Macroscopic fundamental diagram with volume-delay relationship: model derivation, empirical validation and invariance property

This paper presents a macroscopic fundamental diagram model with volume-delay relationship (MFD-VD) for road traffic networks, by exploring two new data sources: license plate cameras (LPCs) and road congestion indices (RCIs). We derive a first-order, nonlinear and implicit ordinary differential equation involving the network accumulation (the volume) and average congestion index (the delay), and use empirical data from a 266 km$^2$ urban network to fit an accumulation-based MFD with $R^2>0.9$. The issue of incomplete traffic volume observed by the LPCs is addressed with a theoretical derivation of the observability-invariant property: The ratio of traffic volume to the critical value (corresponding to the peak of the MFD) is independent of the (unknown) proportion of those detected vehicles. Conditions for such a property to hold is discussed in theory and verified empirically. This offers a practical way to estimate the ratio-to-critical-value, which is an important indicator of network saturation and efficiency, by simply working with a finite set of LPCs. The significance of our work is the introduction of two new data sources widely available to study empirical MFDs, as well as the removal of the assumptions of full observability, known detection rates, and spatially uniform sensors, which are typically required in conventional approaches based on loop detector and floating car data.Comment: 31 pages, 17 figure

Empirical Estimation of a Macroscopic Fundamental Diagram (MFD) for the City of Cape Town Freeway Network

The City of Cape Town is the most congested city in South Africa, with Johannesburg coming in second. Capetonians are spending 75% more time in traffic because of the congestion during peak hours, thus reducing time spent on leisure and other activities. Due to population growth, increasing car ownership and declining capacity of rail infrastructure, Cape Town's road infrastructure will continue to be under severe pressure if the status quo is maintained. Research shows that congestion levels in urban areas are key factors in determining the effectiveness and productivity of the transport system. Traffic congestion poses a threat to the economy and the environment. Increasing corridors' capacity by increasing the number of lanes does not necessarily solve the problem. Effective urban traffic management and efficient utilization of existing infrastructure are critical in creating sustainable solutions to congestion problems. To achieve this, it is important that appropriate urban-scale models and monitoring strategies are put in place. Effective traffic management and monitoring strategies require accurate characterization of the traffic state of an urban-scale network. Several approaches, including kinetic wave theory and cell transmission models or macroscopic traffic simulation models, have been proposed and developed to describe the traffic state of an urban-scale network. However, these approaches are limited and require significant amounts of computational time and effort. The application of macroscopic fundamental diagram (herein referred to as MFD) to characterize the state of an urban-scale network has thus far proven to be more effective than other approaches. MFD represents the state of urban traffic by defining the traffic throughput of an area at given traffic densities. It describes the characteristics and dynamics of urban-scale traffic conditions, allowing for improved and sustainable urban scale traffic management and monitoring strategies. Against this backdrop, the existence of MFD for the City of Cape Town (CoCT) urbanscale network is yet to be established and the implications yet to be understood, as in other parts of the world. The main aim of this research was, therefore, to empirically estimate the macroscopic fundamental diagram for the CoCT's freeway network and analyse its observed features. To achieve this, observed data of 5 minutes periods for the month of May 2019 was used to estimate the MFD. The results confirmed that when the chaotic scatter-plots of flow and density from individual fixed loop detectors were aggregated the scatter nearly disappeared and points grouped neatly to form a clearly defined free-flow state, critical state and the formation of hysteresis loops past the critical density corresponding with the network observed maximum flow. Further analysis of the MFDs showed that a single hysteresis loop always forms past the critical density during the evening peak in a weekday MFD. However, it was inconclusive during the morning peak period in weekday MFDs. Lastly, an explicit hysteresis loop seldom appears in a Saturday MFD when the peak of traffic demand is lower than on weekdays. In order to understand the dynamics of the congestion spread, the freeway network was partitioned into penetrating highways network and the ring highway network. The results showed that the maximum flows observed for the two sub-networks were significantly different (943 veh/hr/lane for the penetrating highways network and 1539 veh/hr/lane for the ring highway network). The penetrating highways network's MFD indicated the presence of congestion in the network whereas the ring highway network indicated only the free-flow state (no indication of congestion) during peak periods. The congestion seen on the penetrating highways network was found not to be sufficiently spread on those highways. On the 24th May, congestion on the penetrating highway network was observed during both the morning and evening peak periods, whereas on the 31st May congestion was observed mainly during the evening peak period, with hysteresis-like shape. These observations confirmed that congestion during peak periods is not homogenously spread across the entire network, certain areas are more congested than others, hence the observed formation of hysteresis loops and slight scatters. Lastly, the hysteresis loops observed in the penetrating highways network's MFD was further characterized in terms of their shape and size. First, the results showed that the slight scatter and hysteresis patterns observed in penetrating highways network MFD's vary in size and shape across different days. The shapes of the hysteresis loops observed during both the morning and evening peak periods, were type H2 hysteresis loops, signifying a stable recovery of the network with the average network flow remaining unchanged as average network density decreases during the recovery. Characterization of the size of the observed hysteresis loops showed that the drop of the hysteresis (an indicator of network level of instability during recovery phase) was smaller, signifying a more stable network traffic and homogenous distribution of congestion during the recovery phase

Macroscopic Fundamental Diagram Estimation Considering Traffic Flow Condition of Road Network

A macroscopic fundamental diagram (MFD) is an important basis for road network research. It describes the functional relationship between the average flow and average density of the road network. We proposed an MFD estimation method based on the traffic flow condition. Firstly, according to statistical theories, the road network data are divided into three traffic flow conditions (free flow, chaotic and congested) bounded by a 95% confidence interval of the maximum traffic capacity of each intersection in the road network. Then, in each condition, we combined principal component analysis and the Jolliffe B4 method to reduce dimension for extracting critical intersections. Finally, the full-scale dataset of the road network was reconstructed to estimate the road network MFD. Through numerical simulation and empirical research, it is found that the root mean square error and absolute percentage error between estimated MFD and true MFD considering the traffic flow condition are smaller than those without considering the traffic flow condition. The MFD estimation and the division of the traffic states of the road network were completed at the same time. The proposed method effectively saves the time cost of road network research and is highly accurate

Establishment & Assessment of the Macroscopic Fundamental Diagrams for the City of Durban Freeway Network Using Empirical Data

The history of traffic flow studies dates to the years between the 1960s and 1970s. This paper reviews the history of traffic flow studies in the context of Macroscopic Fundamental Diagrams (MFD) to date. The recent findings have shown that understanding the Macroscopic Fundamental Diagrams (MFD) in cities can bring success in managing congestions. This study aimed to establish the Macroscopic Fundamental Diagrams (MFD) for the City of Durban Freeway network. Motivated the study was a failure seen in various transportation systems after the 2010 FIFA world cup in South African cities. This failure was associated with the adoption of the transportation system from first-world countries. The South African cities are not densified when compared to the first world countries' cities, of course, due to spatial urban planning and segregation of the past. The key lesson was that SA transportation systems problems are unique; solutions should be attributed to the existing travel demand conditions. This birthed the idea that the performance of a traffic system should uniquely serve the specific travel demands. The core aim of this study was to establish the MFD for the freeway network in the City of Durban, South Africa. Two major freeway corridors were evaluated, i,e. the National route 2 and 3. The study used loop detector data extracted from a total of 88 loop detector stations. The loop detector stations were dispersed 100-500 m apart over the network. The data was recorded in September 2019. The collected data was analysed in five minutes intervals. When the MFD was established on the network, aggregated detector loops produced a well defined MFD on the 2 nd,3rd ,16th, and the 23rd of September, whereas, on a separate day (30th of September), a scattered MFD forming a hysteresis loop was observed. The formation of the hysteresis was associated with the lack of alternative routes for drivers to avoid congestions in the network. These observations are discussed later in this paper. The study was a success as it did reveal that the MFD was an attribute of the City of Durban freeway network. The established MFD showed that the freeway network operates between the unsaturated and saturated state. This MFD does not reach the saturated flow. The highest recorded density was found at 10.11 veh/km while the highest recorded flow was found at 733.28 veh/hr. The network operates at an average speed of vav= 79.84 km/hr. The estimated average density for the network to reach the gridlocked state was calculated to be 75veh/km

Macroscopic Urban Network Dynamics: Estimation and Applications

During the past decade there has been significant research efforts in developing traffic control and management methods based on an aggregated representation of traffic networks. In fact, the traditional link-level network representation imposes prohibitive computational costs for typical large-scale urban networks. Thankfully, it has been observed that at a macroscopic level, the relationship between any pair of network-average traffic variables can be described by simple functions called macroscopic fundamental diagrams (MFD). However, current MFD estimation methods were mainly conceived for individual arterial corridors and their application to urban networks has not been validated using extensive empirical data. This dissertation fills this gap by extending current MFD estimation methods to large-scale real-life networks, while using empirical data from 41 cities around the world for calibration and validation. This dissertation further investigates the efficient application of MFD in travelers' route choice using the dynamic traffic assignment (DTA) methods and sets forth the discrete- and continuum-space DTA approaches are intrinsically similar and can be seen as equivalents on different aggregation levels, although they previously seemed to be the two extreme ends of the macroscopic DTA spectrum. A novel continuum-space DTA modeling framework consistent with the MFD theory and assumptions has been developed and a semi-Lagrangian solution method has been proposed by splitting up the network into smaller zones, which can be implemented for minimizing either the travel times of individual users or the total travel time of all users in the network. Finally, the potentiality of implementing the MFD in microscopic vehicular emissions estimation models has been explored. The major findings of this dissertation are as follows. The empirical MFD validation results identify the most important challenges in both analytical and empirical MFD estimation approaches as: (i) the distribution of loop detectors within the links, (ii) the distribution of loop detectors across the network, and (iii) the treatment of unsignalized intersections and their impact on the block length. The numerical experiment results using the proposed DTA framework indicate that partitioning the network into a finer grid of zones can yield more accurate results with respect to the approximated analytical solutions without significant loss of efficiency and demonstrate the potential of application of this framework for real-life networks with arbitrary network and zone shapes. The comparison between the results and runtimes of the emissions estimations conducted in 4 different aggregation levels: lane, link, corridor, and network, reveals that the efficiency can be significantly improved by utilizing more aggregated network representation under some considerations. This will make the MFD a powerful tool for real-time emissions estimation and control.Ph.D

Complex Traffic Network Modeling & Area-wide Hierarchical Control

This thesis presents a novel methodology to divide a traffic region into subregions such that in each subregion a Macroscopic Fundamental Diagram (MFD) can be used to determine the state of that subregion. The region division is based on the theory of complex networks. We exploit the inherent network characteristics through PageRank centrality algorithm to identify the most significant nodes in the traffic network. We use these significant nodes as the seeds for a Voronoi diagram based partitioning mechanism of the network. A network wide hierarchical control framework is then presented which controls these sub regions individually and the network as a whole. At the subregion level a feedback controller is designed based on MFD concept. At the network level we develop a dynamic toll pricing algorithm to control the inflows into the network. This dynamic toll pricing is coupled with the subregion controller and thus forming a network wide hierarchical control. We use optimal control theory to design the dynamic toll pricing. A cost function is designed and then Hamilton-Jacobi-Bellman equation is used to derive an optimal control law that uses real-time information. The objective of the dynamic toll algorithm is to strike a balance between the toll price and optimal traffic conditions in each of the subregions. A case study is performed for the Manhattan area in New York city and results are provided through simulations

Mobile Network Data Analytics for Intelligent Transportation Systems

In this dissertation, we explore how the interplay between transportation and mobile networks manifests itself in mobile network billing and signaling data, and we show how to use this data to estimate different transportation supply and demand models. To perform the necessary simulation studies for this dissertation, we present a simula- tion scenario of Luxembourg, which allows the simulation of vehicular Long-Term Evolu- tion (LTE) connectivity with realistic mobility. We first focus on modeling travel time from Cell Dwell Time (CDT), and show – on a synthetic data set– that we can achieve a prediction Mean Absolute Percentage Error (MAPE) below 12%. We also encounter proportionality between the square of the mean CDT and the number of handovers in the system, which we confirmed in the aforementioned simulation scenario. This motivated our later studies of traffic state models generated from mobile network data. We also consider mobile network data for supporting synthetic population generation and demand estimation. In a study on Call Detail Records (CDR) data from Senegal, we estimate CDT distributions to allow generating the duration of user activities, and validate them at a large scale against a data set from China. In a different study, we show how mobile network signaling data can be used for initializing the seed Origin- Destination (O-D) matrix in demand estimation schemes, and show that it increases the rate of convergence. Finally, we address the traffic state estimation problem, by showing how handovers can be used as a proxy metric for flows in the underlying urban road network. Using a traffic flow theory model, we show that clusters of mobile network cells behave characteristically, and with this model we reach a MAPE of 11.1% with respect to floating-car data as ground truth. The presented model can be used in regions without traffic counting infrastructure, or complement existing traffic state estimation systems

Estimating Traffic Disruption Patterns with Volunteered Geographic Information

This is the final version. Available from Nature Research via the DOI in this record. Data are available from Zenodo at https://zenodo.org/record/3383443.Accurate understanding and forecasting of traffic is a key contemporary problem for policymakers. Road networks are increasingly congested, yet traffic data is often expensive to obtain, making informed policy-making harder. This paper explores the extent to which traffic disruption can be estimated using features from the volunteered geographic information site OpenStreetMap (OSM). We use OSM features as predictors for linear regressions of counts of traffic disruptions and traffic volume at 6,500 points in the road network within 112 regions of Oxfordshire, UK. We show that more than half the variation in traffic volume and disruptions can be explained with OSM features alone, and use cross-validation and recursive feature elimination to evaluate the predictive power and importance of different land use categories. Finally, we show that using OSM’s granular point of interest data allows for better predictions than the broader categories typically used in studies of transportation and land use.Natural Environment Research Council (NERC)Innovate UKEngineering and Physical Sciences Research Council (EPSRC

On agent-based modeling: Multidimensional travel behavioral theory, procedural models and simulation-based applications

This dissertation proposes a theoretical framework to modeling multidimensional travel behavior based on artificially intelligent agents, search theory, procedural (dynamic) models, and bounded rationality. For decades, despite the number of heuristic explanations for different results, the fact that "almost no mathematical theory exists which explains the results of the simulations" remains as one of the large drawbacks of agent-based computational process approach. This is partly the side effect of its special feature that "no analytical functions are required". Among the rapidly growing literature devoted to the departure from rational behavior assumptions, this dissertation makes effort to embed a sound theoretical foundation for computational process approach and agent-based microsimulations for transportation system modeling and analyses. The theoretical contribution is three-fold: (1) It theorizes multidimensional knowledge updating, search start/stopping criteria, and search/decision heuristics. These components are formulated or empirically modeled and integrated in a unified and coherent approach. (2) Procedural and dynamic agent-based decision-making is modeled. Within the model, agents make decisions. They also make decisions on how and when to make those decisions. (3) Replace conventional user equilibrium with a dynamic behavioral user equilibrium (BUE). Search start/stop criteria is defined in the way that the modeling process should eventually lead to a steady state that is structurally different to user equilibrium (UE) or dynamic user equilibrium (DUE). The theory is supported by empirical observations and the derived quantitative models are tested by agent-based simulation on a demonstration network. The model in its current form incorporates short-term behavioral dimensions: travel mode, departure time, pre-trip routing, and en-route diversion. Based on research needs and data availability, other dimensions can be added to the framework. The proposed model is successfully integrated with a dynamic traffic simulator (i.e. DTALite, a light-weight dynamic traffic assignment and simulation engine) and then applied to a mid-size study area in White Flint, Maryland. Results obtained from the integration corroborate the behavioral richness, computational efficiency, and convergence property of the proposed theoretical framework. The model is then applied to a number of applications in transportation planning, operations, and optimization, which highlights the capabilities of the proposed theory in estimating rich behavioral dynamics and the potential of large-scale implementation. Future research should experiment the integration with activity-based models, land-use development, energy consumption estimators, etc. to fully develop the potential of the agent-based model