairs and in different time periods. Toll charge on each link in each period is differentiated across vehicle types on the basis of their observable differences to reflect their different congestion externalities. The evolutionary pricing scheme updates link tolls from only observed link flows without requiring explicit forms of demand functions. Given a trial of toll pattern, the revealed link flows can be observed easily; then a new set of tolls can be determined based on the observed flow volume and sequentially used for next trial. The detailed implementation procedure is examined with both theoretical analyses and numerical experiments.

Estimation of freight transportation

Transportation is an important human activity which has many economic, social and other effects. In particular, freight transportation is economically very important for any country, and includes transporting a wide variety of goods ranging from raw materials to finished goods. These freights must be transported to the market efficiently and safely at reasonable cost. In addition, the external effects caused by freight transportation must be at an environmentally and socially acceptable level. To achieve these goals, an effective freight transportation planning model is required for forecasting the future trends of freight transportation. This paper presents a framework which includes empirical modelling methods to estimate the freight transportation between defined zones. The gravity method was used to estimate origin and destination matrices by using observed link flows, gross domestic product by provinces and interzonal distances. The coefficients of the gravity method were estimated by using advanced statistical techniques and regression analyses. The final freight transportation matrix was calibrated with the link flows data by using iterative techniques. The suggested framework was successfully applied to a data set provided by the Turkish General Directorate of Highways.

A Bayesian Approach to Traffic Estimation in Stochastic User Equilibrium Networks

This study proposes a statistical model to estimate route traffic flows in congested networks. In the study, it is assumed that route traffic flows conform to the stochastic user equilibrium (SUE) principle while being treated as random variables in order to exploit the stochastic nature of traffic. The proposed model formulates the distribution of these random variables as the conditional distribution of route flows and origin–destination (O-D) travel demand, given the observed link flows and the SUE principle. Here, the SUE principle is accounted for through the likelihood of user behaviours rather than by using a bi-level formulation. In this study, the Bayesian theorem is applied to derive the probability density function (PDF) of the conditional distribution. Based on the PDF, characteristics such as the means and variances of route/link traffic flows are estimated using a blocked Metropolis–Hastings (M–H) algorithm. To facilitate the use of prior knowledge, a hierarchical form is designed to provide a straightforward way to integrate prior knowledge into the traffic estimation model. The performance of the proposed method is tested on the Sioux–Falls network through a series of numerical examples.

Bayesian inference for day-to-day dynamic traffic models

There is significant current interest in the development of models to describe the day-to-day evolution of traffic flows over a network. We consider the problem of statistical inference for such models based on daily observations of traffic counts on a subset of network links. Like other inference problems for network-based models, the critical difficulty lies in the underdetermined nature of the linear system of equations that relates link flows to the latent path flows. In particular, Bayesian inference implemented using Markov chain Monte Carlo methods requires that we sample from the set of route flows consistent with the observed link flows, but enumeration of this set is usually computationally infeasible.We show how two existing conditional route flow samplers can be adapted and extended for use with day-to-day dynamic traffic. The first sampler employs an iterative route-by-route acceptance–rejection algorithm for path flows, while the second employs a simple Markov model for traveller behaviour to generate candidate entire route flow patterns when the network has a tree structure. We illustrate the application of these methods for estimation of parameters that describe traveller behaviour based on daily link count data alone.

Bilevel Generalized Least Squares Estimation of Dynamic Origin–Destination Matrix for Urban Network with Probe Vehicle Data

Methods of estimating dynamic origin–destination (O-D) matrices for urban networks from probe vehicle data are explored. A speed–density function is derived and fitted for different types of roads with the use of the maximum likelihood method. Both a Bayesian method that carefully incorporates prior information and an ordinary method are used to estimate link flows from probe vehicle speed. A dynamic traffic assignment–based bilevel generalized least squares (GLS) estimator considering the distance between the estimated and target O-D matrices as well as the distance between the calculated and observed link flows is formulated to estimate dynamic O-D matrices from estimated link flows. In the iterative solution procedure, the upper level is solved with the extended Bell algorithm, and the microscopic dynamic traffic assignment system VISSIM is applied to produce the assignment matrix in the lower level. A medium-sized signalized network in Tokyo is modeled in a case study in which Bayesian and ordinary methods are compared both in link flow estimation and O-D matrix estimation. Further, the bilevel GLS estimator and bilevel ordinary least squares estimator are implemented and then compared in O-D estimation. The results validate the proposed bilevel GLS estimator.

Sensitivity Analysis of an Evolutionary-Based Time-Dependent Origin/Destination Estimation Framework

This paper presents sensitivity analysis results for a distributed evolutionary implementation of the estimation of time-dependent origin-destination (TDOD) matrices. The system uses a noniterative origin-destination (OD) estimation process, which attempts to minimize the discrepancy between observed link flow counts and assigned counts. At the same time, the system anchors the search process to the vicinity of an a priori OD matrix to maintain travel patterns and OD structure. The sensitivity analysis examines various factors that are expected to affect the performance of the evolutionary-based TDOD estimation method. The factors examined are congestion levels, network size, size of the search space, and degree of precision of the a priori matrix. Simulation results for the waterfront network in Toronto, ON, Canada, show that the algorithm is robust in terms of replicating observed vehicle counts and the closeness to the real demand. The use of distributed evolutionary algorithm is also shown to provide good results for a large network and within fast computing speeds. However, the quality of the estimated OD relative to the true OD is shown to deteriorate if a totally random a priori matrix is used as a starting point, which has no structural resemblance to the prevailing OD patterns in the network. In addition, the quality of the estimated OD matrix was found to deteriorate as congestion levels and the network size increased. It is notable that, in all cases, the estimated OD matrix resulted in better matching flows.

Network Equilibrium Model with Dogit and Nested Logit Structures

This paper develops a combined equilibrium model for the simultaneous prediction of trip distribution, mode choice, and trip assignment. Trip distribution is formulated as a dogit model to take into account travel behavior of compulsory (work) and discretionary (nonwork) trips. Mode choice is given by a two-level nested logit model to avoid the independence from irrelevant alternatives restriction. Trip assignment is based on Wardrop's user-equilibrium principle. The log sums of the mode choice model were computed and fed back into the trip distribution step. Under this iterative process, destination choice of discretionary trips would respond to changing travel cost conditions occurring in mode choice and trip assignment steps, whereas destination choice of compulsory trips would remain fixed in the study time period. The proposed combined trip distribution, mode choice, and trip assignment (CDMA) model was reformulated as an equivalent convex programming problem with linear constraints and applied empirically to a county-level network in New Jersey. The results indicate that the CDMA model is better than the commonly used logit combined model in reproducing the observed link flows, origin–destination (O-D) trip flows, and O-D trip flows by mode.

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

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.

Method for estimating population OD matrix based on probe vehicles

Origin-Destination (OD) has always been a concern in obtaining accurate link traffic volume, because it is one of the major inputs to the travel demand forecasting procedure. This paper examines a new approach for estimating static OD using Radio Frequency Identification (RFID) sensors embedded in probe vehicles. More specifically, sample OD based on RFID and route information were used for deriving static OD set. This type of method allows for relative ease in data collection for large scale areas. However, data collected by probe vehicles do not represent the entire traffic on the links, because the number of probe vehicles is limited in practice. Thus, the traffic data collected from probe vehicles are a partial OD matrix, although vehicles can be tracked from origin to destination. In this regard, a sample OD can be expanded to a population OD matrix through sampling ratio. Sampling ratios are then specified to minimize the difference between assigned and observed link flows. The proposed algorithm has performed successfully with an example network and an actual site in Jeju, Korea.

Road pricing for congestion control with unknown demand and cost functions

It is widely recognized that precise estimation of road tolls for various pricing schemes requires a few pieces of information such as origin–destination demand functions, link travel time functions and users’ valuations of travel time savings, which are, however, not all readily available in practice. To circumvent this difficulty, we develop a convergent trial-and-error implementation method for a particular pricing scheme for effective congestion control when both the link travel time functions and demand functions are unknown. The congestion control problem of interest is also known as the traffic restraint and road pricing problem, which aims at finding a set of effective link toll patterns to reduce link flows to below a desirable target level. For the generalized traffic equilibrium problem formulated as variational inequalities, we propose an iterative two-stage approach with a self-adaptive step size to update the link toll pattern based on the observed link flows and given flow restraint levels. Link travel time and demand functions and users’ value of time are not needed. The convergence of the iterative toll adjustment algorithm is established theoretically and demonstrated on a set of numerical examples.

Limits and perspectives of effective O–D matrix correction using traffic counts

Correction of the O–D matrix from traffic counts is a classical procedure usually adopted in transport engineering by practitioners for improving the overall reliability of transport models. Recently, Papola and Marzano [Papola, A., Marzano, V., 2006. How can we trust in the O–D matrix correction procedure using traffic counts? In: Proceedings of the 2006 ETC Conference, Strasbourg] showed through laboratory experiments that this procedure is generally unable to provide for effective correction of the O–D matrix. From a theoretical standpoint, this result can be justified by the lower number of (stochastic) equations (independent observed link flows) with respect to the unknowns (O–D flows). This paper first confirms that this represents the main reason for the failure of this procedure, showing that satisfactory correction is generally obtained when the number of equations is greater than the number of unknowns. Then, since this circumstance does not occur in practice, where the number of O–D pairs usually far exceeds the number of link counts, we explore alternative assumptions and contexts, allowing for a proper balance between unknowns and equations. This can be achieved by moving to within-day dynamic contexts, where a much larger number of equations are generally available. In order to bound the corresponding increase in the number of unknowns, specific reasonable hypotheses on O–D flow variation across time slices must be introduced. In this respect, we analyze the effectiveness of the O–D matrix correction procedure in the usually adopted linear hypothesis on the dynamic process evolution of O–D flows and under the assumption of constant distribution shares. In the second case it is shown that satisfactory corrections can be performed using a small number of time slices of up to 3 min in length, leading to a time horizon in which the hypothesis of constant distribution shares can be regarded as trustworthy and realistic.

Effectiveness of Origin-Destination Matrix Correction Procedure Using Traffic Counts

The estimation and correction of the origin-destination (O-D) matrix from traffic counts is a classical procedure usually adopted in transport engineering by practitioners to improve the overall reliability of transport models. Recently, Papola and Marzano showed through laboratory experiments that this procedure is generally not able to provide an effective correction of the O-D matrix. This result can be justified from a theoretical standpoint because of the lower number of stochastic equations (independent observed link flows) with respect to the unknowns (O-D flows). The current study confirms, first, that this circumstance represents the main reason for failure of the procedure by showing that good correction is generally obtained when the number of equations is greater than the number of unknowns. Then, since this circumstance does not occur in practice, in which the number of O-D pairs is usually much greater than the number of link counts, the study explores alternative assumptions and contexts that allow for a proper balance between unknowns and equations. In more detail, this balance can be achieved by moving to within-day dynamic contexts, in which a much larger number of equations is generally available. Obviously, to bound the corresponding increase in the number of unknowns, specific reasonable hypotheses in O-D flow variation across time slices must be introduced. In that respect, the effectiveness of the O-D matrix correction procedure in the usually adopted linear hypothesis on the dynamic process evolution of O-D flows and under the assumption of constant distribution shares is analyzed.

Trial-and-error implementation of marginal-cost pricing on networks in the absence of demand functions

Conventional analysis of optimal congestion pricing relies on three primary elements, namely, the speed–flow relationship, the demand function, and the generalized cost. Analytical demand functions tailed for congestion pricing are, however, difficult to establish in practice even with advanced transport modeling techniques. Inspired and motivated by the recent commentary and analytical works in the literature, this study proposes a trial-and-error implementation scheme of marginal-cost pricing on a general road network when the demand functions are unknown. Given a trial of a set of link tolls, the revealed aggregate link flows can be observed at ease; based on the observed link flows, a new set of link tolls can be determined and used for the next trial. We propose such an iterative toll adjustment procedure based on the method of successive averages, and present a rigorous theoretical proof of its convergence. The iterative procedure presented here allows for a traffic planner to estimate easily the socially optimal congestion tolls in a network without resorting to demand functions.

Real-Time Dynamic Origin-Destination Matrix Adjustment with Simulated and Actual Link Flows in Urban Networks

The efficiency and robustness of different real-time dynamic origin–destination (O-D) matrix adjustment algorithms were investigated when implemented in large-scale transportation networks. The proposed algorithms produce time-dependent O-D trip matrices based on the maximum-entropy trip departure times with simulated and actual observed link flows. Implementation of the algorithms, which are coupled with a quasi-dynamic traffic assignment model, indicated their convergent behavior and their potential for handling realistic urban-scale network problems in terms of both accuracy and computational time. The main factors influencing the numerical performance of each algorithm were identified and analyzed. Their relative efficiency was found to be particularly dependent on the level at which the assigned flows approximate the observed link flows. These results may provide insights into the suitability of each algorithm for diverse application domains, including freeways, small networks, and large-scale urban networks, where a different quality of O-D information is usually available.

A STOCHASTIC FLOW-DEPENDENT MODEL FOR PATH FLOW ESTIMATION

This study proposes an improved stochastic PFE (Path Flow Estimator) that considers explicitly traffic congestion on the network. Basically, the PFE model can estimate both the path and the OD flows from the observed link flows. The link travel cost is assumed to consist of the flow-dependent running time and the overload delay. Due to the strong influence of the observed link flow constraint, the distribution of estimated path flows is determined more by the observed link flow than by the logit-type assignment principle adopted in the PFE. This characteristic of the stochastic PFE model has been confirmed through two cases of numerical examples. And then a modified iterative balancing procedure is set out the equivalent convex programming problem.

Approaching OD Trip Volumes Based on Inverse T-V Equation

An inverse trip distribution-volume of link flow (T-V) equation is derived by the introduction of a new concept, the pass through coefficient. Based on this, a new approach to calculate OD trip volumes from the observed link flows is presented along with the calibration of the related factors.

Estimation of an origin-destination matrix with random link choice proportions: A statistical approach

The use of statistical modeling in the estimation of Origin-Destination (OD) matrix from traffic counts is reviewed. In particular, statistical models that consider explicitly the presence of measurement and sampling errors in the observed link flows are discussed. This paper proposes treating the link choice proportions as random variables. Accordingly, new statistical models are formulated and the corresponding Maximum Likelihood Estimator and Bayesian Estimator of the OD matrix are developed. The accuracies of these estimators are compared with those obtained by previous methods.

An overview of a simulation study of the Highway 401 freeway traffic management system

This paper discusses the application of the network traffic simulation model INTEGRATION to a 35-km section of Highway 401 in Toronto, Canada. Results for the eastbound direction from 4 a.m. to 12 noon are presented. Existing freeway conditions are quantified using data from the COMPASS freeway traffic management system and from a floating car travel time survey. Variations that exist in observed link flows and trip travel durations over time of day and day of week are examined. The extent to which COMPASS data meets the data requirements of the INTEGRATION model is examined. Since the current COMPASS system encompassed less than 50% of the network analyzed, complications arise in accurately estimating the prevailing time-varying origin–destination demands, as well as in comprehensively validating the simulation model's results. The present level of model calibration results in a correlation coefficient of estimated and observed link flows of 97.23%. This level of discrepancy is generally within the natural day-to-day variations that are inherent within the system. However, travel times estimated by the simulation model tend to be underestimated, particularly for the express lanes. Further model calibration, to improve the model's results, is deferred until more of the network is covered by COMPASS. Key words: traffic simulation, COMPASS, model calibration, model validation, speed–flow relationship.

A linear programming approach for synthesizing origin-destination trip tables from link traffic volumes

We present a nonproportional-assignment, user-equilibrium motivated, linear programming model for estimating origin-destination (O-D) trip tables from available data on link traffic volumes. The model is designed to determine a traffic equilibrium network flow solution that reproduces the link volume data, if such a solution exists. However, it recognizes that due to incomplete information, the traffic may not conform to an equilibrium flow pattern, and moreover, there might be inconsistencies in the observed link flow data. Accordingly, the model permits violations in the equilibrium conditions as well as deviations from the observed link flows but at suitable incurred penalties in the objective function. A column generation solution technique is presented to optimally solve the problem. This methodology is extended to the situation in which a specified prior target trip table is available and one is required to find a solution that also has a tendency to match this table as closely as possible. Implementation strategies are discussed and the proposed method is illustrated using some sample test networks from the literature.

The equilibrium-based origin-destination matrix estimation problem

This paper examines a model due to Nguyen for estimating origin-destination (O-D) matrices from observed traffic flows on each network link. It is shown that the previous bilevel optimization models for choosing an O-D matrix can be transformed into single convex programs. Under the condition that the observed link flow pattern is an equilibrium, Nguyen's model is demonstrated to be equivalent to an underspecified system of linear equations with non-negative variables. By exploiting the properties of the system's feasible region, simpler methods, such as a least squares technique, can be used to obtain an O-D matrix that, when user-optimally assigned to the network, reproduces the observed link flows.