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.     

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.     

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 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.     

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.     

Development of origin–destination matrices using mobile phone call data

In this research, we propose a methodology to develop OD matrices using mobile phone Call Detail Records (CDR) and limited traffic counts. CDR, which consist of time stamped tower locations with caller IDs, are analyzed first and trips occurring within certain time windows are used to generate tower-to-tower transient OD matrices for different time periods. These are then associated with corresponding nodes of the traffic network and converted to node-to-node transient OD matrices. The actual OD matrices are derived by scaling up these node-to-node transient OD matrices. An optimization based approach, in conjunction with a microscopic traffic simulation platform, is used to determine the scaling factors that result best matches with the observed traffic counts. The methodology is demonstrated using CDR from 2.87 million users of Dhaka, Bangladesh over a month and traffic counts from 13 key locations over 3 days of that month. The applicability of the methodology is supported by a validation study.     

Modeling origin-destination uncertainty using network sensor and survey data and new approaches to robust control

This study develops new methods for network assessment and control by taking explicit account of demand variability and uncertainty using partial sensor and survey data while imposing equilibrium conditions during the data collection phase. The methods consist of rules for generating possible origin–destination (OD) matrices and the calculation of average and quantile network costs. The assessment methodology leads to improved decision-making in transport planning and operations and is used to develop management and control strategies that result in more robust network performance. Specific contributions in this work consist of: (a) Characterization of OD demand variability, specifically with or without equilibrium assumptions during data collection; (b) exhibiting the highly disconnected nature of OD space demonstrating that many current approaches to the problem of optimal control may be computationally intractable; (c) development of feasible Monte Carlo procedures for the generation of possible OD matrices used in an assessment of network performance; and (d) calculation of robust network controls, with state-of-the-art cost estimation, for the following strategies: Bayes, p-quantile and NBNQ (near-Bayes near-Quantile). All strategies involve the simultaneous calculation of controls and equilibrium conditions. A numerical example for a moderate sized network is presented where it is shown that robust controls can provide approx. 20% cost reduction.     

Vehicle identification sensor models for origin–destination estimation

The traditional approach to origin–destination (OD) estimation based on data surveys is highly expensive. Therefore, researchers have attempted to develop reasonable low-cost approaches to estimating the OD vector, such as OD estimation based on traffic sensor data. In this estimation approach, the location problem for the sensors is critical. One type of sensor that can be used for this purpose, on which this paper focuses, is vehicle identification sensors. The information collected by these sensors that can be employed for OD estimation is discussed in this paper. We use data gathered by vehicle identification sensors that include an ID for each vehicle and the time at which the sensor detected it. Based on these data, the subset of sensors that detected a given vehicle and the order in which they detected it are available. In this paper, four location models are proposed, all of which consider the order of the sensors. The first model always yields the minimum number of sensors to ensure the uniqueness of path flows. The second model yields the maximum number of uniquely observed paths given a budget constraint on the sensors. The third model always yields the minimum number of sensors to ensure the uniqueness of OD flows. Finally, the fourth model yields the maximum number of uniquely observed OD flows given a budget constraint on the sensors. For several numerical examples, these four models were solved using the GAMS software. These numerical examples include several medium-sized examples, including an example of a real-world large-scale transportation network in Mashhad.     

Estimation of origin‐destination matrices for a multimodal public transit network

This paper presents a procedure for the estimation of origin‐destination (O‐D) matrices for a multimodal public transit network. The system consists of a number of favored public transit modes that are obtained from a modal split process in a traditional four‐step transportation model. The demand of each favored mode is assigned to the multimodal network, which is comprised of a set of connected links of different public transit modes. An entropy maximization procedure is proposed to simultaneously estimate the O‐D demand matrices of all favored modes, which are consistent with target data sets such as the boarding counts and line segment flows that are observed directly in the network. A case study of the Hong Kong multimodal transit network is used to demonstrate the effectiveness of the proposed methodology.     

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.     

Validating travel behavior estimated from smartcard data

In this paper, we present a validation of public transport origin–destination (OD) matrices obtained from smartcard and GPS data. These matrices are very valuable for management and planning but have not been validated until now. In this work, we verify the assumptions and results of the method using three sources of information: the same database used to make the estimations, a Metro OD survey in which the card numbers are registered for a group of users, and a sample of volunteers. The results are very positive, as the percentages of correct estimation are approximately 90% in all cases.     

A theoretical foundation for the relationship between generalized origin–destination matrix and flow matrix based on ordinal graph trajectories

This paper shows the relationship between flow, generalized origin–destination (OD), and alternative route flow from a set of ordinal graph trajectories. In contrast to traffic assignment methods that employ OD matrix to produce flow matrix, we use ordinal trajectory on a network graph as input and produce both the generalized OD matrix and the flow matrix, with the alternative and substitute route flow matrices as additional outputs. By using linear algebra‐like operations on matrix sets, the relationship between network utilization (in terms of flow, generalized OD, alternative route flow, and desire line) and network structure (in terms of distance matrix and adjacency matrix) are derived. Copyright © 2012 John Wiley & Sons, Ltd.     

Fine-grained OD estimation with automated zoning and sparsity regularisation

Given a road network, a fundamental object of interest is the matrix of origin destination (OD) flows. Estimation of this matrix involves at least three sub-problems: (i) determining a suitable set of traffic analysis zones, (ii) the formulation of an optimisation problem to determine the OD matrix, and (iii) a means of evaluating a candidate estimate of the OD matrix. This paper describes a means of addressing each of these concerns. We propose to automatically uncover a suitable set of traffic analysis zones based on observed link flows. We then employ regularisation to encourage the estimation of a sparse OD matrix. We finally propose to evaluate a candidate OD matrix based on its predictive power on held out link flows. Analysis of our approach on a real-world transport network reveals that it discovers automated zones that accurately capture regions of interest in the network, and a corresponding OD matrix that accurately predicts observed link flows.     

Mobile phone data in transportation research: methods for benchmarking against other data sources

The ubiquity of personal cellular phones in society has led to a surging interest in using Big Data generated by mobile phones in transport research. Studies have suggested that the vast amount of data could be used to estimate origin–destination (OD) matrices, thereby potentially replacing traditional data sources such as travel surveys. However, constructing OD matrices from mobile phone data (MPD) entails multiple challenges, and the lack of ground truth hampers the evaluation and validation of the estimated matrices. Furthermore, national laws may prohibit the distribution of MPD for research purposes, compelling researchers to work with pre-compiled OD matrices with no insight into the methods used. In this paper, we analyse a set of such pre-compiled OD matrices from the greater Oslo area and perform validation procedures against several sources to assess the quality and robustness of the OD matrices as well as their usefulness in transportation planning applications. We find that while the OD matrices correlate well with other sources at a low resolution, the reliability decreases when a finer level of detail is chosen, particularly when comparing shorter trips between neighbouring areas. Our results suggest that coarseness of data and privacy concerns restrict the usefulness of MPD in transport research in the case where OD matrices are pre-compiled by the operator.

     

Statistical inference on transit route‐level origin–destination flows using automatic passenger counter data

We consider inferring transit route‐level origin–destination (OD) flows using large amounts of automatic passenger counter (APC) boarding and alighting data based on a statistical formulation. One critical problem is that we need to enumerate the OD flow matrices that are consistent with the APC data for each bus trip to evaluate the model likelihood function. The OD enumeration problem has not been addressed satisfactorily in the literature. Thus, we propose a novel sampler to avoid the need to enumerate OD flow matrices by generating them recursively from the first alighting stop to the last stop of the bus route of interest. A Markov chain Monte Carlo (MCMC) method that incorporates the proposed sampler is developed to simulate the posterior distributions of the OD flows. Numerical investigations on an operational bus route under a realistic OD structure demonstrate the superiority of the proposed MCMC method over an existing MCMC method and a state‐of‐the‐practice method. Copyright © 2015 John Wiley & Sons, Ltd.     

Estimation of mean and covariance of peak hour origin–destination demands from day-to-day traffic counts

This paper proposes a generalized model to estimate the peak hour origin–destination (OD) traffic demand variation from day-to-day hourly traffic counts throughout the whole year. Different from the conventional OD estimation methods, the proposed modeling approach aims to estimate not only the mean but also the variation (in terms of covariance matrix) of the OD demands during the same peak hour periods due to day-to-day fluctuation over the whole year. For this purpose, this paper fully considers the first- and second-order statistical properties of the day-to-day hourly traffic count data so as to capture the stochastic characteristics of the OD demands. The proposed model is formulated as a bi-level optimization problem. In the upper-level problem, a weighted least squares method is used to estimate the mean and covariance matrix of the OD demands. In the lower-level problem, a reliability-based traffic assignment model is adopted to take account of travelers’ risk-taking path choice behaviors under OD demand variation. A heuristic iterative estimation-assignment algorithm is proposed for solving the bi-level optimization problem. Numerical examples are presented to illustrate the applications of the proposed model for assessment of network performance over the whole year.     

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.     

Estimation of population origin–interchange–destination flows on multimodal transit networks

Previous research has combined automated fare-collection (AFC) and automated vehicle-location (AVL) data to infer the times and locations of passenger origins, interchanges (transfers), and destinations on multimodal transit networks. The resultant origin–interchange–destination flows (and the origin–destination (OD) matrices that comprise those flows), however, represent only a sample of total ridership, as they contain only those journeys made using the AFC payment method that have been successfully recorded or inferred. This paper presents a method for scaling passenger-journey flows (i.e., linked-trip flows) using additional information from passenger counts at each station gate and bus farebox, thereby estimating the flows of non-AFC passengers and of AFC passengers whose journeys were not successfully inferred.The proposed method is applied to a hypothetical test network and to AFC and AVL data from London’s multimodal public transit network. Because London requires AFC transactions upon both entry and exit for rail trips, a rail-only OD matrix is extracted from the estimated multimodal linked-trip flows, and is compared to a rail OD matrix generated using the iterative proportional fitting method.     

On activity-based network design problems

This paper examines network design where OD demand is not known a priori, but is the subject of responses in household or user itinerary choices to infrastructure improvements. Using simple examples, we show that falsely assuming that household itineraries are not elastic can result in a lack in understanding of certain phenomena; e.g., increasing traffic even without increasing economic activity due to relaxing of space–time prism constraints, or worsening of utility despite infrastructure investments in cases where household objectives may conflict. An activity-based network design problem is proposed using the location routing problem (LRP) as inspiration. The bilevel formulation includes an upper level network design and shortest path problem while the lower level includes a set of disaggregate household itinerary optimization problems, posed as household activity pattern problem (HAPP) (or in the case with location choice, as generalized HAPP) models. As a bilevel problem with an NP-hard lower level problem, there is no algorithm for solving the model exactly. Simple numerical examples show optimality gaps of as much as 5% for a decomposition heuristic algorithm derived from the LRP. A large numerical case study based on Southern California data and setting suggest that even if infrastructure investments do not result in major changes in link investment decisions compared to a conventional model, the results provide much higher resolution temporal OD information to a decision maker. Whereas a conventional model would output the best set of links to invest given an assumed OD matrix, the proposed model can output the same best set of links, the same daily OD matrix, and a detailed temporal distribution of activity participation and travel from which changes in peak period OD patterns can be observed.