OD Matrices Research Articles

Optimisation models for estimating public transport OD matrices using different data types

Efficient public transport systems rely on origin–destination matrices (ODMs) estimation to accurately capture passenger travel patterns, enabling adjustments to frequencies and lines as needed. In this study, we address the ODM estimation problem by employing multiple bi-level programs that consider an outdated ODM and observed passenger flows on specific transit line arcs. Additionally, we consider various optional data types, including boarding and alighting data, as well as the structure of the outdated ODM and passenger flows, either all, separately, in combination, or none. In our study, we reformulate these bi-level programs into single-level models, and we use a commercial solver to address the problem in benchmark instances. In our analysis, we focus on the impact of incorporating different types of information into the estimation process, leading to valuable insights. We find that considering all the data types leads to a higher accuracy than only a subset of these data types. In particular, focussing only on boarding and alighting data leads to improvements in the estimation process, whereas considering only the structure of the outdated ODM and passenger flows leads to reduced accuracy compared to not incorporating either. The latter highlights the significance of data selection in ODM estimations.

Estimation of dynamic Origin–Destination matrices in a railway transportation network integrating ticket sales and passenger count data

Accurately estimating Origin–Destination matrices is a pressing challenge in transportation management and urban planning. However, traditional methods like travel surveys have limitations in availability and comprehensiveness, which have been further exacerbated by the recent changes in mobility patterns induced by the COVID-19 pandemic. To address this issue, we focused on the Trenord railway network in Lombardy, Italy, and developed an innovative pipeline to integrate ticket and subscription sales and Automated Passenger Counting data using the Iterative Proportional Fitting algorithm. By effectively navigating the complexities of diverse and incomplete data sources, our approach showcases adaptability across various transportation contexts. Our research offers a valuable tool for operators, policymakers, and researchers, bridging the gap between data availability and the need for precise OD matrices. Additionally, we emphasise the potential of dynamic OD matrices and showcase methods for detecting anomalies in mobility trends, interpreting them in the context of events from the last months of 2022.

Predicting cycling flows in cities without cycling data

Cycling is a potential tool to mitigate many of the problems faced by urban populations today. Encouraging the use of bicycles as a legitimate mobility tool, however, demands adequate knowledge of current mobility patterns, such as locations of trip generation and attraction. Unfortunately, cities usually do not gather enough data to adequately understand cycling demand. We propose models based on spatial econometrics and gradient boosted regression trees which can be trained with data from cities with mature cycling cultures and then applied to cities still in their cycling infancy to supply city officials with a better estimate of potential future OD matrices. We perform a case study in the Boston Metropolitan Area and show results comparing both types of models.

Impact of Traffic Flow Rate on the Accuracy of Short-Term Prediction of Origin-Destination Matrix in Urban Transportation Networks

Information about spatial distribution (OD flows) is a key element in traffic management systems in urban transport networks that enables efficient traffic control and decisions to redirect traffic to less congested sections of the network in emergencies. With the development of modern techniques of remote sensing, more and more advanced methods are used to measure traffic and determine OD flows. However, they may produce results with different levels of errors caused by various factors. The article examines the impact of traffic volume and its variability on the error values of short-term prediction of the OD matrix in the urban network. The OD flows were determined using a deep learning network based on data obtained from video remote sensing devices. These data were recorded at earlier intervals concerning the forecasting time. The extent to which there is a correlation between the size of OD flows and the prediction error was examined. The most frequently used measure of prediction accuracy, i.e., MAPE (mean absolute percentage error), was considered. The analysis carried out made it possible to determine the ranges of traffic flow rate for which the MAPE stabilizes at the level of approximately 6%. A set of video remote sensing devices was used to collect spatiotemporal data. They were located at the entrances and exits from the study area on important roads of a medium-sized city in Poland. The conclusions obtained may be helpful in further research on improving methods to determine OD matrices and estimate their reliability. This, in turn, involves the development of more precise methods that allow for reliable traffic forecasting and improve the efficiency of traffic management in urban areas.

TomTom Data Applications for the Assessment of Tactical Urbanism Interventions: The Case of Bologna

This work aims to evaluate how a temporary school square implemented in the city of Bologna under the principles of the tactical urbanism approach impacted on vehicular patterns through exploiting TomTom Floating Car Data (FCD) from before and after the intervention. Such data, passively collected by vehicles acting as moving sensors on the network, have been used for the analyses instead of data collected through usual methods. After statistical validation of available datasets through two-tailed paired Student’s t-tests, trend analyses have been performed on sample sizes and speed-related values to detect global variations in the first place, and more thoroughly among clusters of road segments based on graph-calculated distance from the intervention site. Results suggest that traffic flows have been relocated from segments directly affected by the intervention, where a decrease has been registered (−23.87%), towards adjacent streets or segments in a buffer area, which have recorded an increase (+3.51% and +3.50%, respectively), so the phenomenon of traffic evaporation did not take place as opposed to more widespread tactical urbanism interventions described in the literature. OD matrices per 15-min time fractions over the three selected peak time slots have been extracted in order to obtain reliable input data for a future development of traffic microsimulation models. The extraction method is based on least squares optimization problems solving systems of linear equations representing OD flows assigned to the observed link, after selecting a set of k¯ shortest paths through a Path Size Logit (PSL) model. Even though the availability of large amounts of data could not overcome typical underdetermination of the problem, due to the key issue of data dependence among traffic counts, the validation of retrieved matrices returned good results in terms of correlation between observed and estimated link flows. In the few cases where the quality of correlation fell, underlying causes have been investigated and the influence of outliers, amplified by the high fragmentation of the provided road graph, might represent the core problem.

A Stepwise Approach of Generating Agent-based Simulation Model for Brussels Using Ubiquitous Big Data

Synthetic travel demands are essential for agent-based traffic models which explicitly define the entire population of the study area's respective personal attributes and travel behaviours on disaggregated levels. Several papers specifically concentrate on synthetic population or travel demand generation, but they are seldom integrated into one pipeline. As such, this paper presents a pipeline for generating ABM using big data such as cell phone OD matrices. A case study of our pipeline is carried out for Brussels, Belgium, using the currently most popular ABM simulator MATSim, which results in the first ABM considering reality-based mobility behaviours for the "capital of the European Union". Notably, all data inputs of our pipeline are ubiquitous, which means our approach is transferable to modellers who would like to generate representative ABMs for their study areas in the future.

Toward learning dynamic origin-destination matrices from crowd density heatmaps

Knowing the origins and destinations of pedestrians’ paths is key to the initialization of crowd simulations. Unfortunately, they are difficult to measure in the real world. This is one major challenge for live predictions during events such as festivals, soccer games, protest marches, and many others. Sensor data can be used to feed real-world observations into simulations in real-time. As input data for this study, we use density heatmaps generated from real-world trajectory data obtained from stereo sensors. Density information is compact, of constant size, and in general easier to obtain than e.g., individual trajectories. Therefore, the information limitation improves the applicability to other scenarios. We include the absolute pedestrian trip counts from origins to destinations during a brief time interval in an OD matrix, including unknown destinations due to sensor errors. Our goal is to estimate these OD matrices from a series of density heatmaps for the same interval. For this, we compute the ground truth OD matrices and density heatmaps using real-world trajectory data from a train station. We employ linear regression as a statistical learning method for estimation. We observe that the linear share of the relationship between density and OD matrix is estimated successfully. Nevertheless, a portion of the data remains that cannot be explained. We attempt to overcome this difficulty with random forest as a nonlinear model. The results indicate that both a linear and a nonlinear model can estimate some features of the OD matrices. However, there is no clear winner in terms of the chosen metric, the R 2 score. Overall, our findings are a strong indicator that OD matrices can indeed be estimated from density heatmaps extracted automatically from sensors.

Real-Time System for Daily Modal Split Estimation and OD Matrices Generation Using IoT Data: A Case Study of Tartu City.

In recent years, we have witnessed the emergence of the implementation and integration of significant working solutions in transportation, especially within the smart city concept. A lot of cities in Europe and around the world support this initiative of making their cities smarter for enhanced mobility and a sustainable environment. In this paper, we present a case study of Tartu city, where we developed and designed a daily real-time system for extracting and performing a modal split analysis. Our web-based platform relied on an optimization approach for calibrating our simulation in order to perform the analysis with the use of real data streams from IoT devices installed around the city. The results obtained from our system demonstrated acceptable performance versus the quality of the available data source. In addition, our platform provides downloadable OD matrices for each mode of mobility for the community.

Real-Time Forecasting of Metro Origin-Destination Matrices with High-Order Weighted Dynamic Mode Decomposition

Forecasting short-term ridership of different origin-destination pairs (i.e., OD matrix) is crucial to the real-time operation of a metro system. However, this problem is notoriously difficult due to the large-scale, high-dimensional, noisy, and highly skewed nature of OD matrices. In this paper, we address the short-term OD matrix forecasting problem by estimating a low-rank high-order vector autoregression (VAR) model. We reconstruct this problem as a data-driven reduced-order regression model and estimate it using dynamic mode decomposition (DMD). The VAR coefficients estimated by DMD are the best-fit (in terms of Frobenius norm) linear operator for the rank-reduced full-size data. To address the practical issue that metro OD matrices cannot be observed in real time, we use the boarding demand to replace the unavailable OD matrices. Moreover, we consider the time-evolving feature of metro systems and improve the forecast by exponentially reducing the weights for historical data. A tailored online update algorithm is then developed for the high-order weighted DMD model (HW-DMD) to update the model coefficients at a daily level, without storing historical data or retraining. Experiments on data from two large-scale metro systems show that the proposed HW-DMD is robust to noisy and sparse data, and significantly outperforms baseline models in forecasting both OD matrices and boarding flow. The online update algorithm also shows consistent accuracy over a long time, allowing us to maintain an HW-DMD model at much low costs.

A Framework for the Comparative Analysis of Multi-Modal Travel Demand: Case Study on Brisbane Network

Comparative analysis of multimodal travel demand can help transport planners to improve the sustainability of a transport system. This research proposes a framework to qualitatively compare and analyze multimodal travel demand (of constrained and free transport modes) to identify opportunities and prioritize areas for improvement of constrained mode usage. The framework includes two methods. First method, CLAN is a Coarser Level ANalysis, comparing travel patterns and demand ratios of the two modes. Second method, FLAN is a Finer Level ANalysis based on density distributions of zones and OD pairs. The proposed framework is applied to the car (relatively free mode) and transit (constrained mode) OD matrices developed from observed Bluetooth and smart card data, respectively, for the Brisbane City Council region, Australia. The gaps in transit service usage are identified at different sections of the network using both methods. The findings from this study reveal that CLAN can be effectively used to prioritize OD pairs for transit improvement at a coarser level. The OD pairs with the highest and least priority from CLAN are further tested using FLAN. The results from FLAN further confirmed the findings from CLAN. The study showed that both methods have their own advantages and disadvantages if applied independently. However, when applied together, the two methods can help prioritize zones and OD pairs for wider benefits of transport systems such as improvement in transit patronage. The methodological framework proposed in this study is generic and can be applied to compare other multimodal combinations.

Adaptive Sampling Simulated Annealing for the Synthesis of Disaggregate Mobility Data from Origin–Destination Matrices

Agent-based modelling has been suggested as a highly suitable approach for the tackling of future mobility challenges. However, the application of disaggregate models is often hindered by the high granularity of the required input. Recent research has suggested a combinatorial optimization-based framework to enable the conversion of typical origin–destination matrices (ODs) to suitable input for agent-based modelling (e.g., trip-chains, tours, or activity-schedules). Nonetheless, the combinatorial nature of the approach requires very efficient and scalable optimization processes to handle large-scale ODs. This study suggests an advanced optimization technique, coined as the adaptive sampling simulated annealing (ASSA) algorithm, able to exploit high-level calibration information (in the form of a joint distribution) for the efficient addressing of large-scale combinatorial problems. The proposed optimization algorithm was evaluated using high-level information about the departure profile, the types of activities, and the travel time of the expected output and a set of large-scale trip-purpose- and time-period-segmented OD matrices of 253,000 trips. The obtained results showcase the ability of the methodology to accurately and efficiently convert large-scale ODs into disaggregate mobility traces since the inputted ODs were converted into thousands of travel-demand equivalent, disaggregate mobility traces with an accuracy exceeding 90%. The implications are significant since the abundance of travel-demand information in ODs can be now exploited for the preparation of disaggregate mobility traces, suitable for sophisticated agent-based transport modelling.

Knowledge-Assisted Visualization of Multi-Level Origin-Destination Flows Using Ontologies

Origin-destination matrices help understand the movement of people within cities. This work is built upon the premise that stakeholders, e.g. decision makers, need to analyze mobility flows from spatio-temporal perspectives that are appropriate to their context of analysis. The data retrieved from sensors and Intelligent Transportation Systems are useful for this purpose due to their lower acquisition costs and fine granularity, although it is complex to use such data in an integrated way, as they might have heterogeneous representations of spatio-temporal attributes and granularities. Most of the related works on the analysis of OD flows consider matrices with a fixed spatio-temporal aggregation level, and do not explore the intrinsic issue of data heterogeneity. Herein we report our findings on building the semantic foundation of knowledge-assisted visualization tools for analyzing OD matrices from multiple stakeholder levels. We propose a set of ontology design patterns for modeling the semantics of OD data, and the relations between the spatio-temporal constructs that stakeholders ought to choose when visualizing urban mobility flows. Our approach aims to be reusable by researchers and practitioners. We describe a practical implementation using estimated flows from smart card data from Porto, Portugal.

The gravity model as a tool for decision making. Some highlights for Indian roads

For many decades, there have been plenty of analyses about the relationship between socio-economic attributes and transport flows.For ascertaining whether in India socio-economic structure and transport flows follow a common pattern, complete corridor OD matrices were calibrated. These matrices were later analyzed by means of gravity models that included parameters such as population or GDP per district and road distance among district centroids.Results for main corridors are rather homogeneous, and rather consistent with research carried out in other countries, even if the huge mega-cities of Delhi and Mumbai are included in the analysis.

Estimation and prediction of dynamic matrix travel on a public transport corridor using historical data and real-time information

In this paper a new methodology to estimate/update and forecast dynamic real time origin–destination travel matrices (OD) for a public transport corridor is presented. The main objective is to use available historical data, and combine it with online information regarding the entry and exit of each particular user (e.g. through the fare system, FS), to make predictions and updates for the OD matrices. The proposed methodology consists of two parts: (1) an estimation algorithm for OD matrices of public transport (EODPT), and (2) a prediction algorithm (PODPT) based on artificial neural networks (ANNs). The EODPT is based on a model that incorporates the travel time distribution between OD pairs and the modeling of the travel destination choice as a multinomial distribution, which is updated using a Bayesian approach with new available information. This approach makes it possible to correct the estimates of both the current OD interval matrices and of preceding intervals. The proposed approach was tested using actual demand data for the Metro of Valparaiso corridor in Chile (Merval), and simulated travel information in the corridor. The results are compared favorably with a static approach and can support the use of this methodology in real applications. The execution times obtained in the test cases do not exceed 10 s.

Fare evasion correction for smartcard-based origin-destination matrices

Origin-Destination matrices obtained from smartcard data are very valuable because they contain vast amounts of information and can be obtained at a very low cost. However, they can only account for trips paid by smartcard. Trips paid by other means, as well as non-paid trips, must be incorporated using additional information. This paper discusses the biases that are introduced due to fare evasion and presents a sequential method to estimate correction factors due to partial evasion in some trip stages, as well as total fare evasion in all trip stages, using external information regarding trips not registered in the smartcard database. We apply this method to the case of Santiago, Chile, where partial evasion (during a bus trip stage prior to a Metro trip stage) and total evasion (during all bus-only trip stages) are relevant fare evasion situations. Information from the Santiago Metro Origin-Destination survey and from external fare evasion measurements is used. The results indicate a 5% partial evasion rate for bus trip stages prior to Metro trip stages, and a 37% total fare evasion rate for bus-only trips. This paper is a contribution towards establishing new methods to feasibly obtain OD matrices through the adequate merging of automatically-collected data with complementary traditional measurements and survey instruments.

A Data Driven Approach to Match Demand and Supply for Public Transport Planning

The estimation of OD flows from mobile phone and GPS positioning data is an important application that can naturally support urban and transport studies. In this work, we first present an approach to generate OD matrices from mobile phone positioning and GPS data, and scale them with traffic counts. Then we compare these matrices, that we consider as an estimate of the potential demand for public transport, with matrices describing the actual routes of public transportation services, that represent the supply. Finally, we present a data driven approach to identify <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">where</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">when</i> the demand for transport is not satisfied. We run experiments with different mobility datasets and the actual public transportation routes in a mid-sized Italian city. In this scenario, our approach allows to detect similar areas of unmatched demand with both such datasets. In particular, two case studies show that the proposed methodology is able to identify two existing bus lines that were recently introduced by the public transport company and local government. Finally, we show an upper bound for the reduced impact of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$CO_{2}$ </tex-math></inline-formula> emissions, if the unmet demand for transport is entirely shifted to public transport.

Investigating the quality of Spiess-like and SPSA approaches for dynamic OD matrix estimation

Since OD matrices are not directly observable, indirect procedures have been developed to estimate OD matrices from traffic data. Traffic management must move toward dynamic traffic assignment models because they capture congestion propagation effects. In this context, dynamic OD matrices are needed. This paper first explores the extension of a conventional bilevel analytical static method to the dynamic context, then analyses the solutions obtained regarding both convergence to measured traffic data and structural similarity to an a priori OD matrix. A simulation optimization technique, SPSA, is then proposed because its flexibility allows inclusion of traffic counts (as in Spiess method) and emerging ICT traffic measurements. The performances of these two types of algorithms are analyzed in detail, focussing on faults of classical convergence measures to obtain an estimated dynamic OD matrix structurally similarity to the a priori OD matrix and pros and cons of variants of selected methods.

A dynamic OD prediction approach for urban networks based on automatic number plate recognition data

OD flows provide important information for traffic management and planning. The prediction of dynamic OD matrices gives the possibility to apply anticipatory traffic management measures. In this paper, we propose an OD prediction approach based on the data obtained by Automated Number Plate Recognition (ANPR) cameras. The principal component analysis (PCA) is applied to reduce the dimension of the original OD matrices and to separate the main structure patterns from the noisier components. A state-space model is established for the main structure patterns and the structure deviations, and is incorporated in the Kalman filter framework to make predictions. We further propose three K-Nearest Neighbour (K-NN) based long-term pattern recognition approaches. The proposed approaches are validated with field ANPR data from Changsha city, P.R. China. The results show that the observed OD flows can be accurately predicted by our proposed approaches. Which prediction method performs best depends on the quality of the available data: for regular, periodic OD matrices the Kalman filter is better, for irregular OD matrices the pattern recognition that looks at different time periods in the historical data, gives better results.

Optimal synthesis of tours from multi-period origin-destination matrices using elements from graph theory and integer programming

Nowadays, mobility modelling at individual level is receiving significant attention. Moreover, the technological advances in the field of travel behaviour analysis have supported and promoted the modelling paradigm shift to disaggregate methods such as agent/activity-based modelling Nonetheless, such approaches usually require significant amounts of detailed and fine-grained data which are not always easily accessible. The methodology presented in this paper aims to generate individual home-based trip-chains (i.e. tours) utilising aggregated sources of information, primarily, typical Origin-Destination matrices (ODs) and secondarily travel surveys. A suitable framework able to optimally identify ‘hidden’ tours in typical ODs is proposed and evaluated through its application on a set of multi-period OD matrices, covering an urban area of realistic size. This novel methodological framework synthesises the individual tours by combining and elevating advanced graph theory and integer programming concepts. The performance of the proposed methodology proves particularly encouraging since high estimation accuracy (greater than 85%) was achieved even for the most challenging examined test-case. The presented results provide positive evidence that information regarding travel behaviour on an individual level can be produced based on aggregated data sources such as OD matrices. This element is particularly valuable towards the analysis of mobility at the person-level, especially within the framework of agent-based modelling.

Urban travel time data cleaning and analysis for Automatic Number Plate Recognition

Data recorded by Automated Number Plate Recognition (ANPR) cameras can be used to determine several important traffic characteristics, such as real time travel time, travel time statistics, travel time reliability and OD matrices. In this paper ANPR data collected in Chinese city Changsha have been validated. Travel time extracted from ANPR data includes some outliers which are often caused by drivers who have an intermediate stop between two observation points or deviate from the straight route. Exceptional travel time reduces the validity of the estimation of the travel time and reliability. Firstly, the Rapid-Moving Window method is introduced to identify outliers. Afterwards, another method based on wavelet analysis is put forward to identify and remove the outliers in the travel time series. The wavelet analysis method is compared with the Rapid-Moving Window method and shows to be more accurate in outlier identification. The method for eliminating outliers in travel times can be implemented in real time to enhance the data quality for traffic network monitoring and management. After the removal of the outliers, the resulting travel times are used for the analysis of the relation between average travel time and standard deviation/skewness.