Real-time estimation of turning movement counts at signalized intersections using signal phase information

A variety of sensor technologies, such as loop detectors, traffic cameras, and radar have been developed for real-time traffic monitoring at intersections most of which are limited to providing link traffic information with few being capable of detecting turning movements. Accurate real-time information on turning movement counts at signalized intersections is a critical requirement for applications such as adaptive traffic signal control. Several attempts have been made in the past to develop algorithms for inferring turning movements at intersections from entry and exit counts; however, the estimation quality of these algorithms varies considerably. This paper introduces a method to improve accuracy and robustness of turning movement estimation at signalized intersections. The new algorithm makes use of signal phase status to minimize the underlying estimation ambiguity. A case study was conducted based on turning movement data obtained from a four-leg signalized intersection to evaluate the performance of the proposed method and compare it with two other existing well-known estimation methods. The results show that the algorithm is accurate, robust and fairly straightforward for real world implementation.     

Norm approximation method for handling traffic count inconsistencies in path flow estimator

Path flow estimator (PFE) is a one-stage network observer proposed to estimate path flows and hence origin–destination (O–D) flows from traffic counts in a transportation network. Although PFE does not require traffic counts to be collected on all network links when inferring unmeasured traffic conditions, it does require all available counts to be reasonably consistent. This requirement is difficult to fulfill in practice due to errors inherited in data collection and processing. The original PFE model handles this issue by relaxing the requirement of perfect replication of traffic counts through the specification of error bounds. This method enhances the flexibility of PFE by allowing the incorporation of local knowledge, regarding the traffic conditions and the nature of traffic data, into the estimation process. However, specifying appropriate error bounds for all observed links in real networks turns out to be a difficult and time-consuming task. In addition, improper specification of the error bounds could lead to a biased estimation of total travel demand in the network. This paper therefore proposes the norm approximation method capable of internally handling inconsistent traffic counts in PFE. Specifically, three norm approximation criteria are adopted to formulate three L_p-PFE models for estimating consistent path flows and O–D flows that simultaneously minimize the deviation between the estimated and observed link volumes. A partial linearization algorithm embedded with an iterative balancing scheme and a column generation procedure is developed to solve the three L_p-PFE models. In addition, the proposed L_p-PFE models are illustrated with numerical examples and the characteristics of solutions obtained by these models are discussed.     

A programmable calculation procedure for number of traffic conflict points at highway intersections

Traffic movement conflict points at intersections are the points at which traffic movements intersect (including crossing, merging, and diverging). Numbers and distribution of different types of conflict points are used to evaluate intersection access management designs and safety performance. Traditionally, the determination of the numbers of conflict points for different traffic movements is based on manual methods, which causes the difficulty for computerized procedures to evaluate safety performance of different access management designs. Sometimes, a programmable calculation procedure may provide more effective solutions as compared with manual methods. This paper presents a programmable calculation procedure for the determination of the numbers of conflict points, which could be used as a basis for a computerized procedure. Concepts of virtual movement lanes and intersection quadrants are introduced to specify types of intersections, traffic lane configurations, and traffic movement regulations. Calculation models, based on such concepts, for traffic movement conflict points at signalized and unsignalized intersections can be obtained. In support of the procedure, case studies are presented in the paper. The procedure presented in the paper can be programmed into a computer program for the purpose of a computerized evaluation of intersection safety and design performance of different access management or control approaches. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

Identification of vehicle sensor locations for link-based network traffic applications

Information on link flows in a vehicular traffic network is critical for developing long-term planning and/or short-term operational management strategies. In the literature, most studies to develop such strategies typically assume the availability of measured link traffic information on all network links, either through manual survey or advanced traffic sensor technologies. In practical applications, the assumption of installed sensors on all links is generally unrealistic due to budgetary constraints. It motivates the need to estimate flows on all links of a traffic network based on the measurement of link flows on a subset of links with suitably equipped sensors. This study, addressed from a budgetary planning perspective, seeks to identify the smallest subset of links in a network on which to locate sensors that enables the accurate estimation of traffic flows on all links of the network under steady-state conditions. Here, steady-state implies that the path flows are static. A “basis link” method is proposed to determine the locations of vehicle sensors, by using the link-path incidence matrix to express the network structure and then identifying its “basis” in a matrix algebra context. The theoretical background and mathematical properties of the proposed method are elaborated. The approach is useful for deploying long-term planning and link-based applications in traffic networks.     

Using stop bar detector information to determine turning movement proportions in shared lanes

Turning vehicle volumes at signalized intersections are critical inputs for various transportation studies such as level of service, signal timing, and traffic safety analysis. There are various types of detectors installed at signalized intersections for control and operation. These detectors have the potential of producing volume estimates. However, it is quite a challenge to use such detectors for conducting turning movement counts in shared lanes. The purpose of this paper was to provide three methods to estimate turning movement proportions in shared lanes. These methods are characterized as flow characteristics (FC), volume and queue (VQ) length, and network equilibrium (NE). FC and VQ methods are based on the geometry of an intersection and behavior of drivers. The NE method does not depend on these factors and is purely based on detector counts from the study intersection and the downstream intersection. These methods were tested using regression and genetic programming (GP). It was found that the hourly average error ranged between 4 and 27% using linear regression and 1 to 15% using GP. A general conclusion was that the proposed methods have the potential of being applied to locations where appropriate detectors are installed for obtaining the required data. Copyright © 2016 John Wiley & Sons, Ltd.     

Quasi-dynamic traffic assignment with residual point queues incorporating a first order node model

Static traffic assignment models are still widely applied for strategic transport planning purposes in spite of the fact that such models produce implausible traffic flows that exceed link capacities and predict incorrect congestion locations. There have been numerous attempts to constrain link flows to capacity. Capacity constrained models with residual queues are often referred to as quasi-dynamic traffic assignment models. After reviewing the literature, we come to the conclusion that an important piece of the puzzle has been missing so far, namely the inclusion of a first order node model. In this paper we propose a novel path-based static traffic assignment model for finding a stochastic user equilibrium in general transportation networks. This model includes a first order (steady-state) node model that yields more realistic turn capacities, which are then used to determine consistent capacity constrained traffic flows, residual point (vertical) queues (upstream bottleneck links), and path travel times consistent with queuing theory. The route choice part of the model is specified as a variational inequality problem, while the network loading part is formulated as a fixed point problem. Both problems are solved using existing techniques to find a solution. We illustrate the model using hypothetical examples, and also demonstrate feasibility on large-scale networks.     

A decomposition scheme for estimating dynamic origin–destination flows on actuation-controlled signalized arterials

This paper presents a decomposition framework for estimating dynamic origin–destination (O–D) flows on actuation-controlled signalized arterials from link counts, mainly addressing the issues of incomplete information and the large number of O–D pairs. The framework decomposes the original high-dimensional problem into much smaller sub-problems at the intersection and corridor levels. At the intersection level, turning movements are inferred with incomplete information; at the corridor level, the final estimates of O–D flows are constructed as weighted averages of the estimates from the column and row decompositions. Numerical examples are presented to demonstrate the effectiveness and the computational efficiency of the decomposition framework.     

Simultaneous estimation of an origin–destination matrix and link choice proportions using traffic counts

A procedure for the simultaneous estimation of an origin–destination (OD) matrix and link choice proportions from OD survey data and traffic counts for congested network is proposed in this paper. Recognizing that link choice proportions in a network change with traffic conditions, and that the dispersion parameter of the route choice model should be updated for a current data set, this procedure performs statistical estimation and traffic assignment alternately until convergence in order to obtain the best estimators for both the OD matrix and link choice proportions, which are consistent with the survey data and traffic counts.Results from a numerical study using a hypothetical network have shown that a model allowing θ to be estimated simultaneously with an OD matrix from the observed data performs better than the model with a fixed predetermined θ. The application of the proposed model to the Tuen Mun Corridor network in Hong Kong is also presented in this paper. A reasonable estimate of the dispersion parameter θ for this network is obtained.     

Real-time estimation of turning movement proportions from partial counts on urban networks

Modern traffic signal control systems require reliable estimates of turning flows in real time to formulate effective control actions, and accommodate disturbances in traffic demand without deteriorating the system performance. The more accurate the estimation is, the more effective the control plan is. Most of the previous research works assumed that a full set of detector counts is available and employed the least-squares methods to produce unbiased estimates of the turning movement proportions. However, in practice, such a dense detector configuration is expensive to install and maintain. Also, the least-squares estimates are not feasible when the travel time between inflows and outflows is significant, or when intervening traffic conditions change the travel time. This study proposes a nonlinear least-square (NLS) approach and a quasi maximum likelihood (QML) approach to recursively estimate turning movement proportions in a network of intersections where only a partial set of detector counts are available. Using large population approximation technique, a class of nonlinear, discrete-time traffic flow models are transformed into a linear state–space model tractable for on-line applications. The quality of estimates is demonstrated by implementing the proposed algorithms with simulation and real data. As a comparison, the NLS estimator shows less bias but with higher variance than the QML estimator. The QML estimator outperforms the NLS estimator in terms of total mean square error, due to an increase in bias being traded for a decrease in variance.     

Link choice proportions from trip distribution and assignment models: An overview and comparison

A number of estimation procedures have been suggested for the situation where a prior estimate of an origin-destination matrix is to be updated on the basis of recently-acquired traffic counts. These procedures assume that both the link flows and the proportionate usage of each link made by each origin-destination flow (referred to collectively as the link choice proportions) are known. This paper examines the possibility and methods for estimating the link choice proportions. Three methods are presented: (1) using ad hoc iteration between trip distribution and traffic assignment; (2) combining trip distribution and assignment in one step; (3) solving a new optimization problem in which the path flows are directly considered as variables and its optimal solution is governed by a logit type formula. The algorithms, covergencies and computational efficiencies of these methods are investigated. Results of testing the three methods on example networks are discussed.     

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.     

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.     

Innovative detector layout for automated traffic turning volume counting

Because of many advantages, loop detectors are the most common practice for obtaining data to control intersections. However, they have some drawbacks, including the fact that multiple detectors are usually required to monitor a location. The current practice in many cities is to install four consecutive loop detectors per lane, or two at the stop bar and one as an advanced detector. In some cities, there are also departure detectors. All these configurations have some practical problems and do not produce accurate counts especially in shared lanes. In this paper, a new placement configuration for departure detectors is proposed and named the mid‐intersection detector (MID). In this configuration, departure detectors are moved back to the middle of the intersection in such a way that they can be activated by more than one movement at different times. In some cases, departure detectors lack equations for calculating turning movements, a problem solved by MIDs because each movement passes more detectors along its path (without increasing the number of loops), and therefore they can produce more accurate and reliable data for obtaining turning movement counts. Copyright © 2017 John Wiley & Sons, Ltd.     

A generalized sensor location model for the estimation of network origin–destination matrices

This study examined the network sensor location problem by using heterogeneous sensor information to estimate link-based network origin–destination (O–D) demands. The proposed generalized sensor location model enables different sensors’ traffic monitoring capabilities to be used efficiently and the optimal number and deployment locations of both passive- and active-type sensors to be determined simultaneously without path enumeration. The proposed sensor location model was applied to solve the network O–D demand estimation problem. One unique aspect of the proposed model and solution algorithms is that they provide satisfactory network O–D demand estimates without requiring unreasonable assumptions of known prior information on O–D demands, turning proportions, or route choice probabilities. Therefore, the proposed model and solution algorithms can be practically used in numerous offline transportation planning and online traffic operation applications.     

Node modeling for congested urban road networks

First-order network flow models are coupled systems of differential equations which describe the build-up and dissipation of congestion along network road segments, known as link models. Models describing flows across network junctions, referred to as node models, play the role of the coupling between the link models and are responsible for capturing the propagation of traffic dynamics through the network. Node models are typically stated as optimization problems, so that the coupling between the link dynamics is not known explicitly. This renders network flow models analytically intractable. This paper examines the properties of node models for urban networks. Solutions to node models that are free of traffic holding, referred to as holding-free solutions, are formally defined and it is shown that flow maximization is only a sufficient condition for holding-free solutions. A simple greedy algorithm is shown to produce holding-free solutions while also respecting the invariance principle. Staging movements through nodes in a manner that prevents conflicting flows from proceeding through the nodes simultaneously is shown to simplify the node models considerably and promote unique solutions. The staging also models intersection capacities in a more realistic way by preventing unrealistically large flows when there is ample supply in the downstream and preventing artificial blocking when some of the downstream supplies are restricted.     

A two-stage fuzzy logic controller for traffic signals

This paper presents the design and evaluation of a fuzzy logic traffic signal controller for an isolated intersection. The controller is designed to be responsive to real-time traffic demands. The fuzzy controller uses vehicle loop detectors, placed upstream of the intersection on each approach, to measure approach flows and estimate queues. These data are used to decide, at regular time intervals, whether to extend or terminate the current signal phase. These decisions are made using a two-stage fuzzy logic procedure. In the first stage, observed approach traffic flows are used to estimate relative traffic intensities in the competing approaches. These traffic intensities are then used in the second stage to determine whether the current signal phase should be extended or terminated. The performance of this controller is compared to that of a traffic-actuated controller for different traffic conditions on a simulated four-approach intersection.     

Real-time traffic estimation using data expansion

This paper presents a method for estimating missing real-time traffic volumes on a road network using both historical and real-time traffic data. The method was developed to address urban transportation networks where a non-negligible subset of the network links do not have real-time link volumes, and where that data is needed to populate other real-time traffic analytics. Computation is split between an offline calibration and a real-time estimation phase. The offline phase determines link-to-link splitting probabilities for traffic flow propagation that are subsequently used in real-time estimation. The real-time procedure uses current traffic data and is efficient enough to scale to full city-wide deployments. Simulation results on a medium-sized test network demonstrate the accuracy of the method and its robustness to missing data and variability in the data that is available. For traffic demands with a coefficient of variation as high as 40%, and a real-time feed in which as much as 60% of links lack data, we find the percentage root mean square error of link volume estimates ranges from 3.9% to 18.6%. We observe that the use of real-time data can reduce this error by as much as 20%.     

Estimation of link performance functions from incomplete flow data

Despite the pivotal importance of link performance functions to models of transport systems, relatively little work has been done on practical aspects of estimating these functions from observed data. Furthermore it is difficult to find any examples in the literature of estimated urban link performance functions faithfully reproducing theoretical travel time-flow relationships. One reason for the paucity of research in this area is the difficulty and expense of obtaining the requisite data. The increase in automatic collection of traffic flow data goes part way to resolving this problem, but matching such flows to manually recorded travel times can present considerable statistical difficulties in the estimation procedure. This paper considers the estimation of link performance functions from a combination of automatically recorded traffic counts and travel collected by hand, using a non-standard statistical methodology. The study is motivated by a set of data of precisely this type, from the UK city of Leicester.     

A time-dependent freight tour synthesis model

This paper introduces a model of urban freight demand that seeks to estimate tour flows from secondary data sources e.g., traffic counts, to bypass the need for expensive surveys. The model discussed in this paper, referred as Freight Tour Synthesis (FTS), enhances current techniques by incorporating the time-dependent tour-based behavior of freight vehicles, and the decision maker’s (e.g., metropolitan planning agency planner) preferences for different sources of information. The model, based on entropy maximization theory, estimates the most likely set of tour flows, given a set of freight trip generation estimates, a set of traffic counts per time interval, and total freight transportation cost in the network. The type of inputs used allows the assessment of changes in infrastructure, policy and land use. The ability of the model to replicate actual values is assessed using the Denver Region (CO) as a case study.