Destination Matrix Estimation Research Articles

Data driven origin–destination matrix estimation on large networks—A joint origin–destination-path-choice formulation

This paper presents a novel approach to data-driven time-dependent origin–destination (OD) estimation using a joint origin–destination-path choice formulation, inspired by the well-known equivalence of doubly constraint gravity models and multinomial logit models for joint O–D choice. This new formulation provides a theoretical basis and generalizes an earlier contribution. Although including path choice increases the dimensionality of the problem, it also dramatically improves the quality of the data one can directly use to solve it (e.g. measured path travel times versus coarse centroid-to-centroid travel times); and opens up possibilities to combine different assimilation techniques in a single framework: (1) fast shortest path set computation using static (e.g. road type) and dynamic (speed, travel time) link properties; (2) predicting a “prior OD matrix” using the resulting path-shares and (estimated or measured) production and attraction totals; and (3) scaling/constraining this prior using link flows (informative of demand). If the resulting system of equations has insufficient rank, we use principal component analysis to reduce the dimensionality, solve this reduced problem, and transform that solution back to a full OD matrix. Comprehensive tests and sensitivity analysis on 7 networks with different sizes and characteristics give an empirical underpinning of the extended equivalence principle; demonstrate good accuracy and reliability of the OD estimation method overall; and suggest that the method is robust with respect to major assumptions and contributing factors.

Origin–destination matrix estimation for public transport: A multi-modal weighted graph approach

Estimating the large-scale Origin–Destination (OD) matrices for multi-modal public transport (PT) in different cities can vary largely based on the network itself, what modes exist, and what traffic data is available. In this study, to overcome the issue of traffic data unavailability and effectively estimate the demand matrix, we employ several data sets like the total boarding and alighting, smart card as well as the General Transit Feed Specification (GTFS) in order to capture the PT dynamic patronage patterns.First, we propose a new method to model the dynamic large-scale stop-by-stop OD matrix for PT networks by developing a new enhancement of the Gravity Model via graph theory and Shannon’s entropy. Second, we introduce a method entitled “Entropy-weighted Ensemble Cost Features” that incorporates diverse sources of costs extracted from traffic states and the topological information in the network, scaled appropriately. Last, we compare the efficiency of a single travel cost versus various combinations of travel costs when using traditional methods like the Traverse Searching and the Hyman’s method, alongside our proposed “Entropy-weighted” method; we demonstrate the advantages of using topological features as travel costs and prove that our method, coupled with multi-modal PT OD matrix modelling, is superior to traditional methods in improving estimation accuracy, as evidenced by lower MAE, MAPE and RMSE, and reducing computing time.

Evaluating the Effect of Multiple Data Types on a Large Scale Static Origin–Destination Matrix Estimation, Case Study of Tehran, Iran

Evaluating the Effect of Multiple Data Types on a Large Scale Static Origin–Destination Matrix Estimation, Case Study of Tehran, Iran

Simulation-based dynamic origin–destination matrix estimation on freeways: A Bayesian optimization approach

This study focuses on dynamic origin–destination demand estimation problem on freeway networks. Existing studies on this problem rely on high-coverage of traffic measurements and assumptions on travel times, exhibiting limitations in real-world applications. We formulate the problem as a bi-level programming model, where micro-simulations are incorporated to precisely model traffic flows/travel times on freeways. The bi-level programming model cannot provide explicit closed-form expressions for the objective function and its derivatives, and also intrinsically high-dimensional. Thus, it is highly challenging to find efficient solution algorithms. In this regard, a problem-specific and computationally efficient Bayesian optimization approach is designed. Herein, a novel surrogate model is proposed by embedding a physical surrogate model (it characterizes underlying physical mechanisms and provides global yet less precise approximations) into a functional surrogate model (it provides precise local approximations). The embedding provides problem-specific knowledge for the surrogate model. More importantly, it also restricts the feasible region, enabling the surrogate model to efficiently deal with high-dimensional problems. Gaussian process can be served as the functional surrogate model. Two linear physical surrogate models are proposed to capture interactions between travel demand and traffic measurements. To deal with constraints in the surrogate model, a projection-distance based acquisition function is designed. In searching for new points, the proposed acquisition function is capable of assigning unique weight of exploration to each feasible solution. The proposed approach is validated based on a freeway corridor example, which indicates its outperformance over existing dynamic origin–destination estimation methods in terms of computational efficiency and solution accuracy.

On Heterogenous Sampling Rates in Origin–Destination Matrix Estimation Based on Trajectory Data and Link Counts

Being a fundamental metric of the transportation network, the origin–destination (O-D) flow matrix is a critical input for various transportation models and studies. This paper deals with the estimation of an O-D matrix of trip flows based on two kinds of data: probe trajectory data and local traffic counts. A Bayesian assignment framework is developed for demonstrating the relationship between the link probe sampling rates and the fractional contributions from the sampling rates on different O-D pairs. The unknown O-D matrix is estimated by applying cross entropy minimization using a prior matrix from the probe trajectories, along with the Bayesian assignment rules on link sample rates as the constraints. The methodology was applied using floating car data and camera link flow counts for a numerical experiment. The results show that the method can achieve a robust estimation of O-D matrices, even using different prior matrices. The issue of the heterogeneous sampling rates can be well addressed with link count constraints, effectively correcting the unknown bias in the probe sampling. The case study using real data also proves the feasibility of mining observed trajectory data to obtain the assignment fractions and estimate the O-D matrix inversely, avoiding the conventional sophisticated process of traffic assignment modeling.

A practical approach to assignment-free Dynamic Origin–Destination Matrix Estimation problem

Dynamic traffic models require dynamic inputs, one of the main ones being the Dynamic Origin–Destinations (OD) matrices describing the variability over time of the trip patterns across the network. The Dynamic OD Matrix Estimation (DODME) is a challenging problem since no direct observations are available, and therefore one should resort to indirect estimation approaches. Among the most efficient approaches, the one that formulates the problem in terms of a bi-level optimization problem has been widely used. This formulation solves at the upper level a nonlinear optimization problem that minimizes some distance measures between observed and estimated link flow counts at certain counting stations located in a subset of links in the network, and at the lower level a traffic assignment that estimates these link flow counts assigning the current estimated matrix. The variants of this formulation differ in the analytical approaches that estimate the link flows in terms of the traffic assignment and their time dependencies. Since these estimations are based on a traffic assignment at the lower level, these analytical approaches, although numerically efficient, imply a high computational cost. The advent of ICT applications has made available new sets of traffic-related measurements enabling new approaches; under certain conditions, the data collected allows to estimate the most likely used paths, from which a de facto assignment matrix can be computed. This allows extracting empirically similar information to that provided by the dynamic traffic assignment that is used in the analytical approaches. This paper explores how to extract such information from the recorded commercial data, proposes a new constrained non-linear optimization model to solve the DODME problem, with a reduced number of variables linearly depending on network size instead of quadratically. Moreover, the bilevel iterative process and the traffic assignment need are avoided. Validation and computational results on its performance are presented.

Exploring the Direct and Indirect Use of ICT Measurements in DODME (Dynamic OD Matrix Estimation)

The estimation of the network traffic state, its likely short-term evolution, the prediction of the expected travel times in a network, and the role that mobility patterns play in transport modeling is usually based on dynamic traffic models, whose main input is a dynamic origin–destination (OD) matrix that describes the time dependencies of travel patterns; this is one of the reasons that have fostered large amounts of research on the topic of estimating OD matrices from the available traffic information. The complexity of the problem, its underdetermination, and the many alternatives that it offers are other reasons that make it an appealing research topic. The availability of new traffic data measurements that were prompted by the pervasive penetration of information and communications technology (ICT) applications offers new research opportunities. This study focused on GPS tracking data and explored two alternative modeling approaches regarding how to account for this new information to solve the dynamic origin–destination matrix estimation (DODME) problem, either including it as an additional term in the formulation model or using it in a data-driven modeling method to propose new model formulations. Complementarily, independently of the approach used, a key aspect is the quality of the estimated OD, which, as recent research has made evident, is not well measured by the conventional indicators. This study also explored this problem for the proposed approaches by conducting synthetic computational experiments to control and understand the process.

The value of additional data for public transport origin–destination matrix estimation

Passenger origin–destination data is an important input for public transport planning. In recent years, new data sources have become increasingly common through the use of the automatic collection of entry counts, exit counts and link flows. However, collecting such data can be sometimes costly. The value of additional data collection hence has to be weighed against its costs. We study the value of additional data for estimating time-dependent origin–destination matrices, using a case study from the London Piccadilly underground line. Our focus is on how the precision of the estimated matrix increases when additional data on link flow, destination count and/or average travel distance is added, starting from origin counts only. We concentrate on the precision of the most policy-relevant estimation outputs, namely, link flows and station exit flows. Our results suggest that link flows are harder to estimate than exit flows, and only using entry and exit data is far from enough to estimate link flows with any precision. Information about the average trip distance adds greatly to the estimation precision. The marginal value of additional destination counts decreases only slowly, so a relatively large number of exit station measurement points seem warranted. Link flow data for a subset of links hardly add to the precision, especially if other data have already been added.

Temporal origin–destination matrix estimation of passenger car trips. Case study: Medellin, Colombia

This paper develops a passenger car demand synthesis model based on entropy maximization to estimate origin–destination matrices for passenger cars trips using traffic counts for different years in an urban area. The model discussed in this paper improve current Origin-Destination matrix estimation techniques incorporating the total number of passenger car trips in the transportation network as a constraint, and secondary data sources for different years, giving a point of comparison for the results.The resulting model reveals that the trips are an exponential function of the Lagrange multipliers related to the trip cost, the observed traffic counts in the links, and the total number of passenger cars trips in the transportation network.Based on the results of this research, the authors recommend to the transportation authorities to collect traffic counts in strategic locations in the urban road network for different years to estimate OD matrices in an easier and cheaper way than the traditional OD surveys.The performance of the formulation for different years (2005–2008) is tested in the Medellín (Colombia) network.

A Bicycle Origin–Destination Matrix Estimation Based on a Two-Stage Procedure

As more people choose to travel by bicycle, transportation planners are beginning to recognize the need to rethink the way they evaluate and plan transportation facilities to meet local mobility needs. A modal shift towards bicycles motivates a change in transportation planning to accommodate more bicycles. However, the current methods to estimate bicycle volumes on a transportation network are limited. The purpose of this research is to address those limitations through the development of a two-stage bicycle origin–destination (O–D) matrix estimation process that would provide a different perspective on bicycle modeling. From the first stage, a primary O–D matrix is produced by a gravity model, and the second stage refines that primary matrix generated in the first stage using a Path Flow Estimator (PFE) to build the finalized O–D demand. After a detailed description of the methodology, the paper demonstrates the capability of the proposed model for a bicycle demand matrix estimation tool with a real network case study.

Estimation of origin–destination matrices using link counts and partial path data

After several decades of work by several talented researchers, estimation of the origin–destination matrix using traffic data has remained very challenging. This paper presents a set of innovative methods for estimation of the origin–destination matrix of large-scale networks, using vehicle counts on links, partial path data obtained from an automated vehicle identification system, and combinations of both data. These innovative methods are used to solve three origin–destination matrix estimation models. The first model is an extension of Spiess’s model which uses vehicle count data while the second model is an extension of Jamali’s model and it uses partial path data. The third model is a multiobjective model which utilizes combinations of vehicle counts and partial path data. The methods were tested to estimate the origin–destination matrix of a large-scale network from Mashhad City with 163 traffic zones and 2093 links, and the results were compared with the conventional gradient-based algorithm. The results show that the innovative methods performed better as compared to the gradient-based algorithm.

Estimation of Origin – Destination Matrix from Traffic Counts Based On Fuzzy Logic

Determining trip demand matrix is among the basic data in transportation planning. This matrix is derived by surveys, interviews with citizens or questionnaires that required time, money and manpower. Thus, in recent years, demand estimation methods based on network information is taken into consideration. In these methods with the information including: volume, travel time, capacity of the links and initial demand matrix it is possible to estimate the demand matrix. In this paper, we removed the additional parameters in previous studies and used a simple solution to estimate the matrix. This paper proposes a Fuzzy-PFE estimation method that allows to improve the estimation performances of PFE estimator. The objective function presented based on the reduction of travel time and travel time of routs in networks is uncertain. The method is developed by fuzzy sets theory and fuzzy programming that seems to be convenient theoretical framework to represent uncertainty in the available data. The new model is the removal of iterative process of origin - destination matrix estimation using travel time and increase convergence of the model for the large-scale and congested networks by applying little changes in the basic model. In this paper we used TRANSCAD Software to determine the shortest path in the network and optimization of objective function is performed by CPLEX.

Origin–destination synthesis for aviation network data: examining hub operations in the domestic and international US markets

SummaryHub‐and‐spoke networking is a key feature of current aviation markets in which hubs, as connecting points, function to consolidate and redistribute flows. This indicates that observation of traffic on a segment does not necessarily convey information about the origin to destination routing of passenger journeys because of the unavoidable detours in the system. This paper examines the heterogeneity of the flow composition in domestic and international US markets, which in turn allows us to observe the variation of operations across major hubs. A modified Route Flow Estimator for origin–destination synthesis (or origin–destination matrix estimation) is designed to decompose the segment traffic into itinerary‐based passenger trips. Several public and commercial databases, which are easily accessible, are exploited (and reconciled) for the model in order to (i) generate possible trip itineraries using those segment markets, and (ii) link data‐driven operational conditions with the underlying segment flows. The results are validated with US domestic trip observations and empirical knowledge related to the air transportation system. Then, the variability of the hub operations is examined based on sensitivity tests using the model parameters. From the resolution of itinerary‐based estimates, we observe that major airports' hub operations are spatially uneven, particularly with respect to domestic and international connecting passengers. Copyright © 2017 John Wiley & Sons, Ltd.

A zonal inference model based on observed smart-card transactions for Santiago de Chile

The collection of origin–destination data for a city is an important but often costly task. This way, there is a need to develop more efficient and inexpensive methods of collecting information about citizens’ travel patterns. In this line, this paper presents a generic methodology that allows to infer the origin and destination zones for an observed trip between two public transport stops (i.e., bus stops or metro stations) using socio-economic, land use, and network information. The proposed zonal inference model follows a disaggregated Logit approach including size variables. The model enables the estimation of a zonal origin–destination matrix for a city, if trip information passively collected by a smart-card payment system is available (in form of a stop-to-stop matrix). The methodology is applied to the Santiago de Chile’s morning peak period, with the purpose of serving as input for a public transport planning computational tool. To estimate the model, information was gathered from different sources and processed into a unified framework; data included a survey conducted at public transport stops, land use information, and a stop-to-stop trip matrix. Additionally, a zonal system with 1176 zones was constructed for the city, including the definition of its access links and associated distances. Our results shows that, ceteris paribus, zones with high numbers of housing units have higher probabilities of being the origin of a morning peak trip. Likewise, health facilities, educational, residential, commercial, and offices centres have significant attraction powers during this period. In this sense, our model manages to capture the expected effects of land use on trip generation and attraction. This study has numerous policy implications, as the information obtained can be used to predict the impacts of changes in the public transport network (such as extending routes, relocating their stops, designing new routes or changing the fare structure). Further research is needed to improve the zonal inference formulation and origin–destination matrix estimation, mainly by including better cost measures, and dealing with survey and data limitations.

C-SPSA: Cluster-wise simultaneous perturbation stochastic approximation algorithm and its application to dynamic origin–destination matrix estimation

The simultaneous perturbation stochastic approximation (SPSA) algorithm has been used in the literature for the solution of the dynamic origin–destination (OD) estimation problem. Its main advantage is that it allows quite general formulations of the problem that can include a wide range of sensor measurements. While SPSA is relatively simple to implement, its performance depends on a set of parameters that need to be properly determined. As a result, especially in cases where the gradient of the objective function changes quickly, SPSA may not be as stable and even diverge. A modification of the SPSA algorithm, referred to as c-SPSA, is proposed which applies the simultaneous perturbation approximation of the gradient within a small number of carefully constructed “homogeneous” clusters one at a time, as opposed to all elements at once. The paper establishes the theoretical properties of the new algorithm with an upper bound for the bias of the gradient estimate and shows that it is lower than the corresponding SPSA bias. It also proposes a systematic approach, based on the k-means algorithm, to identify appropriate clusters. The performance of c-SPSA, with alternative implementation strategies, is evaluated in the context of estimating OD flows in an actual urban network. The results demonstrate the efficiency of the proposed c-SPSA algorithm in finding better OD estimates and achieve faster convergence and more robust performance compared to SPSA with fewer overall number of function evaluations.

A fuzzy set-based approach to origin–destination matrix estimation in urban traffic networks with imprecise data

An important issue in the management of urban traffic networks is the estimation of origin–destination (O–D) matrices whose entries represent the travel demands of network users. We discuss the challenges of O–D matrix estimation with incomplete, imprecise data. We propose a fuzzy set-based approach that utilises successive linear approximation. The fuzzy sets used have triangular membership functions that are easy to interpret and enable straightforward calibration of the parameters that weight the discrepancy between observed data and those predicted by the proposed approach. The method is potentially useful when prior O–D matrix entry estimates are unavailable or scarce, requiring trip generation information on origin departures and/or destination arrivals, leading to multiple modelling alternatives. The method may also be useful when there is no O–D matrix that can be user-optimally assigned to the network to reproduce observed link counts exactly. The method has been tested on some numerical examples from the literature and the results compare favourably with the results of earlier methods. It has also been successfully used to estimate O–D matrices for a practical urban traffic network in Brazil.

A fixed point approach to origin–destination matrices estimation using uncertain data and fuzzy programming on congested networks

Origin–destination (O–D) matrix estimation methods based on traffic counts have been largely discussed and investigated. The most used methods are based on Generalised Least Square estimators (GLS) that use as input data a starting O–D matrix and a set of traffic counts. In addition to traffic counts, the analysts could know other general information about travel demand or link flows, based on their experience, or spot data, but few works deal with the matter of including effectively these sources of information.This paper proposes a Fuzzy-GLS estimation method that allows to improve the estimation performances of classic GLS estimator by including, in addition to traffic counts, uncertain information about starting O–D demand (i.e. outdated estimates, spot data, expert knowledge, etc.). The methods explicitly take into account the relevant level of uncertainty by taking as much advantage as possible from the few vague available data. The method is developed using fuzzy sets theory and fuzzy programming that seems to be a convenient theoretical framework to represent uncertainty in the available data. A solution algorithm for the proposed problem is also presented. The method has been tested by numerical applications and then compared to the classical GLS method under different sets of constraints to the problem.

Treating Uncertain Demand Information in Origin–Destination Matrix Estimation with Traffic Counts

This paper investigates the problem of estimating dynamic origin–destination (O–D) trip matrices in large-scale transportation networks, using automatic link traffic counts and uncertain prior demand information, to facilitate the real-time monitoring of network traffic conditions through intelligent transportation systems. The paper proposes and evaluates the performance of two algorithms to estimate the temporal distribution of trip departures used to produce dynamic O–D matrices, through several test experimentations in a real case study. The accuracy and the computing speed of the proposed algorithms is investigated in relation to different bounds, wherein trip departure estimates are sought to be included, levels of link count availability and network sizes. Results show that an optimization algorithm proposed for the fast estimation of trip departure rates with incorporated lower and upper bound constraints lead to dynamic O–D matrices with considerably increased reliability, in comparison to the al...

Discussion of “Multiple-Vehicle Origin–Destination Matrix Estimation from Traffic Counts Using Genetic Algorithm” by Seungkirl Baek, Hyunmyung Kim, and Yongtaek Lim

A discussion of an article with the aforementioned title, published in this journal (Vol. 130, No. 3, May/June 2004), is presented. The original paper suggested a multiple-vehicle origin-destination matrix estimation from traffic counts using a genetic algorithm (GAMUC). The discussers express reservations about the practicality, particularly in relation to computational efficiency, of the proposed algorithm for application in realistic transportation network problems or even for simpler artificial network situations.

Multiple-Vehicle Origin–Destination Matrix Estimation from Traffic Counts Using Genetic Algorithm

Existing methods for estimating origin–destination (O–D) matrix from link traffic counts cannot consider multiple-vehicle information, which is easily obtained from a field survey. Those methods use a single-vehicle information and it may decrease the performance of an O–D matrix estimator. Up until now, there is little research regarding multiple-vehicle O–D matrix estimation from multiple-vehicle link counts. This paper suggests a multiple-vehicle O–D matrix estimation from traffic counts using a genetic algorithm (GAMUC). From the numerical tests, we found that the performance of GAMUC was better than those of the previous methods for the error of target O–D matrix and for the number of link counts. In this paper, we also found that the method provided good results on the error of target O–D matrix and on the varied O–D matrix structure, which occurred when the target O–D matrix was different from the true one.