Estimating total annual traffic flow from short period counts

The total annual traffic flow at a road site is probably the single most important item of data needed in transport studies. In this article we describe a method of estimating this flow from a traffic count of less than 24 hours duration. The method is extended to enable an assessment to be made of the merits of repeating a count. The application of the method is discussed in relation to the United Kingdom, but we believe this method to be generally applicable to most countries.

     

Estimation of origin-destination matrices from link traffic counts on congested networks

Conventional methods for estimating origin-destination (O-D) trip matrices from link traffic counts assume that route choice proportions are given constants. In a network with realistic congestion levels, this assumption does not hold. This paper shows how existing methods such as the generalized least squares technique can be integrated with an equilibrium traffic assignment in the form of a convex bilevel optimization problem. The presence of measurement errors and time variations in the observed link flows are explicitly considered. The feasibility of the model is always guaranteed without a requirement for estimating consistent link flows from counts. A solution algorithm is provided and numerical simulation experiments are implemented in investigating the model's properties. Some related problems concerning O-D matrix estimation are also discussed.     

A unified framework for estimating or updating origin/destination matrices from traffic counts

This paper presents an in-depth study of the methodology for estimating or updating origin-to-destination trip matrices from traffic counts. Following an analysis of the statistical foundation of the estimation and updating problems, various basic approaches are reviewed using a generic traffic assignment map. Computational issues related to specific assignment maps and estimation models for both road and transit networks are then discussed. Finally, additional insight into the relative performance of several estimators is provided by a set of test problems with varying input data.     

The most likely trip matrix estimated from traffic counts

For a large number of applications conventional methods for estimating an origin destination matrix become too expensive to use. Two models, based on information minimisation and entropy maximisation principles, have been developed by the authors to estimate an O-D matrix from traffic counts. The models assume knowledge of the paths followed by the vehicles over the network. The models then use the traffic counts to estimate the most likely O-D matrix consistent with the link volumes available and any prior information about the trip matrix. Both models can be used to update and improve a previous O-D matrix. An algorithm to find a solution to the model is then described. The models have been tested with artificial data and performed reasonably well. Further research is being carried out to validate the models with real data.     

The symmetric intersection design and traffic control optimization

It is well recognized that the left-turning movement reduces the intersection capacity significantly, because exclusive left turn phases are needed to discharge left turn vehicles only. This paper proposes the concept of Left-Hand Traffic (LHT) arterial, on where vehicles follow left-hand traffic rules as in England and India. The unconventional intersection where a LHT arterial intersects with a Right-Hand Traffic (RHT) arterial is named as symmetric intersection. It is only need three basic signal phases to separate all conflicts at symmetric intersection, while it at least need four signal phases at a conventional intersection. So, compared with the conventional intersection, the symmetric intersection can provide longer green time for the left-turning and the through movement, which can increase the capacity significantly. Through-movement waiting areas (TWAs) can be set at the symmetric intersection effectively, which can increase the capacity and short the cycle length furthermore. And the symmetric intersection is Channelized to improve the safety of TWAs. The Binary-Mixed-Integer-Linear-Programming (BMILP) model is employed to formulate the capacity maximization problem and signal cycle length minimization problem of the symmetric intersection. The BMILP model can be solved by standard branch-and-bound algorithms efficiently and outputs the lane allocation, signal timing decisions, and other decisions. Experiments analysis shows that the symmetric intersection with TWAs can increase the capacity and short the signal cycle length.     

Estimating origin-destination matrices from roadside survey data

The purpose of this study is to develop a valid and efficient method for estimating origin-destination tables from roadside survey data. Roadside surveys, whether conducted by interviews or postcard mailback methods, typically have in common the sampling of trip origin and destination information at survey stations. These survey stations are generally located where roads cross “screenlines,” which are imaginary barriers drawn to intercept the trip types of interest.Such surveys also include counts of traffic volumes, by which the partial origin-destination (O-D) tables obtained at the different stations can be expanded and combined to obtain the complete O-D table which represents travel throughout the entire study area. The procedure used to expand the sample O-D information from the survey stations must recognize and deal appropriately with a number of problems:

• 1.(i) The “double counting” problem: Long-distance trips may pass through more than one survey station location; thus certain trips have the possibility of being sampled and expanded more than once, leading to a potentially serious overrepresentation of long-distance trips in the complete expanded trip table.
• 2.(ii) The “leaky screenline” problem: Some route choices, particularly those using very lightly traveled roads, may miss the survey stations entirely, leading to an underestimation of certain O-D patterns, or to distorted estimates if such sites are arbitrarily coupled with actual nearby station locations.
• 3.(iii) The efficient use of the data: There is a need to adjust expansion factors to compensate for double counting and leaky screenlines. How can this be accomplished such that all of the data obtained at the stations are used without loss of information?
• 4.(iv) The consequences of uncertainty and unknown travel behavior: Since the O-D data and other sampled variables are subject to random error, and since in general the probability of encountering a long-distance trip at some survey stations is affected by traveler route-choice behavior, which is not understood, the sample expansion procedure must rely on the use of erroneous input data and questionable assumptions. The preferred procedure must minimize, rather than amplify, the effects of such input errors.

Here, five alternate methods for expanding roadside survey data in an unbiased manner are proposed and evaluated. In all cases, it is assumed that traveler route choice generally follows the pattern described by Dial's multipath assignment method. All methods are applied to a simple hypothetical network in order to examine their efficiency and error amplification properties. The evaluation of the five methods reveals that their performance properties vary considerably and that no single method is best in all circumstances. A microcomputer program has been provided as a tool to facilitate comparison among methods and to select the most appropriate expansion method for a particular application.     

Recursive estimation of origin-destination matrices from input/output counts

The application of recursive prediction error techniques to the problem of estimating origin-destination patterns from input and output volume counts is described. Each algorithm deals with the special case where route choice between origin and destination can be ignored. A gradient algorithm developed by Cremer and Keller (1983) turns out to be a special case of a family of methods described by Ljung and Söderström (1983). After describing how the methods developed in Ljung and Söderström (1983) could be modified so that the resulting estimates satisfy natural constraints, a number of algorithm possibilities are tested. Generally, those algorithms employing Gauss-Newton search directions appear superior to gradient-based methods, while the constraining procedures improve accuracy.     

Estimation of origin-destination matrices from link counts and sporadic routing data

Estimation of origin-destination (OD) matrices from link count data is a challenging problem because of the highly indeterminate relationship between the observations and the latent route flows. Conversely, estimation is straightforward if we observe the path taken by each vehicle. We consider an intermediate problem of increasing practical importance, in which link count data is supplemented by routing information for a fraction of vehicles on the network. We develop a statistical model for these combined data sources and derive some tractable normal approximations thereof. We examine likelihood-based inference for these normal models under the assumption that the probability of vehicle tracking is known. We show that the likelihood theory can be non-standard because of boundary effects, and provide conditions under which such irregular behaviour will be observed in practice. For regular cases we outline connections with existing generalised least squares methods. We then consider estimation of OD matrices under estimated and/or misspecified models for the probability of vehicle tracking. Theoretical developments are complemented by simulation experiments and an illustrative example using a section of road network from the English city of Leicester.     

A time-series forecast of average daily traffic volume

This paper presents a procedure for forecasting average daily traffic using a time-series analysis. The procedure assumes a logistic function to model traffic volume over a period of years. Model parameters are estimated using ordinary least-squares regression. The method was tested empirically. Model parameters were found to be significant for each of the three different thoroughfares. Further, time-series forecasts compared favorably to observed traffic and to interpolated forecasts for the same period. The method is simpler to and more economical than the standard demand forecasting procedure and is recommended where land-use patterns are stable and only small modifications to the thoroughfare network are planned.     

Empirical analysis of short period traffic counts and their efficiency: the case of Indian traffic

Short period traffic counts (SPTCs) are conducted routinely to estimate the annual average daily traffic (AADT) at a particular site. This paper uses Indian traffic volume data to methodically and extensively study the effect of four aspects related to the design of SPTCs. These four aspects are: (i) for how long, (ii) on which days should SPTCs be carried out, (iii) how many times, and (iv) on which months should SPTCs be carried out? The analyses indicate that the best durations for conducting SPTCs are 3 days (starting with a Thursday) and 7 days, for total traffic and truck traffic, respectively. Further, these counts should be repeated twice a year keeping a separation of two months between the counts to obtain good estimates of AADT at minimal cost. An additional outcome of this study has been the determination of seasonal factor values for roads in developing economies, like India.     

Some observed details of freeway traffic evolution

Certain details of traffic evolution were studied along a 2 km, homogenous freeway segment located upstream of a bottleneck. By comparing (transformed) cumulative curves constructed from the vehicle counts measured at neighboring loop detectors, it was found that waves propagated through queued traffic like a random walk with predictable statistical variation. There was no observed dependency of wave speed on flow. As such, these waves neither focused nor fanned outward and shocks arose only at the interfaces between free-flowing traffic and the back of queues. Although these traffic features may have long been suspected, actual observations of this kind have hitherto not been documented. Also of note, the shocks separating queued and unqueued traffic sometimes exhibited unexpectedly long transitions between these two states. Finally, some observations presented here corroborate earlier reports that, in unqueued traffic, vehicle velocity is insensitive to flows and that forward-moving changes in traffic states therefore travel with vehicles. Taken together, these findings suggest that certain rather simple models suffice for describing traffic on homogeneous freeway segments; brief discussion of this is offered in Section 5.     

Estimation of mean and covariance of stochastic multi-class OD demands from classified traffic counts

This paper proposes a new model to estimate the mean and covariance of stochastic multi-class (multiple vehicle classes) origin–destination (OD) demands from hourly classified traffic counts throughout the whole year. It is usually assumed in the conventional OD demand estimation models that the OD demand by vehicle class is deterministic. Little attention is given on the estimation of the statistical properties of stochastic OD demands as well as their covariance between different vehicle classes. Also, the interactions between different vehicle classes in OD demand are ignored such as the change of modes between private car and taxi during a particular hourly period over the year. To fill these two gaps, the mean and covariance matrix of stochastic multi-class OD demands for the same hourly period over the year are simultaneously estimated by a modified lasso (least absolute shrinkage and selection operator) method. The estimated covariance matrix of stochastic multi-class OD demands can be used to capture the statistical dependency of traffic demands between different vehicle classes. In this paper, the proposed model is formulated as a non-linear constrained optimization problem. An exterior penalty algorithm is adapted to solve the proposed model. Numerical examples are presented to illustrate the applications of the proposed model together with some insightful findings on the importance of covariance of OD demand between difference vehicle classes.     

The effect of bus detection on the performance of a traffic signal controlled intersection

An investigation has been carried out to determine any possible improvement to the overall performance of a traffic signal controlled intersection when a bus-actuated system is superimposed on fixed-time control. A hypothetical site downstream from a set of genuine signals was selected and data concerning flows, journey times and arrival patterns of vehicles were recorded. The Transyt program was used to obtain the appropriate offsets and splits at the hypothetical site for different levels of side road volume and these were fed into a simulation program together with the arrival times of vehicles to calculate the respective performance indices. The simulation program was then altered to represent a bus-actuated system where the signals would change at the detection of buses according to a predetermined policy but subject to overriding constraints imposed by the fixed-time settings. It was found that the bus-actuated system of control best suited a low flow of buses while fixed-time control gave a better performance index with a higher bus flow.     

Stochastic simulation of the traffic of an uncontrolled road intersection

The paper describes the logic and results of a stochastic simulation model for uncontrolled intersections with poor visibility where the right of way belongs to the driver on the right. The model deals with crossings with and without turning movements. Several runs have been made with realistic input values. Finally, conclusions are drawn and traffic volume warrants are proposed for establishing two way stop/yield controls on uncontrolled crossings.     

Assessing greenhouse gas and related air pollutant emissions from road traffic counts: A case study for Mauritius

The road transport sector is one of the major contributors of greenhouse gases and other air pollutants emissions. Regional emissions levels from road vehicles were investigated, in Mauritius, by applying a fuel-based approach. We estimated fuel consumption and air emissions based on traffic counts on the various types of classified roads at three different regional set ups, namely urban, semi urban and rural. The Relative Development Index (RDI), a composite index calculated from socio-economic and environmental indicators was used to classify regions. Our results show that the urban motorways were the most polluting due to heavy traffic. Some rural areas had important pollution levels as well. Our analysis of variance (ANOVA), however, showed little difference in emissions among road types and regions. The study can provide a simple tool for researchers in countries where data are very scarce, as is the case for many developing countries.     

Calibrating aggregate travel demand models with traffic counts: Estimators and statistical performance

Traffic counts on network links constitute an information source on travel demand which is easy to collect, cheap and repeatable. Many models proposed in recent years deal with the use of traffic counts to estimate Origin/Destination (O/D) trip matrices under different assumptions on the type of "a-priori" information available on the demand (surveys, outdated estimates, models, etc.) and the type of network and assignment mapping (see Cascetta & Nguyen 1988). Less attention has been paid to the possibility of using traffic counts to estimate the parameters of demand models. In this case most of the proposed methods are relative to particular demand model structures (e.g. gravity-type) and the statistical analysis of estimator performance is not thoroughly carried out. In this paper a general statistical framework defining Maximum Likelihood, Non Linear Generalized Least Squares (NGLS) and Bayes estimators of aggregated demand model parameters combining counts-based information with other sources (sample or a priori estimates) is proposed first, thus extending and generalizing previous work by the authors (Cascetta & Russo 1992). Subsequently a solution algorithm of the projected-gradient type is proposed for the NGLS estimator given its convenient theoretical and computational properties. The algorithm is based on a combination of analytical/numerical derivates in order to make the estimator applicable to general demand models. Statistical performances of the proposed estimators are evaluated on a small test network through a Monte Carlo method by repeatedly sampling "starting estimates" of the (known) parameters of a generation/distribution/modal split/assignment system of models. Tests were carried out assuming different levels of "quality" of starting estimates and numbers of available counts. Finally NGLS estimator was applied to the calibration of the described model system on the network of a real medium-size Italian town using real counts with very satisfactory results in terms of both parameter values and counted flows reproduction.     

W-SPSA in practice: Approximation of weight matrices and calibration of traffic simulation models

The development and calibration of complex traffic models demands parsimonious techniques, because such models often involve hundreds of thousands of unknown parameters. The Weighted Simultaneous Perturbation Stochastic Approximation (W-SPSA) algorithm has been proven more efficient than its predecessor SPSA (Spall, 1998), particularly in situations where the correlation structure of the variables is not homogeneous. This is crucial in traffic simulation models where effectively some variables (e.g. readings from certain sensors) are strongly correlated, both in time and space, with some other variables (e.g. certain OD flows). In situations with reasonably sized traffic networks, the difference is relevant considering computational constraints. However, W-SPSA relies on determining a proper weight matrix (W) that represents those correlations, and such a process has been so far an open problem, and only heuristic approaches to obtain it have been considered.This paper presents W-SPSA in a formally comprehensive way, where effectively SPSA becomes an instance of W-SPSA, and explores alternative approaches for determining the matrix W. We demonstrate that, relying on a few simplifications that marginally affect the final solution, we can obtain W matrices that considerably outperform SPSA. We analyse the performance of our proposed algorithm in two applications in motorway networks in Singapore and Portugal, using a dynamic traffic assignment model and a microscopic traffic simulator, respectively.     

Statistical methods for detecting nonlinearity and non-stationarity in univariate short-term time-series of traffic volume

Short-term traffic volume data are characterized by rapid and intense fluctuations with frequent shifts to congestion. Currently, research in short-term traffic forecasting deals with these phenomena either by smoothing them or by accounting for them by nonlinear models. But, these approaches lead to inefficient predictions particularly when the data exhibit intense oscillations or frequent shifts to boundary conditions (congestion). This paper offers a set of tools and methods to assess on underlying statistical properties of short-term traffic volume data, a topic that has largely been overlooked in traffic forecasting literature. Results indicate that the statistical characteristics of traffic volume can be identified from prevailing traffic conditions; for example, volume data exhibit frequent shifts from deterministic to stochastic structures as well as transitions between cyclic and strongly nonlinear behaviors. These findings could be valuable in the implementation of a variable prediction strategy according to the statistical characteristics of the prevailing traffic volume states.     

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.     

A dynamic linear model for the estimation of time‐varying origin–destination matrices from link counts

We propose a dynamic linear model (DLM) for the estimation of day‐to‐day time‐varying origin–destination (OD) matrices from link counts. Mean OD flows are assumed to vary over time as a locally constant model. We take into account variability in OD flows, route flows, and link volumes. Given a time series of observed link volumes, sequential Bayesian inference is applied in order to estimate mean OD flows. The conditions under which mean OD flows may be estimated are established, and computational studies on two benchmark transportation networks from the literature are carried out. In both cases, the DLM converged to the unobserved mean OD flows when given sufficient observations of traffic link volumes despite assuming uninformative prior OD matrices. We discuss limitations and extensions of the proposed DLM. Copyright © 2017 John Wiley & Sons, Ltd.