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.     

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.     

A framework for neighbour links travel time estimation in an urban network

This paper proposes a solution to the problem of limited network sensor coverage caused by insufficient sample size of probe vehicles or inadequate numbers of fixed sensors. A framework is proposed to estimate link travel times using available data from neighbouring links. Two clues are used for real-time travel time estimation: link historical travel time data and online travel time data from neighbour links. In the absence of online travel time data from neighbour links, historical records only have to be relied upon. However, where the two types of data are available, a data fusion scheme can be applied to make use of the two clues. The proposed framework is validated using real-life data from the City of Vancouver, British Columbia. The estimation accuracy is found to be comparable to the existing literature. Overall, the results demonstrate the feasibility of using neighbour links data as an additional source of information that might not have been extensively explored before.     

Improving the resolution of gridded-hourly mobile emissions: incorporating spatial variability and handling missing data

To more accurately predict hourly running stabilized link volumes for emissions modeling, a new method was recently developed that disaggregates the period-based model link volumes into hourly volumes using observed traffic count data and multivariate multiple regression (MMR). This paper extends the MMR methodology with clustering and classification analyses to account for spatial variability and to accommodate model links that do not have matching observed traffic count data. The methodology was applied to data collected in the South Air Basin. The spatial analysis resulted in identifying five clusters (or 24-h profiles) for San Diego and two clusters for Los Angeles. The MMR models were then estimated with and without clustering. For San Diego, the disaggregated model volumes with clustering were much closer to the observed volumes than those without clustering, with the exception of the a.m. period. For most hours in Los Angeles, the predicted volumes with clustering were only slightly closer to the observed volumes than those predicted without clustering, suggesting that spatial effects are minimal in Los Angeles (i.e., that 24-h volume profiles are fairly similar throughout the region) and clustering is not necessary. Finally, two classification models, one for San Diego and one for Los Angeles were developed and tested for network link data that does not have matching observed count data. The results indicate the procedure is relatively good at predicting a cluster assignment for the unmatched location for Los Angeles but less accurate for San Diego.     

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.     

Short-term speed predictions exploiting big data on large urban road networks

Big data from floating cars supply a frequent, ubiquitous sampling of traffic conditions on the road network and provide great opportunities for enhanced short-term traffic predictions based on real-time information on the whole network. Two network-based machine learning models, a Bayesian network and a neural network, are formulated with a double star framework that reflects time and space correlation among traffic variables and because of its modular structure is suitable for an automatic implementation on large road networks. Among different mono-dimensional time-series models, a seasonal autoregressive moving average model (SARMA) is selected for comparison. The time-series model is also used in a hybrid modeling framework to provide the Bayesian network with an a priori estimation of the predicted speed, which is then corrected exploiting the information collected on other links. A large floating car data set on a sub-area of the road network of Rome is used for validation. To account for the variable accuracy of the speed estimated from floating car data, a new error indicator is introduced that relates accuracy of prediction to accuracy of measure. Validation results highlighted that the spatial architecture of the Bayesian network is advantageous in standard conditions, where a priori knowledge is more significant, while mono-dimensional time series revealed to be more valuable in the few cases of non-recurrent congestion conditions observed in the data set. The results obtained suggested introducing a supervisor framework that selects the most suitable prediction depending on the detected traffic regimes.     

Estimating historical hourly traffic volumes via machine learning and vehicle probe data: A Maryland case study

This paper focuses on the problem of estimating historical traffic volumes between sparsely-located traffic sensors, which transportation agencies need to accurately compute statewide performance measures. To this end, the paper examines applications of vehicle probe data, automatic traffic recorder counts, and neural network models to estimate hourly volumes in the Maryland highway network, and proposes a novel approach that combines neural networks with an existing profiling method. On average, the proposed approach yields 24% more accurate estimates than volume profiles, which are currently used by transportation agencies across the US to compute statewide performance measures. The paper also quantifies the value of using vehicle probe data in estimating hourly traffic volumes, which provides important managerial insights to transportation agencies interested in acquiring this type of data. For example, results show that volumes can be estimated with a mean absolute percent error of about 21% at locations where average number of observed probes is between 30 and 47 vehicles/h, which provides a useful guideline for assessing the value of probe vehicle data from different vendors.     

Dynamic prediction of traffic volume through Kalman filtering theory

Two models employing Kalman filtering theory are proposed for predicting short-term traffic volume. Prediction parameters are improved using the most recent prediction error and better volume prediction on a link is achieved by taking into account data from a number of links. Based on data collected from a street network in Nagoya City, average prediction error is found to be less than 9% and maximum error less than 30%. The new models perform substantially (up to 80%) better than UTCS-2.     

Origin-destination pattern estimation based on trajectory reconstruction using automatic license plate recognition data

Origin-destination (OD) pattern estimation is a vital step for traffic simulation applications and active urban traffic management. Many methods have been proposed to estimate OD patterns based on different data sources, such as GPS data and automatic license plate recognition (ALPR) data. These data can be used to identify vehicle IDs and estimate their trajectories by matching vehicles identified by different sensors across the network. OD pattern estimation using ALPR data remains a challenge in real-life applications due to the difficulty in reconstructing vehicle trajectories. This paper proposes an offline method for historical OD pattern estimation based on ALPR data. A particle filter is used to estimate the probability of a vehicle’s trajectory from all possible candidate trajectories. The initial particles are generated by searching potential paths in a pre-determined area based on the time geography theory. Then, the path flow estimation process is conducted through dividing the reconstructed complete trajectories of all detected vehicles into multiple trips. Finally, the OD patterns are estimated by adding up the path flows with the same ODs. The proposed method was implemented on a real-world traffic network in Kunshan, China and verified through a calibrated microscopic traffic simulation model. The results show that the MAPEs of the OD estimation are lower than 19%. Further investigation shows that there exists a minimum required ALPR sampling rate (60% in the test network) for accurately estimating the OD patterns. The findings of this study demonstrate the effectiveness of the proposed method in OD pattern estimation.     

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.     

A data fusion approach for real-time traffic state estimation in urban signalized links

Real-time estimation of the traffic state in urban signalized links is valuable information for modern traffic control and management. In recent years, with the development of in-vehicle and communication technologies, connected vehicle data has been increasingly used in literature and practice. In this work, a novel data fusion approach is proposed for the high-resolution (second-by-second) estimation of queue length, vehicle accumulation, and outflow in urban signalized links. Required data includes input flow from a fixed detector at the upstream end of the link as well as location and speed of the connected vehicles. A probability-based approach is derived to compensate the error associated with low penetration rates while estimating the queue tail location, which renders the proposed methodology more robust to varying penetration rates of connected vehicles. A well-defined nonlinear function based on traffic flow theory is developed to attain the number of vehicles inside the queue based on queue tail location and average speed of connected vehicles. The overall scheme is thoroughly tested and demonstrated in a realistic microscopic simulation environment for three types of links with different penetration rates of connected vehicles. In order to test the efficiency of the proposed methodology in case that data are available at higher sampling times, the estimation procedure is also demonstrated for different time resolutions. The results demonstrate the efficiency and accuracy of the approach for high-resolution estimation, even in the presence of measurement noise.     

A new fuzzy approach to estimate the O–D matrix from link volumes

Abstract

Estimation of the origin–destination (O–D) trip demand matrix plays a key role in travel analysis and transportation planning and operations. Many researchers have developed different O–D matrix estimation methods using traffic counts, which allow simple data collection as opposed to the costly traditional direct estimation methods based on home and roadside interviews.

In this paper, we present a new fuzzy model to estimate the O–D matrix from traffic counts. Since link data only represent a snapshot situation, resulting in inconsistency of data and poor quality of the estimated O–Ds, the proposed method considers the link data as a fuzzy number that varies within a certain bandwidth. Shafahi and Ramezani's fuzzy assignment method is improved upon and used to assign the estimated O–D matrix, which causes the assigned volumes to be fuzzy numbers similar to what is proposed for observed link counts. The shortest path algorithm of the proposed method is similar to the Floyd–Warshall algorithm, and we call it the Fuzzy Floyd–Warshall Algorithm. A new fuzzy comparing index is proposed by improving the fuzzy comparison method developed by Dubois and Prade to estimate and compare the distance between the assigned and observed link volumes. The O–D estimation model is formulated as a convex minimization problem based on the proposed fuzzy index to minimize the fuzzy distance between the observed and assigned link volumes. A gradient-based method is used to solve the problem. To ensure the original O–D matrix does not change more than necessary during the iterations, a fuzzy rule-based approach is proposed to control the matrix changes.     

Travel time estimation for urban road networks using low frequency probe vehicle data

The paper presents a statistical model for urban road network travel time estimation using vehicle trajectories obtained from low frequency GPS probes as observations, where the vehicles typically cover multiple network links between reports. The network model separates trip travel times into link travel times and intersection delays and allows correlation between travel times on different network links based on a spatial moving average (SMA) structure. The observation model presents a way to estimate the parameters of the network model, including the correlation structure, through low frequency sampling of vehicle traces. Link-specific effects are combined with link attributes (speed limit, functional class, etc.) and trip conditions (day of week, season, weather, etc.) as explanatory variables. The approach captures the underlying factors behind spatial and temporal variations in speeds, which is useful for traffic management, planning and forecasting. The model is estimated using maximum likelihood. The model is applied in a case study for the network of Stockholm, Sweden. Link attributes and trip conditions (including recent snowfall) have significant effects on travel times and there is significant positive correlation between segments. The case study highlights the potential of using sparse probe vehicle data for monitoring the performance of the urban transport system.     

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.     

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

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

The estimation of a time-dependent OD trip table with vehicle trajectory samples

Abstract

In this paper we discuss a dynamic origin–destination (OD) estimation problem that has been used for identifying time-dependent travel demand on a road network. Even though a dynamic OD table is an indispensable data input for executing a dynamic traffic assignment, it is difficult to construct using the conventional OD construction method such as the four-step model. For this reason, a direct estimation method based on field traffic data such as link traffic counts has been used. However, the method does not account for a logical relationship between a travel demand pattern and socioeconomic attributes. In addition, the OD estimation method cannot guarantee the reliability of estimated results since the OD estimation problem has a property named the ‘underdetermined problem.’ In order to overcome such a problem, the method developed in this paper makes use of vehicle trajectory samples with link traffic counts. The new method is applied to numerical examples and shows promising capability for identifying a temporal and spatial travel demand pattern.     

Exposing the role of exposure: Public transport network risk analysis

Network risk assessment takes into consideration the probability that adverse events occur and the impacts of such disruptions on network functionality. In the context of transport networks, most studies have focused on vulnerability, the reduction in performance indicators given that a disruption occurs. This study presents and applies a method to explicitly account for exposure in identifying and evaluating link criticality in public transport networks. The proposed method is compared with conventional measures that lack exposure information. A criticality assessment is performed by accounting for the probability of a certain event occurring and the corresponding welfare loss. The methodology was applied for a multi-modal public transport network in the Netherlands where data concerning disruptions was available. The results expose the role of exposure in determining link criticality and overall network vulnerability. The findings demonstrate that disregarding exposure risks prioritizing links with high passenger volumes over links with a higher failure probability that are significantly more critical to network performance. The inclusion of exposure allows performing a risk analysis and has consequences on assessing mitigation measures and investment priorities.     

Decomposing travel times measured by probe-based traffic monitoring systems to individual road segments

In probe-based traffic monitoring systems, traffic conditions can be inferred based on the position data of a set of periodically polled probe vehicles. In such systems, the two consecutive polled positions do not necessarily correspond to the end points of individual links. Obtaining estimates of travel time at the individual link level requires the total traversal time (which is equal to the polling interval duration) be decomposed. This paper presents an algorithm for solving the problem of decomposing the traversal time to times taken to traverse individual road segments on the route. The proposed algorithm assumes minimal information about the network, namely network topography (i.e. links and nodes) and the free flow speed of each link. Unlike existing deterministic methods, the proposed solution algorithm defines a likelihood function that is maximized to solve for the most likely travel time for each road segment on the traversed route. The proposed scheme is evaluated using simulated data and compared to a benchmark deterministic method. The evaluation results suggest that the proposed method outperforms the bench mark method and on average improves the accuracy of the estimated link travel times by up to 90%.     

A virtual vehicle probe model for time-dependent travel time estimation on signalized arterials

Estimation of time-dependent arterial travel time is a challenging task because of the interrupted nature of urban traffic flows. Many research efforts have been devoted to this topic, but their successes are limited and most of them can only be used for offline purposes due to the limited availability of traffic data from signalized intersections. In this paper, we describe a real-time arterial data collection and archival system developed at the University of Minnesota, followed by an innovative algorithm for time-dependent arterial travel time estimation using the archived traffic data. The data collection system simultaneously collects high-resolution “event-based” traffic data including every vehicle actuations over loop detector and every signal phase changes from multiple intersections. Using the “event-based” data, we estimate time-dependent travel time along an arterial by tracing a virtual probe vehicle. At each time step, the virtual probe has three possible maneuvers: acceleration, deceleration and no-speed-change. The maneuver decision is determined by its own status and surrounding traffic conditions, which can be estimated based on the availability of traffic data at intersections. An interesting property of the proposed model is that travel time estimation errors can be self-corrected, because the trajectory differences between a virtual probe vehicle and a real one can be reduced when both vehicles meet a red signal phase and/or a vehicle queue. Field studies at a 11-intersection arterial corridor along France Avenue in Minneapolis, MN, demonstrate that the proposed model can generate accurate time-dependent travel times under various traffic conditions.     

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.