Trip Matrices Research Articles

Computational Architecture of an Integrated Urban Model Considering Physical-Virtual Activity Spaces

This study presents the computational architecture of the integrated transport, land-use, and emission (iTLE) modeling system. It incorporates the effects of physical-virtual activity-space interactions within the microsimulation framework, making it a comprehensive tool for predicting travel demand and evaluating the impacts of evolving activity-travel behavior on transport and land-use systems. The model systematically integrates households’ and individuals’ long-term, medium-term, and short-term travel related decisions, and traffic assignment allowing for more reliable estimates of travel demand. Application of the iTLE prototype in the Halifax Regional Municipality (HRM), Canada reveals notable trends, including a reduction in travel time for work activities, highlighting the potential of teleworking as a pragmatic strategy for traffic management. The model’s flexibility is demonstrated through its ability to capture the trade-offs between physical and virtual activity environments, aligning with the intricacies of modern digitalized societies. Integration of iTLE with the traffic assignment system enhances its applicability across diverse urban contexts, streamlining the process of setting origin-destination trip matrices and significantly improving computational efficiency. By systematically coupling the micro-behavioral decision processes, iTLE generates robust estimates of traffic flow, emissions, and energy use, providing reliable insights for sustainable and efficient transportation planning. This study contributes to advancing integrated urban modeling, offering a valuable tool that can be replicable for multiple cities in Canada and beyond.

Metrics for Quantifying Shareability in Transportation Networks: The Maximum Network Flow Overlap Problem

Cities around the world vary in terms of the structure of their transportation networks and travel demand patterns. Despite these variations significantly impacting opportunities for travelers to share trips, no metrics are available to jointly characterize a region’s transportation network and travel demand in terms of the potential for travelers to share space with each other on network links, or what we call person-trip shareability. This study proposes metrics to quantify the shareability of person-trips in a city subregion, as a function of three inputs—the underlying transportation network, origin–destination (OD) travel demand, and a maximum permissible detour parameter. After defining person-trip shareability and providing principles for operationalizing this definition, we formulate a fundamental metric, called flow overlap. Flow overlap measures, for a person-trip traversing a given path, the weighted (by link distance) average number of other person-trips sharing the links along the original person-trip’s path. We then formulate the Maximum Network Flow Overlap Problem (MNFLOP), a math program that assigns person-trips to network paths that maximize network-wide flow overlap. We utilize the MNFLOP output to calculate shareability metrics at various levels of aggregation: person-trip level, OD level, origin or destination level, network level, and link level. The study applies the MNFLOP and associated shareability metrics to different OD demand scenarios in the Sioux Falls network. The computational results verify that MNFLOP (i) assigns person-trips to paths such that flow overlaps significantly increase relative to shortest path assignment, (ii) can meaningfully differentiate between different OD trip matrices in terms of flow overlap, and (iii) metrics can meaningfully quantify demand dispersion from a single network node/location considering the underlying road network. Finally, we validate MNFLOP’s ability to quantify shareability by showing that demand patterns with higher flow overlap are strongly associated with lower mileage routes for a last-mile microtransit service. The paper includes an extensive discussion of other potential future uses of the MNFLOP and its associated shareability metrics.

Adequacy of the Gravity Model of Railway Passenger Flows

The most accurate modelling of spatial distribution of passenger flows is a prerequisite for successful planning of development of the transport system. It is the basis for calculation of a predictive trip matrix. An approach based on the gravity model is among main modelling methods.The work investigates the issue of the adequacy of the gravity model with a double constraint and an exponential-power function of gravitation. It is this specification of the model and its particular cases with exponential and power functions of gravitation that are most often used to estimate spatial distribution of passenger flows both in theoretical and applied research.Calibration and validation of the specified model is shown on the observed (actual) matrix of railway passenger origin­destination matrix. It was built with the help of the data of Express [railway ticketing] ADB ACS: the number of tickets sold for long-distance trains for all the pairs of directly linked stations.Since calibration of the gravity model can be carried out by different methods (depending on how the model incorporates stochasticity, which is responsible for differences between the modelled and observed data), after a detailed analysis of the most common methods for calibrating the gravity model, the approach was chosen based on the maximum likelihood estimation. The work also analyses the gravity model validation tools used to estimate the proximity between the observed and modelled trip matrices.Comparison of the modelled and observed trip matrices resulted in the conclusion that the gravity model under consideration predicts several aggregate indicators with a high degree of accuracy: total passenger turnover, average travel distance, and travel distance distribution. At the same time, it is shown that the error in the forecast of passenger flow for most individual origin-destination trips is quite large. This circumstance significantly reduces the possibility of practical application of the gravity model or the analysis and modelling of passenger flows in long-distance railway passenger traffic.

COMMUTING PREFERENCES IN EASTERN EUROPE: CASE STUDY IN TOWN OF ŠIAULIAI

This article presents a study conducted in the Town of Šiauliai with a population of 100 thousand, located in the Republic of Lithuania, where the market economy has been operating for 32 years and which is a member of the European Union for 20 years. In the town, the share of commuting travels by car is significantly higher than by public transport. Since the availability of the public transport network is identified in scientific publications as one of the many criteria for choosing public transport, it was decided to conduct a study and check to what extent the availability of the public transport network determines the choice to travel by bus or car. The research hypothesizes that residents who live in neighbourhoods with worse access to bus routes and stops choose more cars than those who live in neighbourhoods with better access to public transport. The results of the study showed that residents choose to travel by bus or car regardless of the availability of the route network. It was found that the origin–destination pairs and relative proportions of those commuting to work match both those traveling by car and by bus. The results of this study may not necessarily be the same in Western European cities or towns. The main limitation of this article is that the trip matrices were compiled from population survey data, as statistical information on origin–destination pairs in Town of Šiauliai is not regularly collected.

Knot Theory in Linear Algebra: An Example with Trip Matrices

Summary The trip matrix, introduced by Louis Zulli [6], gives a method for computing the Jones polynomial of a knot using basic Linear Algebra. We use this method to provide an alternative proof of the formula for the Jones polynomial of torus knots. In doing so, we provide a partial solution to an open question related to finding an elementary proof of the formula for general torus knots.

Frequency-based path flow estimator for transit origin-destination trip matrices incorporating automatic passenger count and automatic fare collection data

A frequency-based path flow estimator is proposed to estimate the transit passenger origin–destination (OD) matrix in an urban congested transit network. The proposed model not only considers the effect of congestion under an equilibrium framework, but also benefits from being formulated as a single-level model with the route-section-based network representation. Multiple transit data sources are incorporated, including automatic passenger count, automatic fare collection and automatic vehicle location data. A path-based diagonalization approach embedded with an iterative balancing scheme is developed to solve the model. Case studies are conducted to demonstrate the features and applicability of the proposed model and algorithm.

Vehicle scheduling for on-demand vehicle fleets in macroscopic travel demand models

The planning of on-demand services requires the formation of vehicle schedules consisting of service trips and empty trips. This paper presents an algorithm for building vehicle schedules that uses time-dependent demand matrices (= service trips) as input and determines time-dependent empty trip matrices and the number of required vehicles as a result. The presented approach is intended for long-term, strategic transport planning. For this purpose, it provides planners with an estimate of vehicle fleet size and distance travelled by on-demand services. The algorithm can be applied to integer and non-integer demand matrices and is therefore particularly suitable for macroscopic travel demand models. Two case studies illustrate potential applications of the algorithm and feature that on-demand services can be considered in macroscopic travel demand models.

How comparable are origin-destination matrices estimated from automatic fare collection, origin-destination surveys and household travel survey? An empirical investigation in Lyon

Abstract Origin–destination (OD) matrices are one of the key elements in travel behaviour analysis. For decades, transportation researchers have mostly used data obtained by active solicitation such as surveys to construct these matrices but new data sources like automatic fare collection (AFC) are now available and can be used to measure OD flows. As a result, a more heterogeneous corpus of data sources is now available to estimate travel demand. However, little research examines how comparable the estimated demands may be. In this paper, three data sources namely a household travel survey, a large scale origin–destination survey and entry only automated fare collection are processed to derive typical weekday public transit OD trip matrices. Various elements of the resulting matrices are then compared. While all the matrices share some common characteristics, there are also substantial differences that must be addressed. AFC data is not error-free and needs to be supplemented with data from other sources to construct a representative OD trip matrix. This is because not all destinations can be inferred, the smart card penetration rate is far less than 100% and fare evasion cannot be ignored. Our empirical results suggest that scaling an AFC matrix with automated passenger counts may be a viable solution. The results also indicate that the household travel survey significantly underestimates the volume of public transit trips compared to the other sources. The findings of this research contribute to a better understanding of the available data sources for public transit demand estimation. They can help practitioners to improve the quality and accuracy of OD matrices.

Effects of the COVID-19 Lockdown on Urban Mobility: Empirical Evidence from the City of Santander (Spain)

This article analyses the impact that the confinement measures or quarantine imposed in Spain on 15 March 2020 had on urban mobility in the northern city of Santander. Data have been collected from traffic counters, public transport ITS, and recordings from traffic control cameras and environmental sensors to make comparisons between journey flows and times before and during the confinement. This data has been used to re-estimate Origin-Destination trip matrices to obtain an initial diagnostic of how daily mobility has been reduced and how the modal distribution and journey purposes have changed. The impact on externalities such as NO2 emissions and traffic accidents have also been quantified. The analysis revealed an overall mobility fall of 76%, being less important in the case of the private car. Public transport users dropped by up to 93%, NO2 emissions were reduced by up to 60%, and traffic accidents were reduced by up to 67% in relative terms.

Integrating travel demand modeling and flood hazard risk analysis for evacuation and sheltering

In this paper, the risks of flooding hazards to the transportation system in urban Honolulu are assessed using a regional travel demand model (TDM). The approach serves to support understanding of evacuation and sheltering needs. Coastal and inland flooding hazard scenarios were modeled with four different hazard conditions. The inundation defined by the Maximum Envelope of High Water (MEOW) based on a hurricane that struck Hawaii and a tsunami run-up generated by historical earthquake events combined with a one-meter rise in sea level provided the worst possible coastal flooding scenario. A 500-year return period riverine flooding scenario was also included. The critical flooding hazard was transformed into a uniform 100 by 100meter GIS based grid system. The Oahu Metropolitan Planning Organization (OMPO) TransCAD model for 2035 provided the origin and destination trips for eleven trip types including motorized and non-motorized travel modes. The OMPO model includes personal travel, travel to the airport, commercial vehicle travel and visitor travel sub-models. Origin and destination trip matrices for Traffic Analysis Zones (TAZ) and highway and transit assignment details were extracted from the model. The O-D trips and road segment traffic details were transformed to the spatial grid system and overlaid on the flooding hazard layer. The spatial categorization of the flooding along with the trip and travel data from the TDM provided a robust method to quantify and visualize risks to travelers and the transportation system. The analysis shows that flooding hazard scenarios have serious risks in Honolulu. First, a large portion of the study area is susceptible to flooding, threatening the population, economy, and infrastructure. Second, in addition to areas susceptible to flooding, a larger percentage of origins, destinations, trips and vehicle miles of travel (VMT) are affected because of the need to travel through the at-risk areas. Third, commercial, transit and non-motorized trips are disproportionately affected compared to auto travel. This paper demonstrates how hazard data and risk models can be integrated with travel demand models for purposes of evacuation planning and sheltering as well as emergency planning and hazard mitigation and adaptation of the transportation system to climate change.

Advanced demand data collection technologies for multi modal strategic modelling

Abstract New data collection technologies have all, but replaced traditional, site-based data collection methods for trip matrix development in the UK. Event data produced by Mobile Network Operators provides adequate information to identify time and location of trip origin and destination (OD), but only limited information on transport mode, vehicle type or trip purpose. In addition, GPS-based data provides another source of OD and user data. This paper describes the mobile phone and app-based demand data collection, verification and processing toward the multi-modal strategic transportation model of Chelmsford, UK. The mobile data was collected during 30 days by INRIX, and was processed by Jacobs to develop time-of-day, vehicle type, mode and purpose-specific motorised trip matrices. The mobile phone- trip matrices were verified and adjusted against various third party data. A cycle app was developed for Chelmsford to facilitate non-motorised OD data collection by engaging a voluntary user group. Together with other data sources, the data was used to develop cycle OD matrices and to calibrate a cycling route choice model. The paper concludes that the use of mobile phone data provides greater quantity and coverage to develop OD matrices. However, the new data source requires significant effort in post processing and model data segmentation by mode, trip purpose and vehicle type, via applying third party information. The quality and efficiency of this process is likely to improve in the near future, resulting in a step change in the modelling practice. The model was delivered to Essex County Council in April 2017.

Origin-Destination Trip Matrix Development: Conventional Methods versus Mobile Phone Data

Conventionally, trip matrices have been derived by a combination of roadside interviews (RSIs) and the application of trip-end and gravity models (to extrapolate and infill unobserved movements), followed by matrix estimation methods to incorporate evidence from supplementary traffic counts. More recently, mobile phone positioning data are being used increasingly by the transport planning community to develop ‘prior’ demand matrices as an alternative approach to RSI data or synthetic methods. There are a number of known strengths and weaknesses associated with each of these approaches. However, there is lack of robust evidence to suggest whether use of any of these approaches results in a matrix that performs better (or worse) overall. This study provides such evidence through a structured and systematic comparison of trip matrices developed using mobile data, RSI data, and a gravity modelling approach (i.e. synthetic matrices). In addition to comparison of assigned flows with traffic counts across a range of independent screenlines, the following aspects of the matrices are also compared with independent observed data: 1) correlation of trip-ends with estimates based on the UK National Trip-End Model (NTEM); 2) consistency of trip rates with estimates based on Great Britain National Travel Survey (NTS) data; and 3) comparison of trip length distributions with estimates from the NTS. The results suggest that, overall, the outcome of using the mobile phone data, when systematically refined and adjusted using independent data sources to address various known limitations and biases, does not seem to be either biased or less accurate than conventional methods. It has also been observed that areas of the model where no RSI data or other similar observed data are available, use of mobile data could result in a more consistent estimate of trips, benefiting from a significantly larger sample size.

Expanding the Uses of Truck GPS Data in Freight Modeling and Planning Activities

Progress in practical applications of large, passively collected data sets is often hindered by the lack of appropriate analytical tools or the proprietary nature of applicable software. One of the most widely used data sources in the United States is truck GPS data that are commercially available from a few sources nationwide. Although many large GPS data sets are used in the development of tour-based truck models, the development of a fairly general approach to data analysis and processing that can be readily applied to various GPS data sets without need of proprietary software is still of interest. First, this paper presents a set of tools and techniques used to transform low-frequency truck GPS data available from commercial sources into complete trajectories on the network, that is, sequences of links constituting continuous paths traversed by each truck, with corresponding time stamps on each of the nodes. For this exercise, only open-source software was used, and the algorithm implementation was released as an open-source tool under a business-friendly license. Second, use of the truck GPS data was expanded beyond the standard extraction of trip matrices and estimation of tour models. Additional applications include select link analysis, time-of-day analysis, and trajectory data visualization.

Path Flow and Trip Matrix Estimation Using Link Flow Density

A macroscopic model is presented that simultaneously estimates route flows and trip matrices for congested road networks using data on link densities instead of link flows. The advantage of this approach is that it avoids errors that may occur in the individual links’ flow-cost relationships when congestion is heavy. Under the proposed methodology, both the flows and the matrices are estimated by the model using an image of the network such as an aerial photograph in which the number of vehicles on each link can be identified. The model itself is formulated as a maximum entropy optimization problem subject to linear constraints given by vehicle densities on the links, and is validated using analytic examples and traffic microsimulations. The results demonstrate the superiority of the link-density approach over the traditional flow-based method.

Iterative update of route choice proportions in OD estimation

The origin–destination (OD) matrix, as a fundamental element of transportation planning, can be estimated in various ways. Owing to lower costs and the ability to keep matrices up to date, estimating OD matrices from observed traffic counts is gaining interest. These methods find an OD matrix that, when assigned to the network, reproduces the traffic counts. The main weakness of these methods, assuming traffic counts as deterministic values, has been overcome by the TFlowFuzzy (TFF) algorithm, which considers the counts as imprecise values. In this paper, a limitation of TFF is identified and accounted for with a methodological enhancement for modification. A key element in the estimation of trip matrices from traffic counts is the route choice proportions (assignment matrix). In the conventional TFF, the assignment matrix is computed only once and held constant during the whole estimation process. Hence, a modified algorithm is proposed in which the assignment matrix is updated successively. This modification is implemented on the real-size network of Mashad city. Results indicate a considerable improvement in the modified TFF goodness of fit compared to the traditional algorithm, as it is increased by 55%. This shows the effectiveness of the proposed algorithm, considering the assignment matrix endogenously.

Case Study on Cooperative Car Data for Estimating Traffic States in an Urban Network

The use of floating car data as a particular case of probe vehicle data has been the object of extensive research for estimating traffic conditions, travel times, and origin-to-destination trip matrices. It is based on data collected from a GPS-equipped vehicle fleet or available cell phones. Cooperative cars with vehicle-to-vehicle and vehicle-to-infrastructure communication capabilities represent a step forward, as they also allow tracking of vehicles surrounding the equipped car. This paper presents the results of a limited experiment with a small fleet of cooperative cars in the central business district of Barcelona, Spain, known as L’Eixample District. Data collected from the experiment were used to build and calibrate the emulation of cooperative functions in a microscopic simulation model that captured the behavior of vehicle sensors in Barcelona’s central business district. Such a calibrated model allows emulating fleet data on a large scale that goes far beyond what a small fleet of cooperative vehicles could capture. To determine the traffic state, several approaches were developed for estimating traffic variables—whose accuracy depends on the penetration level of the technology—on the basis of extensions of Edie’s generalized definitions of the fundamental traffic variables with the emulated data.

Origin–destination trips by purpose and time of day inferred from mobile phone data

In this work, we present methods to estimate average daily origin–destination trips from triangulated mobile phone records of millions of anonymized users. These records are first converted into clustered locations at which users engage in activities for an observed duration. These locations are inferred to be home, work, or other depending on observation frequency, day of week, and time of day, and represent a user’s origins and destinations. Since the arrival time and duration at these locations reflect the observed (based on phone usage) rather than true arrival time and duration of a user, we probabilistically infer departure time using survey data on trips in major US cities. Trips are then constructed for each user between two consecutive observations in a day. These trips are multiplied by expansion factors based on the population of a user’s home Census Tract and divided by the number of days on which we observed the user, distilling average daily trips. Aggregating individuals’ daily trips by Census Tract pair, hour of the day, and trip purpose results in trip matrices that form the basis for much of the analysis and modeling that inform transportation planning and investments. The applicability of the proposed methodology is supported by validation against the temporal and spatial distributions of trips reported in local and national surveys.

An Excess-Demand Dynamic Traffic Assignment Approach for Inferring Origin-Destination Trip Matrices

The focus of this paper is on the development of an origin–destination (O-D) demand estimation method for dynamic equilibrium traffic networks. It is hypothesized that the underlying equilibrium conditions in such networks are a compromise result of minimization of individual routing costs, minimization of traffic count matching errors, and maximization of O-D demand entropies. By adding an upper bound of travel demand and a dummy path with constant travel cost to each O-D pair, we formulated the dynamic O-D demand estimation problem as an excess-demand dynamic traffic assignment (DTA) problem defined for an expanded network with dummy paths. Such a formulation enables us to apply existing DTA solution methods and software tools for deriving the path flow pattern in the expanded network and thus simultaneously obtaining the O-D demand pattern in the original network. Following this problem transformation and network expansion strategy, an iterative solution procedure is accordingly proposed, which resorts to repeatedly solving the excess-demand DTA problem and adjusting the dummy path costs. An application of the proposed modeling and solution methods for an example cell-based network problem favorably illustrates great promise of the methodological advance and solution performance.

A Robust Framework for the Estimation of Dynamic OD Trip Matrices for Reliable Traffic Management

Origin-Destination (OD) trip matrices describe the patterns of traffic behavior across the network and play a key role as primary data input to many traffic models. OD matrices are a critical requirement, either in static or dynamic models for traffic assignment. However, OD matrices are not yet directly observable; thus, the current practice consists of adjusting an initial or a priori matrix from link flow counts, speeds, travel times and other aggregate demand data. This information is provided by an existing layout of traffic counting stations, as the traditional loop detectors. The availability of new traffic measurements provided by ICT applications offers the possibility to formulate and develop more efficient algorithms, especially suited for real-time applications. However, the efficiently strongly depends, among other factor, on the quality of the seed matrix. This paper proposes an integrated computational framework in which an off-line procedure generates the time-sliced OD matrices, which are the input to an on-line estimator. The paper also analyzes the sensitivity of the on-line estimator with respect to the available traffic measurements.

Analyzing Cell Phone Location Data for Urban Travel

Travelers today use technology that generates vast amounts of data at low cost. These data could supplement most outputs of regional travel demand models. New analysis tools could change how data and modeling are used in the assessment of travel demand. Recent work has shown how processed origin–destination trips, as developed by trip data providers, support travel analysis. Much less has been reported on how raw data from telecommunication providers can be processed to support such an analysis or to what extent the raw data can be treated to extract travel behavior. This paper discusses how cell phone data can be processed to inform a four-step transportation model, with a focus on the limitations and opportunities of such data. The illustrated data treatment approach uses only phone data and population density to generate trip matrices in two metropolitan areas: Boston, Massachusetts, and Rio de Janeiro, Brazil. How to label zones as home- and work-based according to frequency and time of day is detailed. By using the labels (home, work, or other) of consecutive stays, one can assign purposes to trips such as home-based work. The resulting trip pairs are expanded for the total population from census data. Comparable results with existing information reported in local surveys in Boston and existing origin–destination matrices in Rio de Janeiro are shown. The results detail a method for use of passively generated cellular data as a low-cost option for transportation planning.