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.     

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.     

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.     

Real-time queue length estimation for congested signalized intersections

How to estimate queue length in real-time at signalized intersection is a long-standing problem. The problem gets even more difficult when signal links are congested. The traditional input–output approach for queue length estimation can only handle queues that are shorter than the distance between vehicle detector and intersection stop line, because cumulative vehicle count for arrival traffic is not available once the detector is occupied by the queue. In this paper, instead of counting arrival traffic flow in the current signal cycle, we solve the problem of measuring intersection queue length by exploiting the queue discharge process in the immediate past cycle. Using high-resolution “event-based” traffic signal data, and applying Lighthill–Whitham–Richards (LWR) shockwave theory, we are able to identify traffic state changes that distinguish queue discharge flow from upstream arrival traffic. Therefore, our approach can estimate time-dependent queue length even when the signal links are congested with long queues. Variations of the queue length estimation model are also presented when “event-based” data is not available. Our models are evaluated by comparing the estimated maximum queue length with the ground truth data observed from the field. Evaluation results demonstrate that the proposed models can estimate long queues with satisfactory accuracy. Limitations of the proposed model are also discussed in the paper.     

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.     

Cellpath: Fusion of cellular and traffic sensor data for route flow estimation via convex optimization

A new convex optimization framework is developed for the route flow estimation problem from the fusion of vehicle count and cellular network data. The issue of highly underdetermined link flow based methods in transportation networks is investigated, then solved using the proposed concept of cellpaths for cellular network data. With this data-driven approach, our proposed approach is versatile: it is compatible with other data sources, and it is model agnostic and thus compatible with user equilibrium, system-optimum, Stackelberg concepts, and other models. Using a dimensionality reduction scheme, we design a projected gradient algorithm suitable for the proposed route flow estimation problem. The algorithm solves a block isotonic regression problem in the projection step in linear time. The accuracy, computational efficiency, and versatility of the proposed approach are validated on the I-210 corridor near Los Angeles, where we achieve 90% route flow accuracy with 1033 traffic sensors and 1000 cellular towers covering a large network of highways and arterials with more than 20,000 links. In contrast to long-term land use planning applications, we demonstrate the first system to our knowledge that can produce route-level flow estimates suitable for short time horizon prediction and control applications in traffic management. Our system is open source and available for validation and extension.     

Some comments on origin–destination matrix estimation

Estimation of origin–destination (O–D) matrices from link count data is considered. This problem is challenging because the number of parameters to be estimated is typically larger than the number of network links. As a result, it is (usually) impossible to identify a unique optimal estimate of the O–D matrix from mean link traffic counts. However, information from the covariance matrix of link count data collected over a sequence of days can relieve this problem of indeterminacy. This fact is illustrated through a simple example. The use of second-order statistical properties of the data in O–D matrix estimation is then explored, and a class of estimators proposed. Practical problems of model mis-specification are discussed and some avenues for future research outlined.     

Inferring origin–destination trip matrices from aggregate volumes on groups of links: a case study using volumes inferred from mobile phone data

The origin–destination matrix is an important source of information describing transport demand in a region. Most commonly used methods for matrix estimation use link volumes collected on a subset of links in order to update an existing matrix. Traditional volume data collection methods have significant shortcomings because of the high costs involved and the fact that detectors only provide status information at specified locations in the network. Better matrix estimates can be obtained when information is available about the overall distribution of traffic through time and space. Other existing technologies are not used in matrix estimation methods because they collect volume data aggregated on groups of links, rather than on single links. That is the case of mobile systems. Mobile phones sometimes cannot provide location accuracy for estimating flows on single links but do so on groups of links; in contrast, data can be acquired over a wider coverage without additional costs. This paper presents a methodology adapted to the concept of volume aggregated on groups of links in order to use any available volume data source in traditional matrix estimation methodologies. To calculate volume data, we have used a model that has had promising results in transforming phone call data into traffic movement data. The proposed methodology using vehicle volumes obtained by such a model is applied over a large real network as a case study. The experimental results reveal the efficiency and consistency of the solution proposed, making the alternative attractive for practical applications. Copyright © 2011 John Wiley & Sons, Ltd.     

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%.     

Global convergence of the trial-and-error method for the traffic-restraint congestion-pricing scheme with day-to-day flow dynamics

The traffic-restraint congestion-pricing scheme (TRCPS) aims to maintain traffic flow within a desirable threshold for some target links by levying the appropriate link tolls. In this study, we propose a trial-and-error method using observed link flows to implement the TRCPS with the day-to-day flow dynamics. Without resorting to the origin–destination (O–D) demand functions, link travel time functions and value of time (VOT), the proposed trial-and-error method works as follows: tolls for the traffic-restraint links are first implemented each time (trial) and they are subsequently updated using observed link flows in a disequilibrium state at any arbitrary time interval. The trial-and-error method has the practical significance because it is necessary only to observe traffic flows on those tolled links and it does not require to wait for the network flow pattern achieving the user equilibrium (UE) state. The global convergence of the trial-and-error method is rigorously demonstrated under mild conditions. We theoretically show the viability of the proposed trial-and-error method, and numerical experiments are conducted to evaluate its performance. The result of this study, without doubt, enhances the confidence of practitioners to adopt this method.     

Macroscopic Fundamental Diagrams: A cross-comparison of estimation methods

This paper aims to cross-compare existing estimation methods for the Macroscopic Fundamental Diagram. Raw data are provided by a mesoscopic simulation tool for two typical networks that mimic an urban corridor and a meshed urban center. We mainly focus on homogenous network loading in order to fairly cross-compare the different methods with the analytical reference. It appears that the only way to estimate the MFD without bias is to have the full information of vehicle trajectories over the network and to apply Edie’s definitions. Combining information from probes (mean network speed) and loop detectors (mean network flow) also provides accurate results even for low sampling rate (<10%). Loop detectors fail to provide a good estimation for mean network speed or density because they cannot capture the traffic spatial dynamics over links. This paper proposes a simple adjustment technic in order to reduce the discrepancy when only loop detectors are available.     

Network models in traffic management and control

Abstract

The context for network modelling in traffic management and control is described in terms of the current area‐wide nature of traffic management and the range of objectives to which it can contribute. Representation of a road system and traffic management measures in terms of nodes and links and parameters associated with them is described. It is shown that the pattern of traffic has to be represented not only in terms of flows on links of the network but also in terms of numbers of movements per unit time between points of entry to and points of exit from the area being modelled. In modelling so far, these numbers of movements are regarded as given, but the routes taken are estimated by traffic assignment. Models can so far be used for comparison of a range of given schemes and for optimization of traffic control within a scheme. Variation over time is a central feature of the modelling, and this requires the use of time‐dependent queueing theory, and the specification of numbers of movements for a succession of periods of between 10 and 30 minutes. Theoretical approaches to the resulting problems of modelling and optimization are discussed, and the ways in which these are supplemented by heuristic methods in currently available models is described. Some requirements‐for further research are outlined.     

Evaluating the assumption of independent turning probabilities

Several urban traffic models make the convenient assumption that turning probabilities are independent, meaning that the probability of turning right (or left or going straight through) at the downstream intersection is the same for all travelers on that roadway, regardless of their origin or destination. In reality most travelers make turns according to planned routes from origins to destinations. The research reported here identifies and quantifies the deviations that result from this assumption of independent turning probabilities.An analysis of this type requires a set of reasonably realistic “original” route flows, which were obtained by a static user-equilibrium traffic assignment and an entropy maximization condition for most likely route flows. These flows are compared with those route flows resulting from the Assumption of Independent Turning Probabilities (ITP). A small subnetwork of 3 km by 5 km in Tucson, Arizona, was chosen as a case study. An overall “typical ratio” of 2.2 between original route flows and ITP route flows was obtained. Aggregating route flows to origin–destination flows led to an overall “typical ratio” of 1.7. Such deviations are particularly high for routes that go back-and-forth, reaching a ratio of more than 3 in certain time periods. Substantial deviations for origins and destinations that are on the same border of the subnetwork are also observed in the analyses. In addition, under the ITP assumption, morning rush hour traffic peaking is the same in all directions, while in the original flows some directions do not exhibit a peak in the morning rush hour period. Overall, the conclusion of the paper is that the assumption of independent turning probabilities leads to substantial deviations both at the route level and at the origin–destination level, even for such a small network of the case study. These deviations are particularly detrimental when a network is being modeled and studied for route-based measures of effectiveness such as the number and types of routes passing a point – for monitoring specified vehicles and/or managing detouring strategies.     

A real-time traffic signal control system: architecture, algorithms, and analysis

The paper discusses a real-time traffic-adaptive signal control system referred to as RHODES. The system takes as input detector data for real-time measurement of traffic flow, and “optimally” controls the flow through the network. The system utilizes a control architecture that (1) decomposes the traffic control problem into several subproblems that are interconnected in an hierarchical fashion, (2) predicts traffic flows at appropriate resolution levels (individual vehicles and platoons) to enable pro-active control, (3) allows various optimization modules for solving the hierarchical subproblems, and (4) utilizes a data structure and computer/communication approaches that allow for fast solution of the subproblems, so that each decision can be downloaded in the field appropriately within the given rolling time horizon of the corresponding subproblem. The RHODES architecture, algorithms, and its analysis are presented. Laboratory test results, based on implementation of RHODES on simulation models of actual scenarios, illustrate the effectiveness of the system.     

Estimation of AADT from short period counts in hong kong — A comparison between neural network method and regression analysis

The average annual daily traffic (AADT) volumes can be estimated by using a short period count of less than twenty‐four hour duration. In this paper, the neural network method is adopted for the estimation of AADT from short period counts and for the determination of the most appropriate length of counts. A case study is carried out by analysing data at thirteen locations on trunk roads and primary roads in urban area of Hong Kong. The estimation accuracy is also compared with the one obtained by regression analysis approach. The results show that the neural network approach consistently performed better than the regression analysis approach.     

Deriving macroscopic fundamental diagrams from probe data: Issues and proposed solutions

Well-defined relationships between flow and density averaged spatially across urban traffic networks, more commonly known as Macroscopic Fundamental Diagrams (MFDs), have been recently verified to exist in reality. Researchers have proposed using MFDs to monitor the status of urban traffic networks and to inform the design of network-wide traffic control strategies. However, it is also well known that empirical MFDs are not easy to estimate in practice due to difficulties in obtaining the requisite data needed to construct them. Recent works have devised ways to estimate a network’s MFD using limited trajectory data that can be obtained from GPS-equipped mobile probe vehicles. These methods assume that the market penetration level of mobile probe vehicles is uniform across the entire set of OD pairs in the network; however, in reality the probe vehicle market penetration rate varies regionally within a network. When this variation is combined with the imbalance of probe trip lengths and travel times, the compound effects will further complicate the estimation of the MFD.To overcome this deficit, we propose a method to estimate a network’s MFD using mobile probe data when the market penetration rates are not necessarily the same across an entire network. This method relies on the determination of appropriate average probe penetration rates, which are weighted harmonic means using individual probe vehicle travel times and distances as the weights. The accuracy of this method is tested using synthetic data generated in the INTEGRATION micro-simulation environment by comparing the estimated MFDs to the ground truth MFD obtained using a 100% market penetration of probe vehicles. The results show that the weighted harmonic mean probe penetration rates outperform simple (arithmetic) average probe penetration rates, as expected. This especially holds true as the imbalance of demand and penetration level increases. Furthermore, as the probe penetration rates are generally not known, an algorithm to estimate the probe penetration rates of regional OD pairs is proposed. This algorithm links count data from sporadic fixed detectors in the network to information from probe vehicles that pass the detectors. The simulation results indicate that the proposed algorithm is very effective. Since the data needed to apply this algorithm are readily available and easy to collect, the proposed algorithm is practically feasible and offers a better approach for the estimation of the MFD using mobile probe data, which are becoming increasingly available in urban environments.     

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.     

Network sensor health problem

Many existing studies on the sensor health problem determine an individual sensor’s health status based on the statistical characteristics of collected data by the sensor. In this research, we study the sensor health problem at the network level, which is referred to as the network sensor health problem. First, based on the conservation principle of daily flows in a network, we separate all links into base links and non-base links, such that the flows on the latter can be calculated from those on the former. In reality, the network flow conservation principle can be violated due to the existence of unhealthy sensors. Then we define the least inconsistent base set of links as those that minimize the sum of squares of the differences between observed and calculated flows on non-base links. But such least inconsistent base sets may not be unique in a general road network. Finally we define the health index of an individual sensor as the frequency that it appears in all of the least inconsistent base sets. Intuitively, a lower health index suggests that the corresponding sensor is more likely to be unhealthy. We present the brute force method to find all least inconsistent base sets and calculate the health indices. We also propose a greedy search algorithm to calculate the approximate health indices more efficiently. We solve the network sensor health problem for a real-world example with 16 nodes and 30 links, among which 18 links are monitored with loop detectors. Using daily traffic count data from the Caltrans Performance Measurement System (PeMS) database, we use both the brute-force and greedy search methods to calculate the health indices for all the sensors. We find that all the four sensors flagged as unhealthy (high value) by PeMS have the lowest health indices. This confirms that a sensor with a lower health index is more likely to be unhealthy. Therefore, we can use such health indices to determine the relative reliability of different sensors’ data and prioritize the maintenance of sensors.     

Basic concepts and future directions of road network reliability analysis

The stability of road networks has become an increasingly important issue in recent times, since the value of time has increased considerably and unexpected delay can results in substantial loss to road users. Road network reliability has now become an important performance measure for evaluating road networks, especially when considering changes in OD traffic demand and link flow capacity over time. This paper outlines the basic concepts, remaining problems and future directions of road network reliability analysis. There are two common definitions of road network reliability, namely, connectivity reliability and travel time reliability. As well, reliability analysis is generally undertaken in both normal and abnormal situations. In order to analyse the reliability of a road network, the reliability of the links within the network must be first determined. A method for estimating the reliability of links within road networks is also suggested in this paper.     

Surrogate‐based optimization of cordon toll levels in congested traffic networks

The benefit, in terms of social surplus, from introducing congestion charging schemes in urban networks is depending on the design of the charging scheme. The literature on optimal design of congestion pricing schemes is to a large extent based on static traffic assignment, which is known for its deficiency in correctly predict travel times in networks with severe congestion. Dynamic traffic assignment can better predict travel times in a road network, but are more computational expensive. Thus, previously developed methods for the static case cannot be applied straightforward. Surrogate‐based optimization is commonly used for optimization problems with expensive‐to‐evaluate objective functions. In this paper, we evaluate the performance of a surrogate‐based optimization method, when the number of pricing schemes, which we can afford to evaluate (because of the computational time), are limited to between 20 and 40. A static traffic assignment model of Stockholm is used for evaluating a large number of different configurations of the surrogate‐based optimization method. Final evaluation is performed with the dynamic traffic assignment tool VisumDUE, coupled with the demand model Regent, for a Stockholm network including 1240 demand zones and 17 000 links. Our results show that the surrogate‐based optimization method can indeed be used for designing a congestion charging scheme, which return a high social surplus. Copyright © 2016 John Wiley & Sons, Ltd.