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Dynamics of heterogeneity in urban networks: Aggregated traffic modeling and hierarchical control

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Abstract

Real traffic data and simulation analysis reveal that for some urban networks a well-defined Macroscopic Fundamental Diagram (MFD) exists, which provides a unimodal and low-scatter relationship between the network vehicle density and outflow. Recent studies demonstrate that link density heterogeneity plays a significant role in the shape and scatter level of MFD and can cause hysteresis loops that influence the network performance. Evidently, a more homogeneous network in terms of link density can result in higher network outflow, which implies a network performance improvement. In this article, we introduce two aggregated models, region- and subregion-based MFDs, to study the dynamics of heterogeneity and how they can affect the accuracy scatter and hysteresis of a multi-subregion MFD model. We also introduce a hierarchical perimeter flow control problem by integrating the MFD heterogeneous modeling. The perimeter flow controllers operate on the border between urban regions, and manipulate the percentages of flows that transfer between the regions such that the network delay is minimized and the distribution of congestion is more homogeneous. The first level of the hierarchical control problem can be solved by a model predictive control approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant (reality) is formulated by the subregion-based MFDs, which is a more detailed model. At the lower level, a feedback controller of the hierarchical structure, tries to maximize the outflow of critical regions, by increasing their homogeneity. With inputs that can be observed with existing monitoring techniques and without the need for detailed traffic state information, the proposed framework succeeds to increase network flows and decrease the hysteresis loop of the MFD. Comparison with existing perimeter controllers without considering the more advanced heterogeneity modeling of MFD highlights the importance of such approach for traffic modeling and control.

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... In practice, the density is most commonly estimated using the fundamental 35 relation between density and speed ( = * ), where is the flow, is the density and is the speed. In the presence of a 1 heterogeneous traffic stream, the relationship between occupancy and density is complex (Ramezani et al., 2015). 2 ...
... During the calibration process, the range of parameter values is constrained within meaningful ranges of values for each parameter. 5 The initial values and the range of parameters, being set by the domain experts results in the parameters having some level of 6 physical significance, thus making the models interpretable. The predicted traffic is the net result of the interaction between the 7 agents in the calibrated model. ...
... Instead, the comparison between DQNs using different neural network architectures is common. 5 Unless the DQN based solutions are demonstrated to perform better than the existing methods, the real-world deployment of 6 ...
Article
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Detecting, predicting, and alleviating traffic congestion are targeted at improving the level of service of the transportation network. With increasing access to larger datasets of higher resolution, the relevance of deep learning for such tasks is increasing. Several comprehensive survey papers in recent years have summarised the deep learning applications in the transportation domain. However, the system dynamics of the transportation network vary greatly between the non-congested state and the congested state — thereby necessitating the need for a clear understanding of the challenges specific to congestion prediction. In this survey, we present the current state of deep learning applications in the tasks related to detection, prediction, and alleviation of congestion. Recurring and non-recurring congestion are discussed separately. Our survey leads us to uncover inherent challenges and gaps in the current state of research. Finally, we present some suggestions for future research directions as answers to the identified challenges.
... To facilitate modelling and control of a heterogeneous urban network, it can be partitioned into several smaller homogeneous sub-regions with well-defined MFDs, using spatial properties of congestion (Ji and Geroliminis 2012). Perimeter controllers, metering the amount of flow that is allowed to transfer between any two neighboring regions, were developed for control of urban networks (Daganzo 2007;Geroliminis, Haddad, and Ramezani 2012;Keyvan-Ekbatani et al. 2012;Aboudolas and Geroliminis 2013;Haddad and Shraiber 2014;Ramezani, Haddad, and Geroliminis 2015;Haddad 2017). Model predictive control (MPC) was utilized for modelling control problems for real-time control purposes (Haddad, Ramezani, and Geroliminis 2013;Hajiahmadi et al. 2014;Ramezani, Haddad, and Geroliminis 2015;Yildirimoglu, Ramezani, and Geroliminis 2015;Sirmatel and Geroliminis 2017;Aalipour, Kebriaei, and Ramezani 2018). ...
... Perimeter controllers, metering the amount of flow that is allowed to transfer between any two neighboring regions, were developed for control of urban networks (Daganzo 2007;Geroliminis, Haddad, and Ramezani 2012;Keyvan-Ekbatani et al. 2012;Aboudolas and Geroliminis 2013;Haddad and Shraiber 2014;Ramezani, Haddad, and Geroliminis 2015;Haddad 2017). Model predictive control (MPC) was utilized for modelling control problems for real-time control purposes (Haddad, Ramezani, and Geroliminis 2013;Hajiahmadi et al. 2014;Ramezani, Haddad, and Geroliminis 2015;Yildirimoglu, Ramezani, and Geroliminis 2015;Sirmatel and Geroliminis 2017;Aalipour, Kebriaei, and Ramezani 2018). ...
... n ii denotes the accumulation of region i with a final trip destination within the same region (internal trip) while n ij denotes the accumulation of region i with a final trip destination in another region j (external trip). The general mass conservation equations of the multi-region urban network as described by Ramezani, Haddad, and Geroliminis (2015) are as follows: ...
Article
In this paper, a network-wide anticipatory control (AC) framework, incorporating drivers' route choice behaviour, is proposed. The proposed AC, consisting of two main levels of control and route choice, explicitly accounts for road users' responses to the implemented control. Perimeter control, modelled in an MPC framework for real-time applications, optimizes inter-regional transferring flow at the network level. User equilibrium is established through a logit route choice model and solved using the method of successive averages (MSA). The modelling approach adopted is based on macroscopic fundamental diagram (MFD), which provides a unimodal low-scatter relationship between density and outflow of any region within a network. Numerical results indicate that the proposed AC outperforms no control and basic control cases and shows promising results in alleviating congestion and deriving the network to near-system optimum traffic condition, under various demand patterns and levels.
... Enabled via MFD-based modeling approaches, model-based traffic control design methods also received increasing interest: Nonlinear model predictive control (MPC) for a two-region network actuated with perimeter control , hybrid MPC with perimeter control and switching signal timing plans (Hajiahmadi et al., 2015), dynamical modeling of heterogeneity and hierarchical control with MPC on the upper level (Ramezani et al., 2015), MPC with MFD-based travel time and delays as performance measures (Csikós et al., 2017), two-level hierarchical MPC with MFD-based and link-level models (Zhou et al., 2017), multimodal MFDs network model-based MPC of city-scale ride-sourcing systems (Ramezani and Nourinejad, 2018), MPC with perimeter control and regional route guidance and extensions with a path assignment mechanism (Yildirimoglu et al., 2018), combined operation of state estimation and MPC (Sirmatel and Geroliminis, 2019). Detailed literature reviews of MFD-based modeling and control can be found in Sirmatel and Geroliminis (2019) and Haddad and Zheng (2020). ...
... Further extensions to MFD-based modeling were also proposed to obtain more detailed models considering heterogeneity effects (Ramezani et al., 2015), boundary queues (Haddad, 2017b;Ni and Cassidy, 2019) and dynamic user equilibrium (Guo and Ban, 2020;Ingole et al., 2020). This paper aims to investigate potential advantages that could be obtained by freeing the standard MFD-based dynamical models from the steady-state approximation associated with using an outflow MFD by the production-over-trip length approach. ...
... , R}) (see, e.g., fig. 1(b)), each with a well-defined MFD, aggregated dynamical models of large-scale road traffic networks can be developed based on inter-regional traffic flows as the following vehicle conservation equations (Ramezani et al., 2015): ...
Article
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City-scale control of urban road traffic poses a challenging problem. Dynamical models based on the macroscopic fundamental diagram (MFD) enable development of model predictive perimeter control methods for large-scale urban networks, representing an advanced control solution carrying substantial potential for field implementation. In this paper we develop a multi-region approximation of the trip-based model, which describes in more details the trip length characteristics compared to existing accumulation-based models. The proposed M-model includes effects of the total remaining travel distance on the transfer flows driving the vehicle accumulation dynamics, potentially yielding improved accuracy over the standard production-over-trip length approximation of the outflow MFD considered in many works on MFD-based modeling and control. We explain that to properly perform perimeter control, boundary queue dynamics have to be integrated. Furthermore, model-based parameter estimation (MBPE), nonlinear moving horizon observer (MHO), and model predictive control (MPC) formulations for the proposed models are presented, forming an integrated traffic control framework. Microsimulation-based case studies, considering an urban network with 1500 links, where the model parameters obtained by MBPE method are used in MHO and MPC design, demonstrate the efficient operation of the proposed framework.
... These control strategies often require detailed local traffic information and encompass hefty computational costs. Introduction of network macroscopic fundamental diagram (MFD) enabled a promising direction towards the network-level systematic congestion management at a very low computational cost through perimeter flow control (Geroliminis et al., 2012;Ramezani et al., 2015;Yang et al., 2018;Lei et al., 2019;Ingole et al., 2020;Li et al., 2021), congestion pricing (Daganzo and Lehe, 2015;Simoni et al., 2015;Amirgholy and Gao, 2017;Gu et al., 2018;Zheng and Geroliminis, 2020), route guidance Yildirimoglu et al. (2015), departure time management (Yildirimoglu and Ramezani, 2020), and ride-sourcing operation control (Ramezani and Nourinejad, 2018) among others. ...
... [veh] are the number of vehicles in Subregion ℎ at time and the jam accumulation of Subregion ℎ, respectively. Note that the receiving capacity proposed in Ramezani et al. (2015) considered each incoming flow to Subregion ℎ independently. On the other hand, Eq. (2) takes into account all the incoming flows collectively and distribute the available receiving capacity of Subregion ℎ proportionally (demand pro-rata as investigated in Mariotte et al. (2020b)). ...
... (7) In addition, the subregion-level perimeter control, ( ), are equal to the region-level perimeter control, ( ) ( ∈ ℛ ( ), ∈ ℛ ( )). The perimeter control synthesis based on LQR theory is explained in Section 3. Note that a second level controller to break down regional ( ) to subregional ( ) (see for example Ramezani et al. (2015)), can be investigated as a future research to complement the dynamic cordon feature. ...
Article
With unbalanced travel demand distribution over time and space, a stationary cordon location hinders the full potential of perimeter flow control based on network Macroscopic Fundamental Diagram (MFD). This paper introduces a perimeter control method wherein the region boundaries alter in real-time to tackle propagation of local pockets of congestion. The nonlinear dynamics of the heterogeneous traffic network are modelled as a switching system. The linearization of the derived switching nonlinear dynamics is conducted considering the accumulation heterogeneity. A Linear Quadratic Regulator (LQR) is employed for gating the flow exchange between regions to minimize network congestion. Several scenarios are examined comparing perimeter control schemes with static and dynamic cordons. Results pinpoint the proposed LQR control with location-varying cordon strategy and a moderate switching interval significantly reduces the vehicles total time spent in the network.
... A hybrid MPC formulation is developed in [35] for an urban network equipped with both perimeter control systems and switching signal timing plans. A model with heterogeneity dynamics is described in [36] together with a hierarchical control system with MPC on the upper level. Considering performance constraints on travel time and delay metrics, a model predictive perimeter controller is designed in [37]. ...
... where l ij (m) is the average trip length traveled inside region i for trips from i to j. Details of such models (and their extensions) can be found in [52] and [36]. In [16] the assumption of outflow being approximately equal to production divided by trip length was tested with real data without any OD information. ...
... where a i , b i , and c i are known parameters (which are to be extracted from historical data in practice). Multi-region dynamical modeling formulations for urban networks with more than two regions can be found in [36], [63]. ...
Thesis
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Urbanization intensifies as a global trend, exposing transportation networks to ever increasing levels of congestion. As network usage increases with available infrastructure, building new roads is not a solution. Design of intelligent transportation systems, involving identification, estimation, and feedback control methods with dynamical traffic models, is emerging as a feasible way to improve operation of existing infrastructure. Nevertheless, complexity of large-scale networks, spatiotemporal propagation of congestion, and uncertainty in traveler choices present considerable challenges for modeling, estimation, and control of road transport systems. This dissertation focuses on development of novel and practicable optimization-based traffic control and estimation methods for improving mobility in large-scale urban road networks. Part 1 is dedicated to identification, estimation, and control methods based on macroscopic traffic dynamics for perimeter controlled urban networks. Obtaining accurate estimates of model parameters and traffic states is critical for feedback perimeter control systems. In chapter 2, a nonlinear moving horizon estimation (MHE) scheme is proposed for combined state and demand estimation for a two-region urban network with dynamical modeling via macroscopic fundamental diagram (MFD). A traffic control framework consisting of identification, state estimation, and control methods is developed in chapter 3, enabling model-based feedback perimeter control of city-scale traffic. Part 2 focuses on traffic management methods considering regional route guidance. Equipping traffic controllers with route guidance carries potential for high performance congestion management. Chapter 4 contains model predictive control (MPC) schemes integrating route guidance and perimeter control actuators, capable of superior performance compared to using only perimeter control. A hierarchical traffic controller is designed in chapter 5, employing a path assignment mechanism to realize macroscopic route guidance commands of a network-level MPC.
... The previous model considers the general situation in which all regions are connected bidirectionally; when this assumption does not hold, the model could be adapted by setting to zero the accumulations and control inputs associated to the flow between regions that are not connected. The presented model for the N -region MFD system (2)-(4) considers a N 2 -dimensional state vector, as e.g. in Geroliminis et al. (2013); Ramezani et al. (2015). This description is more accurate than the alternative approach that considers an N -dimensional state vector, i.e, the state vector includes a variable for the accumulation of each region n i , see e.g. ...
... This effect has been attributed in the literature to heterogeneous distribution of vehicles in space and time at the disaggregated level, see e.g. Saberi and Mahmassani (2013); Ramezani et al. (2015); Mazloumian et al. (2010). By considering this multiplicative uncertainty, it is taken into account a phenomenon (scattered MFD) that is not considered in the aggregate model. ...
Article
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The Macroscopic Fundamental Diagram (MFD) concept has become a very valuable tool for modeling the aggregated dynamic of large-scale urban traffic networks. This advance in traffic modeling has fueled the development of many urban traffic control (UTC) policies based on the MFD concept. In particular, perimeter control policies with the aim of maintaining a large-scale urban traffic network operating at its maximum capacity by manipulating the transfer flow of vehicles between adjacent homogeneous regions. In addition to achieve a satisfactory performance level, it is desirable that the control system would maintain a reliable operation under unanticipated events such as cyberattacks. It is important to note that modern UTC systems extensively rely on information technology infrastructures making them vulnerable to cyberattacks. Due to the occurrence of real-world cyberattacks affecting controlled physical systems in different fields, the threat of cyberattacks is becoming a serious and increasing concern for the proper operation of UTC. This paper presents a resilient multivariable control framework for large-scale urban traffic networks subject to several types of cyberattacks such as deception attacks and denial of service (DoS) attacks. Additionally, a feedforward–feedback control scheme combining a time-optimal controller with the resilient multivariable controller is also proposed. The aim of this feedforward–feedback controller is to steer the accumulations to their desired values after a large deviation. Finally, the performance of the proposed resilient controller is demonstrated by means of some realistic simulations of urban traffic networks, including stochastic errors in the traffic demands and in the MFD model, in addition to cyberattacks.
... Consider a network consisting of a set of regions  = {1, 2, … , }, where  is the set containing the index of each region while is the number of regions in the network. Associating each region with a well-defined MFD, aggregated dynamical models of large-scale road traffic networks can be developed based on interregional traffic flows via following vehicle conservation equations (Ramezani et al., 2015): ...
... Such scenarios are typically replicated using inflow demand trajectories that are trapezoidal in time (i.e., starts with zero or low values, rises to high values and stays there for some time, and then falls to zero or low values). Simulation-based analysis of such high demand scenarios with trapezoidal trajectories can be found in most works on feedback perimeter control (see Geroliminis et al., 2013;Ramezani et al., 2015;Sirmatel & Geroliminis, 2019). Here we consider a different traffic scenario that we term congestion recovery. ...
Article
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Traffic control for large-scale urban road networks remains a challenging problem. Aggregated dynamical models of city-scale traffic, based on the macroscopic fundamental diagram (MFD), enable development of model-based perimeter control methods. Involving actuation over aggregated traffic flows, perimeter control specifies an effective and practicable congestion control solution. In this paper, we propose nonlinear model predictive perimeter control schemes, for regulation and economic optimization objectives, with closed-loop stability by construction. Macroscopic and microscopic simulations demonstrate the performance and domain of attraction properties of the proposed formulations. Results indicate potential of the methods for efficient and reliable control of city-scale traffic.
... traffic control based on the static critical point (see e.g. Geroliminis and Levinson (2009), Haddad and Geroliminis (2012), Knoop et al. (2014), Zheng and Geroliminis (2016), He et al. (2019), Ramezani et al. (2015), Ampountolas and Kouvelas (2015), Keyvan-Ekbatani et al. (2016) and Yang et al. (2018)). IIb The dynamic MFD, dMFD, a definition introduced by Mahmassani et al. (2013), considers the MFD as a tool to observe, understand, and model the loading and unloading of urban traffic. ...
... The higher the heterogeneity in density, the lower the average flow. Similarly, Ramezani et al. (2015) look into the relationship between the average flow and the observed heterogeneity. Based on a aggregated modeling approach the authors introduce a hierarchical perimeter flow control that takes into account the neighborhood's heterogeneity. ...
Article
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Urban road transportation performance is the result of a complex interplay between the network supply and the travel demand. Fortunately, the framework around the macroscopic fundamental diagram (MFD) provides an efficient description of network-wide traffic performance. In this paper, we show how temporal patterns of vehicle traffic define the performance of urban road networks. We present two high-resolution traffic datasets covering a year each. We introduce a methodology to quantify the similarity of macroscopic traffic patterns. We do so by using the concepts of the MFD and a dynamic time warping (DTW) based algorithm for time series. This allows us to derive a few representative MFD clusters that capture the essential macroscopic traffic patterns. We then provide an in-depth analysis of traffic heterogeneity in the network which is indicative of the previously found clusters. Thereupon, we define a parsimonious classification approach to predict the expected MFD clusters early in the morning with high accuracy.
... where − and are increasing functions of network average density, ( ) stand for congestion distribution, and other variables are the same as previously defined. Later, Ramezani et al. (2015) proposed that the NMFD can be estimated as the production of two functions. A polynomial function of network accumulation representing the low scattered NMFD and an exponential function of congestion distribution representing the effects of congestion distribution. ...
... A promising example can be found in Shim et al. (2019) where a deep empirical discussion on the appearance of bifurcation was provided highlighting the detouring patterns, heterogeneity, commute trips, and the trip completion rate as bifurcations' influential factors. Besides, the proposed relationships provided in Mahmassani et al. (2013b) and Ramezani et al. (2015) mainly depend on the employed data putting a limitation on providing a general statement. In addition, we think the best address regarding the heterogeneous congestion problem is network partitioning (Ji and Geroliminis, 2012). ...
Article
Network macroscopic fundamental diagrams (NMFD) and related network-level traffic dynamics models have received both theoretical support and empirical validation with the emergence of new data collection technologies. However, the extent to which network-level macroscopic traffic models may be ready for practical implementation remains to be ascertained. This paper aims to shed light on this matter by reviewing the 50-year history of macroscopic modeling of urban networks and assessing remaining gaps and opportunities for further development of both theory and applications. To this end, the existing literature’s chronology is mapped onto three eras of development, and the corresponding theories, assumptions, and limitations are outlined and discussed in two streams, equilibrium relations and traffic dynamics. Among the topics pertaining to equilibrium relations, the highlighted gaps include the lack of empirical studies on the hysteresis and bifurcation phenomena, the existence of multi-modal NMFD (3D-NMFD) in different traffic conditions, the factors that might affect the (3D-) NMFD shape, the accuracy of speed-NMFDs in particular different bus speed NMFDs, and the passenger-oriented NMFDs. Research gaps pertaining to traffic dynamics include the analytical solution of trip-based models, the FIFO violation in the delay-based models, the definition of outflow and entrance functions, the notion of active network length, the trip length distribution, and the path flow distribution. Future research directions targeting topics that might shape the potential next era include the practical implementation of NMFD-based control strategies, the application of NMFD in quality of service assessments, and NMFD in the presence of new technologies such as connected and autonomous vehicles (CAVs).
... Network or macroscopic fundamental diagram (NFD or MFD) represents network traffic flow relationships at the macroscopic scale (Mahmassani et al., 1984, Geroliminis andDaganzo, 2008). The NFD has been widely applied in network-wide traffic control and management , Haddad, 2017, Haddad et al., 2013, Yang et al., 2017, Keyvan-Ekbatani et al., 2012, Ramezani et al., 2015, Mohajerpoor et al., 2020, Ramezani and Nourinejad, 2018, Han et al., 2020 and equilibrium-based macroscopic route guidance (Lamotte, 2017;Lamotte and Geroliminis, 2018;Yildirimoglu, 2018). NFD-based congestion pricing is often conducted by macroscopic modeling of the network with a simulator and the toll level is then adjusted by using the NFD of the pricing zone (Simoni et al., 2015, Zheng et al., 2012 which is used as an indicator for monitoring and controlling the congestion level. ...
... A feedback control strategy is applied to adjust the distance-based toll rates for every toll interval. This approach has wide applications in traffic management and control, including ramp metering (Papageorgiou et al., 1991), perimeter or gating control (Keyvan-Ekbatani et al., 2012, Aboudolas and Geroliminis, 2013, Ramezani et al., 2015, and congestion pricing (Gu et al., 2018b, Zheng et al., 2012. It works by iteratively adjusting the control input based on the feedback output to achieve a predetermined setpoint. ...
Article
Routing controllability of connected and autonomous vehicles (CAVs) has been shown to reduce the adverse effects of selfish routing on the network efficiency. However, the assumption that CAV owners would readily allow themselves to be controlled externally by a central agency for the good of the system is unrealistic. In this paper, we propose a joint routing and pricing control scheme that aims to incentivize CAVs to seek centrally controlled system-optimal (SO) routing by saving on tolls while user equilibrium (UE) seeking human-driven vehicles (HVs) are subject to a congestion charge. The problem is formulated as a bi-level optimization program where the upper level optimizes the dynamic toll rates using the network fundamental diagram (NFD) and the lower level is a mixed equilibrium simulation-based dynamic traffic assignment model (SBDTA) considering different combinations of SO-seeking CAVs. We apply a feedback-based controller to solve for the optimal spatially differentiated distance-based congestion charge from which SO-seeking CAVs are exempt; but UE-seeking HVs are subject to the charge for entering the city center. To capture the distinct microscopic behavior of CAVs in the mixed autonomy traffic, we also implement an adaptive link fundamental diagram (FD) within the SBDTA model. The proposed joint control scheme encourages CAV owners to seek SO routing resulting in less total system travel time. It also discourages UE-seeking HVs from congesting the city center. We demonstrate the performance of the proposed scheme in both a small network and a large-scale network of Melbourne, Australia.
... However, Mahmassani, Saberi, and Zockaie (2013) argued that the simplifications excluded many complications found in real networks. To reduce the spread of the MFD scatter, several novel clustering algorithms and control measures have been proposed (Ramezani, Haddad, and Geroliminis 2015;Saeedmanesh and Geroliminis 2016). ...
Article
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Network topologies are considered to be the fundamental factors that govern the network’s macroscopic fundamental diagram (MFD) and performance. Despite its significance, this domain remains underexplored. This study employed empirical data as evidence to examine the explicit connections between network topologies and the parameters of a specific MFD, in the form of a macroscopic Underwood’s model. Sixty-three 1 × 1 km dense urban networks were sampled in Hong Kong. The macroscopic Underwood’s models of the sampled networks were estimated based on taxi Global Positioning System (GPS) data. The results reveal that the network free-flow speed decreased with the average number of junctions per unit distance, which captures the frequency of network-induced stop-and-go vehicle motion. The network optimal density decreased with the degree density normalized by the trafficable area, which represents the intensity of the conflicts between traffic streams. A spatially variable macroscopic Underwood’s model was subsequently established.
... Some studies have proposed solutions to that issue by considering external queues in the objective function (Hajiahmadi et al., 2015;Yang et al., 2016;Kouvelas et al., 2017;Nie and Cassidy, 2019) or by implementing multiple control cordons to distribute the congestion, e.g. (Aboudolas and Geroliminis, 2013;Ramezani et al., 2015;Haddad and Mirkin, 2017;Ampountolas, K. et al., 2017). ...
Article
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This paper presents a new concept for operating traffic management at a sizeable urban scale. The overall principle is to partition the network into multiple regions, where traffic conditions should remain optimal. Instead of monitoring the inflow, like for perimeter control, deviations in regional mean speed compared to a reference value are transformed into avoidance levels by a centralized controller. That information is broadcasted to vehicles through a public avoidance map. The onboard navigation systems then interpret this map to deliver individual route guidance according to the avoidance levels. In that way, the concept tends to distribute vehicles in the network optimally while preserving privacy. In addition to the controller parameters itself, three other critical parameters define the system: the safety distance, the controller time horizon, and the region sizes. Thorough sensitivity analysis leads to the optimal setting. The concept is proven effective using microsimulation for both a Manhattan and a realistic network. The total travel time is improved by about 15% when traffic is severely congested compared to the uncontrolled case. In the meantime, the mean individual travel distance increase for rerouted vehicles is kept below 10%. Those results have been obtained with a simple decentralized reactive control framework, i.e., an individual proportional feedback system independently governs each region. More advanced formulations introducing cooperation between the regions are also tested. In a nutshell, this paper is a proof of concept for a new control system that appears both practical and valuable to alleviate congestion in urban areas. © 2021 The Authors. Published by Elsevier B.V. Peer-review under responsibility of the scientific committee of the 24th International Symposium on Transportation and Traffic Theory
... capacity as high accumulation in region h might restrict the reception of inflows from the 10 boundary. According toRamezani et al. (2015) and Yildirimoglu et al. ...
Article
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The spatio-temporal imbalance of parking demand and supply results in unwanted on-street cruising-for-parking traffic of conventional vehicles. Autonomous vehicles (AVs) can self-relocate to alleviate the shortage of parking supplies at the trip destinations. The extra floating trips of vacant AVs have adverse impacts on traffic congestion and the parking demand–supply imbalance may still exist when they are not distributed optimally. This paper presents a centralized parking dispatch approach to optimize the distribution of floating AVs and provide regional route guidance. We apply the concept of macroscopic fundamental diagram to represent the evolution of traffic conditions, cruising-for-parking, and dispatched AVs in a congested multi-region network. A model predictive control is suggested to optimize the control inputs. Numerical experiments in a four-region network demonstrate that the proposed parking dispatch and regional route guidance of AVs are effective in reducing intense cruising-for-parking traffic, and the integration of both has the best control performance by regulating the network towards under-saturated conditions. The performance of the proposed schemes is evaluated via simulations with noise in measurement errors and compliance rate prediction. Results show substantial improvements in terms of total time spent, even for low levels of AV market penetration or AV compliance rate to parking dispatch and route guidance.
... These static traffic assignment models are often used to analyze and evaluate network traffic performance under long-term equilibrium conditions, that is, for the planning or design of the road network. On the other hand, dynamic traffic assignment models that consider dynamic travel behavior can be used to study the spatial and temporal distribution characteristics of traffic flow, the formation and diffusion mechanisms of traffic congestion, as well as the impacts of driving behavior (Saberi et al. 2015;Ramezani et al. 2015;Mazloumian et al. 2010). ...
Article
Superblocks are city blocks whose size is significantly larger than average for a city block. They are considered to be close if they only have a few gates connecting the pedestrian and car traffic inside with that outside of the block. The gate setting of superblocks, namely the number and location of gates, despite playing a very important role in the overall traffic performance, has attracted limited attention in research. This paper narrows this gap by proposing a bilevel optimization model to calculate the optimal gate setting for superblocks. The lower-level model involves the traffic assignment, paying attention to travelers' mode and route choice behavior. The upper-level model computes the optimal number and location of gates to minimize the total cost, considering both travelers' cost and infrastructure cost. To solve this model efficiently, we also develop a solution algorithm, whose output is the optimized gate setting. A case study is used to illustrate the impact of the gate-setting problem on the performance of the transportation network, and the applicability of the proposed algorithm. Results indicate that the number and location of gates significantly impact traffic performance. For example, it is possible to have a lower cost with three gates that are well located than with nine gates that are poorly located. Furthermore, for the specific network studied, the optimal gate setting solution reduces the total cost by 17% and leads to a 3% mode shift from private car to metro when compared with the existing conditions.
... Daganzo (2007) applied the MFD framework to devise a control rule that maximizes the network trip completion rate. Geroliminis et al. (2013); Ramezani et al. (2015) solved the optimal perimeter control problem within standard two-region MFD system by model predictive control (MPC) while Haddad et al. (2013) implemented MPC on a mixed network. Other optimal perimeter controls of the MFD system using MPC were in a hierarchical scheme (Zhou et al., 2016;Fu et al., 2017). ...
Article
Existing data-driven and feedback traffic control strategies do not consider the heterogeneity of real-time data measurements. Besides, traditional reinforcement learning (RL) methods for traffic control usually converge slowly for lacking data efficiency. Moreover, conventional optimal perimeter control schemes require exact knowledge of the system dynamics and thus they would be fragile to endogenous uncertainties. To handle these challenges, this work proposes an integral reinforcement learning (IRL) based approach to learning the macroscopic traffic dynamics for adaptive optimal perimeter control. This work makes the following primary contributions to the transportation literature: a) A continuous-time control is developed with discrete gain updates to adapt to the discrete-time sensor data. Different from the conventional RL approaches, the reinforcement interval of the proposed IRL method can be varying with respect to the real-time resolution of data measurements. Approximate optimization methods are carried out to address the curse of dimensionality of the optimal control problem with consideration on the resolution of data measurement. b) To reduce the sampling complexity and use the available data more efficiently, the experience replay (ER) technique is introduced to the IRL algorithm. c) The proposed method relaxes the requirement on model calibration in a "model-free" manner that enables robustness against modeling uncertainty and enhances the real-time performance via a data-driven RL algorithm. d) The convergence of the IRL based algorithms and the stability of the controlled traffic dynamics are proven via the Lyapunov theory. The optimal control law is parameterized and then approximated by neural networks (NN), which moderates the computational complexity. Both state and input constraints are considered while no model linearization is required. Numerical examples and simulation experiments are presented to verify the effectiveness and efficiency of the proposed method.
... Combining the information from the figures above, a clearer illustration of a well-defined 3D e-MFD can be seen in Fig. 9. Compared to the 3D e-MFD reported in Saedi et al. (2020) for an aggregated measure of total emissions per time, the empirical e-MFD does not experience a hysteresis loop as the simulated one. A possible explanation might be that the size of hysteresis in the e-MFD might depend (similarly to the MFD) on the spatial distribution of congestion, the driver adaptability and the unloading demand profile (see for example (Mahmassani et al., 2013;Ramezani et al., 2015)). In principle, most simulation models are calibrated for the onset of congestion and the demand decreases quite sharply in the offset creating a higher hysteresis loop. ...
Article
Vehicle emissions are a major contributor of air pollution in urban areas, with severe consequences for public health and the environment. This paper focuses on analyzing vehicle emissions in a multimodal urban context to better understand its determinants and investigate relations between emissions and congestion patterns. Thousands of naturalistic trajectories collected with a swarm of drones during the pNEUMA experiment are analyzed and EPA’s microscopic emission model, project level MOVES, is implemented to estimate vehicular emissions. The method is developed and illustrated with a CO2 analysis. The results empirically show the aggregated relationships between congestion and vehicular emissions, while accounting for the individual characteristics of each trajectory. These systematic relationships on a network scale with the use of empirical data, allow us to extend the macroscopic fundamental diagram (MFD) to the emissions-MFD (e-MFD). The spatiotemporal distribution of emissions is also studied, highlighting areas with high concentration over the urban area.
... It would mean for example that most of our current control methods based on standard calculus and statistics techniques may no longer apply or may need a major overhaul. Notably, this paradigm is in stark contrast to the currently accepted view in our field that an optimal strategy is to meter the network so that it remains at the "sweet spot": near the critical density where flows are maximized (Geroliminis et al., 2012, Hajiahmadi et al., 2013, Haddad et al., 2013, Ramezani et al., 2015, Keyvan-Ekbatani et al., 2015, Guo and Ye, 2016, Ampountolas et al., 2017, Haddad, 2017, Ding et al., 2017, Fu et al., 2017, Kouvelas et al., 2017, Sirmatel and Geroliminis, 2017, Yang et al., 2017, Yildirimoglu et al., 2018, Zhong et al., 2018, Guo and Ban, 2020. ...
Preprint
This paper shows that the kinematic wave model exhibits self-organized criticality when initialized with random initial conditions around the critical density. A direct consequence is that conventional traffic management strategies seeking to maximize the flow may be detrimental as they make the system more unpredictable and more prone to collapse. Other implications for traffic flow in the capacity state are discussed, such as: \item jam sizes obey a power-law distribution with exponents 1/2, implying that both its mean and variance diverge to infinity, and therefore traditional statistical methods fail for prediction and control, \item the tendency to be at the critical state is an intrinsic property of traffic flow driven by our desire to travel at the maximum possible speed, \item traffic flow in the critical region is chaotic in that it is highly sensitive to initial conditions, \item aggregate measures of performance are proportional to the area under a Brownian excursion, and therefore are given by different scalings of the Airy distribution, \item traffic in the time-space diagram forms self-affine fractals where the basic unit is a triangle, in the shape of the fundamental diagram, containing 3 traffic states: voids, capacity and jams. This fractal nature of traffic flow calls for analysis methods currently not used in our field.
... This would be consistent with the NE assumption (20). However, more recent studies contradict these observations and have reported that the average trip length in an area does change over time (9,21). ...
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For transportation system analysis in a new space dimension with respect to individual trips’ remaining distances, vehicle trips demand has two main components: the departure time and the trip distance. In particular, the trip distance distribution (TDD) is a direct input to the bathtub model in the new space dimension, and is a very important variable to consider in many applications, such as the development of distance-based congestion pricing strategies or mileage tax. For a good understanding of the demand pattern, both the distribution of trip initiation and trip distance should be calibrated from real data. In this paper, it is assumed that the demand pattern can be described by the joint distribution of trip distance and departure time. In other words, TDD is assumed to be time-dependent, and a calibration and validation methodology of the joint probability is proposed, based on log-likelihood maximization and the Kolmogorov–Smirnov test. The calibration method is applied to empirical for-hire vehicle trips in Chicago, and it is concluded that TDD varies more within a day than across weekdays. The hypothesis that TDD follows a negative exponential, log-normal, or Gamma distribution is rejected. However, the best fit is systematically observed for the time-dependent log-normal probability density function. In the future, other trip distributions should be considered and also non-parametric probability density estimation should be explored for a better understanding of the demand pattern.
... In particular, mesoscopic models (Mahmassani and Herman, 1984;Zhou and Taylor, 2014) are used to represent spatial extents of congestion building up and dissipating with individual agents following a macroscopic flow density relationship while ignoring detailed lane-changing and car-following behavior. From a macroscopic aggregated traffic flow modeling perspective, some studies (e.g., Ramezani et al., 2015;-4-Han et al., 2020;Johari et al., 2021) used the macroscopic fundamental diagram to model and control traffic flows through ramp metering, signal control, and perimeter control, etc. ...
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As an active performance evaluation method, the fluid-based queueing model plays an important role in traffic flow modeling and traffic state estimation problems. A critical challenge in the application of traffic state estimation is how to utilize heterogeneous data sources in identifying key interpretable model parameters of freeway bottlenecks, such as queue discharge rates, system-level bottleneck-oriented arrival rates, and congestion duration. Inspired by Newell's deterministic fluid approximation model, this paper proposes a spatial queue model for over-saturated traffic systems with time-dependent arrival rates. The oversaturated system dynamics can be described by parsimonious analytical formulations based on polynomial functional approximation for virtual arrival flow rates. With available flow, density and end-to-end travel time data along traffic bottlenecks, the proposed modeling framework for estimating the key traffic queueing state parameters is able to systematically map various measurements to the bottleneck-level dynamics and queue evolution process. The effectiveness of the developed method is demonstrated based on three case studies with empirical data in different metropolitan areas, including New York, Los Angeles, and Beijing.
... In cordon pricing, number of vehicles entering the region is controlled via tolls drivers have to pay to be permitted to enter the region. These methods have been extensively explained in several studies [2][3][4][5]. ...
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Traffic congestion in large urban networks may take different shapes and propagates non-uniformly variations from day to day. Given the fact that congestion on a road segment is spatially correlated to adjacent roads and propagates spatiotemporally with finite speed, it is essential to describe the main pockets of congestion in a city with a small number of clusters. For example, the perimeter control with macroscopic fundamental diagrams is one of the effective traffic management tools. Perimeter control adjusts the inflow to pre-specified regions of a city through signal timing on the border of a region in order to optimize the traffic condition within the region. The precision of macroscopic fundamental diagrams depends on the homogeneity of traffic condition on road segments of the region. Hence, previous studies have defined the boundaries of the region under perimeter control subjected to the regional homogeneity. In this study, a cost-effective method is proposed for the mentioned problem that simultaneously considers homogeneity, contiguity and compactness of clusters and has a shorter computational time. Since it is necessary to control the cost and complexity of perimeter control in terms of the number of traffic signals, sparse parts of the network could be potential candidates for boundaries. Therefore, a community detection method (Infomap) is initially adopted and then those clusters are improved by refining the communities in relation to roads with the highest heterogeneity. The proposed method is applied to Shenzhen, China and San Francisco, USA and the outcomes are compared to previous studies. The results of comparison reveal that the proposed method is as effective as the best previous methods in detecting homogenous communities, but it outperforms them in contiguity. It is worth noting that this is the first method that guarantees the connectedness of clusters, which is a prerequisite of perimeter control.
... However, this approach is too restrictive and cannot represent the real condition (Mariotte and Leclercq 2019). Later, Ramezani, Haddad, and Geroliminis (2015) presented an entrance function including a constant part and a decreasing part starting from a critical accumulation defined as α.n jam (0 < α < 1). Next, Kim, Tak, and Yeo (2018) and considered an entrance function as depicted in Figure 4(b) and then limited the obtained inflow to reservoir border capacity as well. ...
Article
Network macroscopic fundamental diagram (NMFD) has provided practical convenience to simulate network-level traffic dynamics using NMFD-based models. Nevertheless, only a few works have been conducted on traffic dynamics in bi-modal urban networks. This paper provides a comparison of the application of outflow 2D-NMFD and 3D-NMFD through simulating different scenarios using accumulation-based model in a single reservoir system. The models are verified using micro-simulation data as ground truth performed on a Manhattan-style grid network and a real network. The results reveal the outflow 2D-NMFD can provide accurate traffic state evolution, while the goodness of fit is the main challenge in the application of outflow 3D-NMFD. Besides, the accumulation-based model needs modifications to construct the bus accumulation profile in the test-bed with a low share of buses. Last but not least, the accuracy of the existing network-level speed models in mixed-traffic condition and its effects on traffic dynamics simulation are validated and discussed.
... Existing traffic data analysis methods are either model based or data driven. Techniques that are geared toward the estimation of traffic densities or speeds from both fixed and mobile sensors are examples of the former (Jabari 2012;Jabari andLiu 2012, 2013;Yildirimoglu and Geroliminis 2013;Osorio and Flötteröd 2014;Ramezani, Haddad, and Geroliminis 2015;Seo et al. 2017;Lu and Osorio 2018;Zheng et al. 2018;Jabari et al. 2019;Osorio and Punzo 2019). Data-driven techniques are becoming more popular with the increasing availability of traffic data. ...
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This paper addresses the problem of short-term traffic prediction for signalized traffic operations management. Specifically, we focus on predicting sensor states in high-resolution (second-by-second). This contrasts with traditional traffic forecasting problems, which have focused on predicting aggregated traffic variables, typically over intervals that are no shorter than five minutes. Our contributions can be summarized as offering three insights: first, we show how the prediction problem can be modeled as a matrix completion problem. Second, we use a block-coordinate descent algorithm and demonstrate that the algorithm converges in sublinear time to a block coordinate-wise optimizer. This allows us to capitalize on the “bigness” of high-resolution data in a computationally feasible way. Third, we develop an ensemble learning (or adaptive boosting) approach to reduce the training error to within any arbitrary error threshold. The latter uses past days so that the boosting can be interpreted as capturing periodic patterns in the data. The performance of the proposed method is analyzed theoretically and tested empirically using both simulated data and a real-world high-resolution traffic data set from Abu Dhabi, United Arab Emirates. Our experimental results show that the proposed method outperforms other state-of-the-art algorithms.
... The concept of the network MFD or Network Fundamental Diagram is not new and has been used in various studies, such as in perimeter traffic control (14)(15)(16)(17), modeling and control of urban traffic emissions (18), and validation of microscopic simulation models (19). Although several studies have utilized the MFD to express the traffic dynamics of large-scale urban transport networks, only a few have applied it for the identification of capacity implications of AVs. ...
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The paper proposes a general framework for the assessment of the impacts of the introduction of Connected and Automated Transport Systems (CATS) on traffic. The main objective is to address the question of scalability and transferability of the identified impacts of Autonomous Vehicles (AVs) in particular, focusing on network performance of urban areas. A combination of microscopic and macroscopic simulations as well as statistical methods are applied. Microscopic simulation is conducted to measure the changes in network capacities by utilizing the concept of the Macroscopic Fundamental Diagram (MFD), under different AV penetration rates. The resulting capacities are used to estimate the effects on the Passenger Car Units (PCU) under different AV penetration rates and derive functional relationships, which are further introduced to travel demand models to forecast the macroscopic impacts on network performance. The results indicate a positive impact in relation to capacity changes resulting from the presence of AVs which vary with penetration rate. Analysis of three different urban networks, Barcelona, Bilbao (Spain), and Athens (Greece), reveals consistent trends. However, notable differences are observed on the estimated PCUs for Athens, potentially because of the different mixed-traffic composition. Further exploration of the critical AV modeling specifications and network characteristics is therefore required for deriving transferable PCU functional relationships across networks. Nevertheless, the static assignment results verify the expected trends in network performance impacts in relation to the applied PCU relationships. Finally, the transferability of the proposed methodology across networks is demonstrated.
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The estimation of trip lengths has been proven to be a key feature for the application of aggregated traffic models based on the Macroscopic Fundamental Diagram. The paths and distances to be traveled by vehicles in regional networks vary over time, due to changes in the traffic conditions. In this paper, we develop a methodological framework to ex- plicitly determine traffic-dependent regional paths and estimate their travel distances. This framework is incorporated into a dynamic traffic assignment module designed to target the Deterministic and Stochastic User Equilibrium in regional networks. We first discuss how regional paths and their characteristic trip lengths are influenced by changes in the regional traffic dynamics. We then test the proposed methodology for estimating traffic-dependent travel dis- tances on small and medium-sized networks, considering a simulation environment. We show that our methodology provides good estimations of the traffic-dependent trip lengths. Our results also shed light on the importance of how time-dependent trip lengths influence the traffic dynamics in the regions.
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Accumulation-based Macroscopic Fundamental Diagram (MFD) model is widely employed to design perimeter control methods to improve traffic operation in urban networks. While the accumulation-based MFD assumes a low-scatter, non-linear relationship between region production and accumulation, the outflow relationship in formulating dynamics of multi-region networks requires simplifying assumptions. The existing perimeter control methods are grounded on accumulation-based MFD models where the number of transferring vehicles is approximated by the ratio of the instantaneous number of vehicles based on their destinations. Moreover, perimeter control may lead to more vehicles queuing at the region boundary (i.e. cordon queues) which add local impediments on traveling vehicles and impact the accuracy of well-defined MFDs. To address these shortcomings under time-varying conditions, this paper develops a robust perimeter control method based on the Sliding Mode Control to minimize total travel time in the entire network. To test the performance of the proposed control method, a trip-based MFD model is developed that accounts for cordon queues and various trip lengths of individual travelers. In this paper, two-region accumulation-based and trip-based MFD models are compared through numerical experiments. The results pinpoint the proposed robust perimeter control method can effectively alleviate congestion and improve network efficiency during traffic rush hours.
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Network traffic flow prediction on a fine-grained spatio-temporal scale is essential for intelligent transportation systems, and extensive studies have been carried out in this area. However, existing methods are mostly data-driven, with stringent requirements on the amount and quality of data. The collected network-scale traffic data are expected to be complete, sufficient, and representative, containing most traffic flow patterns in the road network. Unfortunately, it is very rare that sufficient and representative traffic data across the whole road network in several consecutive weeks are available for model calibration. In real-world applications, data insufficiency and dataset shift problems are prevalent, resulting in the ‘cold start’ issue in traffic prediction. To deal with the challenges above, this paper develops a two-stage physics-informed transfer learning method for network-scale link-wise traffic flow knowledge transfer under MFD-based physical constraints. In the first stage, the road network is partitioned and similar traffic regions are identified according to the physical invariants and MFD characteristics. In this way, the network-scale link-wise traffic flow pattern transfer between similar regions can be initiated under the assumption that regions with similar aggregated traffic flow patterns are more likely to share comparable link-wise traffic flow features. In the second stage, we propose our knowledge transfer architecture Deep Tensor Adaptation Network (DTAN) to bridge traffic flow knowledge in source and target regions via the parallel Siamese network structure, and further reduce domain discrepancy by imposing two distribution adaptation regularizations. A real-world traffic dataset on the urban expressway network of Beijing is used for numerical tests. The experiment results show that the proposed framework can leverage the trade-off between specific regression task performance in a single region and generalized domain adaptation capacity across multiple regions. The data insufficiency, dataset shift, and heavy computational cost problems are alleviated by improving model transferability. Finally, extensive empirical analysis is carried out to explore traffic flow pattern transferability and its relation to network traffic properties.
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Technological advancements have focused increasing attention on Automated Mobility-on-Demand (AMOD) as a promising solution that may improve future urban mobility. During the last decade, extensive research has been conducted on the design and evaluation of AMOD systems using simulation models. This paper adds to this growing body of literature by investigating the network impacts of AMOD through high-fidelity activity- and agent-based traffic simulation, including detailed models of AMOD fleet operations. Through scenario simulations of the entire island of Singapore, we explore network traffic dynamics by employing the concept of the Macroscopic Fundamental Diagram (MFD). Taking into account the spatial variability of density, we are able to capture the hysteresis loops, which inevitably form in a network of this size. Model estimation results at both the vehicle and passenger flow level are documented. Environmental impacts including energy and emissions are also discussed. Findings from the case study of Singapore suggest that the introduction of AMOD may bring about significant impacts on network performance in terms of increased VKT, additional travel delay and energy consumption, while reducing vehicle emissions, with respect to the baseline. Despite the increase in network congestion, production of passenger flows remains relatively unchanged.
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In this article, Stochastic Model Predictive Control (SMPC) is employed for optimal perimeter control of traffic flow with uncertain Macroscopic Fundamental Diagram (MFD), traffic accumulation and traffic demand of two regions. Two regions urban traffic networks are described through the MFD. The MFD is a fundamental relation between average flow (production) and density (accumulation) in urban regions. Although the MFD is often assumed as a simple deterministic curve, possible heterogeneity in urban regions results in large scattering of the MFD pattern. Traffic accumulation is considered uncertain due to limited sources of measurements. Moreover, traffic demand is based on the stochastic nature of drivers. The stochastic uncertainty is modeled through appropriate probability distribution functions for MFD, traffic accumulation and demand. Simulation results show the superiority of the proposed method compared to deterministic MPC in the presence of model mismatch.
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In this paper, we propose a new macro-micro approach to modeling parking. We first develop a microscopic parking simulation model considering both on- and off-street parking with limited capacity. In the microscopic model, a parking search algorithm is proposed to mimic cruising-for-parking based on the principle of proximity, and a parking-related state tracking algorithm is proposed to acquire an event-based simulated data set. Some key aspects of parking modeling are discussed based on the sim-ulated evidence and theoretical analysis. Results suggest (i) although the low cruising speed reduces the network performance, it does not significantly alter the macroscopic or network fundamental diagram (MFD or NFD) unless the cruising vehicles dominate the traffic stream; (ii) distance to park is not uniquely determined by parking occupancy because factors such as cruising speed and parking dura-tion also contribute; and (iii) multiscale parking occupancy-driven intelligent parking guidance can re-duce distance to park yielding considerable network efficiency gains. Using the microscopic model, we then extend, calibrate, and validate a macroscopic parking dynamics model with an NFD representation. The demonstrated consistency between the macro- and micro-models permits integration of the two for online parking pricing optimization via model predictive control. Numerical experiments highlight the effectiveness of the proposed approach as well as one caveat. That is, when pricing on-street parking, the road network connected to the alternate off-street parking lots must have sufficient capacity to ac-commodate the increased parking demand; otherwise, local congestion may arise that violates the ho-mogeneity assumption underlying the macroscopic model.
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One of the main challenges for multi-regional application of the aggregated traffic models based on the Macroscopic Fundamental Diagram, lies in the identification and characterization of the most prevailing paths chosen by drivers. In this paper, we propose a methodological framework, based on two distinct methods, to determine these prevailing paths. The first method requires the information about travel patterns in the urban network as well as the information about the city network partitioning. The second method is more parsimonious, and consists on the direct calculation of shortest-cost paths on the aggregated network. For this, we propose four impedance functions that utilize topological features of the urban network and its partitioning. We test the performance of this methodological framework for determining the most prevailing paths on a network representing the metropolitan area of Lyon (France). We consider a set of real trajectories (i.e. GPS data) of drivers in this network as a benchmark. We show that the proposed methods are able to identify the most prevailing paths as the ones chosen by drivers, as evidenced by a large similarity value between the sets of paths. Based on a maximum likelihood estimation, we also show that the Weibull distribution is the one that better reproduces the functional form of the network-wide distribution of travel distances. However, the characterization of the functional form of such distributions characteristic to each region defining a path is not trivial, and depends on the complex topological features of the urban network concerning the definition of its partitioning. We also show that the Euclidean distance metrics provides good estimates of the average travel distances. Interestingly, we also show that the most prevailing paths are not necessarily the ones that have the lowest average travel distances.
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In this paper, we propose a new macro-micro approach to modeling parking. We first develop a microscopic parking simulation model considering both on- and off-street parking with limited capacity. In the microscopic model, a parking search algorithm is proposed to mimic cruising-for-parking based on the principle of proximity, and a parking-related state tracking algorithm is proposed to acquire an event-based simulated data set. Some key aspects of parking modeling are discussed based on the simulated evidence and theoretical analysis. Results suggest (i) although the low cruising speed reduces the network performance, it does not significantly alter the macroscopic or network fundamental diagram (MFD or NFD) unless the cruising vehicles dominate the traffic stream; (ii) distance to park is not uniquely determined by parking occupancy because factors such as cruising speed and parking duration also contribute; and (iii) multiscale parking occupancy-driven intelligent parking guidance can reduce distance to park yielding considerable network efficiency gains. Using the microscopic model, we then extend, calibrate, and validate a macroscopic parking dynamics model with an NFD representation. The demonstrated consistency between the macro- and micro-models permits integration of the two for online parking pricing optimization via model predictive control. Numerical experiments highlight the effectiveness of the proposed approach as well as one caveat. That is, when pricing on-street parking, the road network connected to the alternate off-street parking lots must have sufficient capacity to accommodate the increased parking demand; otherwise, local congestion may arise that violates the homogeneity assumption underlying the macroscopic model.
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Many types of research have been interesting by real-time control of urban networks. This paper, basing on a simplified urban traffic model, proposes a novel control approach based on model predictive control concept to reduce congestion and improve the safety of cars on the roads. The contributions of this paper are: First, we consider vehicle heterogeneity, represented by a mathematical model called "S Model" and integrate it with a realtime simulator to evaluate the performance of controllers on real traffic conditions. Second, in order to assess each controller's success under particular circumstances, the structured network-wide traffic controller based on model predictive control (MPC) theory is compared to a fixed time controller (FTC). Using two scenarios, different indicators are tested, i.e total time spent, vehicle number, queue length. The results show that the model predictive control quickly converges, with the different scenarios, and further improves social welfare. Keywords: Fixed time controller Model predictive control S model Urban traffic control This is an open access article under the CC BY-SA license.
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Understanding the resilience of transportation networks has received considerable research attention. Nevertheless in the field of network traffic flow control, few control approaches target the mitigation from hyper-congestion, and the control objective has rarely touched the system resilience requirement which focuses on system recovering from hyper-congested state. This paper sheds light on a resilience-oriented network control. We firstly define the traffic resilience as the integral of deviation against optimal state from disturbance generation moment t0 to recovery moment tf. Then, we propose a control method under hyper-congested situations by formulating the analytical problem using a two-reservoir transportation system with parabola-shaped Macroscopic Fundamental Diagrams (MFDs), using phase diagram analysis, attraction region derivation and switched controller design. Afterwards, we evaluate the system resilience performances between two classic perimeter control schemes (constant perimeter control (CPC) and state-feedback control (SFC)) and the proposed resilient control scheme. Results show that proposed controller can ensure the system to recover from hyper-congestion to the optimal state while existing studies failed to recover. This resilience is confirmed in various case study scenarios, e.g., when the level of hyper-congestion is different. More promisingly, the proposed control shows high compatibility with the form of the MFDs, e.g., the recover can be achieved under hysteresis conditions which are common for network-level traffic dynamics. These findings will help to design an intelligent transportation system with enhanced resilience.
Conference Paper
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The Macroscopic Fundamental Diagram (MFD) relates traffic flow (vehicles/hour) and density (vehicles/km), and can be used to support decisions on how to mitigate traffic congestion in some region. The MFD is usually computed over an area characterized by a homogeneous traffic pattern. For this reason, when considering multiple traffic assignments for the same transportation infrastructure, the different patterns of traffic densities arising result in MFDs computed over different areas, which cannot be meaningfully compared. In order to allow the use of MFDs to compare the impact of different traffic assignments, partitioning of the region needs to be done based on an infrastructure metric that will not change the resulting area. This paper assesses the use of the administrative boundaries of a city to partition the area in a way that satisfies this requirement. Using this partitioning method, we show how MFDs can be used to quantify the impact of a mode shift from cars to powered two wheelers on traffic congestion in a city-scale multi-modal mobility simulation of Monaco. Our results show that it is possible to use administrative boundaries to generate MFDs, and to use them to evaluate the impact of multiple traffic assignments on the same transportation infrastructure.
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The imminent penetration of low-altitude passenger and delivery aircraft into the urban airspace will give rise to new urban air transport systems, which we call low-altitude air city transport (LAAT) systems. As the urban mobility revolution approaches, we must investigate (i) the collective behavior of LAAT aircraft in cities, and (ii) ways of controlling LAAT systems. Future LAAT systems exemplify a new class of modern large scale engineering systems — networked control systems. They are spatially distributed, consist of many interconnected elements with control loops through digital communication networks such that the system signals can be exchanged among all components through a common network. Therefore, a decentralized controller design in framework of the unilateral event-driven paradigm is considered. Inspired by controlled urban road networks, in this paper we first establish the concept of Macroscopic Fundamental Diagram (MFD) for LAAT systems and develop a collective and aggregate aircraft traffic flow model. Then, based on that, we design an adaptive boundary feedback flow control which is robust to various anomalies in technical devices and network communication links for LAAT systems.
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Several works published over the last two decades have shown for a stylized set-up with homogeneous users that metering-based priority (MBP) schemes may generate Pareto improving departure time adjustments similar to those induced by congestion pricing, but without any financial transaction. We investigate whether MBP (i) still generates significant savings and (ii) remains Pareto-improving, with various sources of heterogeneity (in schedule flexibility, desired arrival time, and capacity usage). We consider two types of schemes: one where the priority status is allocated randomly (R-MBP) and another (HOV-MBP), which only prioritizes users with small capacity usage (e.g., carpoolers). We find that the relative total cost savings of R-MBP decrease with heterogeneity in flexibility, but may increase with heterogeneity in desired arrival time. It fails however to be Pareto-improving, as nonprioritized users are almost systematically worse-off. HOV-MBP circumvents this issue by generating an ordering effect and a modal shift, which both contribute to a better distribution of benefits among users. Under favorable circumstances, they may even restore a Pareto improvement. Overall, MBP appears as a realistic way to alleviate congestion, scoring well both in terms of efficiency and social acceptability.
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Traffic management by applying congestion pricing is a measure for mitigating congestion in protected city corridors. As a promising tool, pricing improves the level of service in a network and reduces travel delays. However, previous advancements in pricing research that are responsive to the prevailing regional traffic conditions did not consider real-time applications and the effect on users’ route choices. This work uses real-time dynamic pricing’s influence and predicts pricing functions to aim for a system optimal traffic distribution. The framework models a large-scale network where every region is considered homogeneous, allowing for the Macroscopic Fundamental Diagram (MFD) application. We compute Dynamic System Optimum (DSO) and Dynamic Route Choice (DRC) of the macroscopic model by formulating a linear optimization problem and utilizing the Dijkstra algorithm and a Multinomial Logit model (MNL), respectively. The equilibria allow us to find an optimal pricing methodology by training Multi-Layer-Neural (MLN) network models. We test our framework on a case study in Zurich, Switzerland, and showcase that (a) our neural network model learns the complex user behavior and (b) allows predicting optimal pricing functions. Results show a significant performance improvement when operating a transportation network in the DSO and highlight how dynamic pricing influences the user’s route choice behavior towards the system optimal equilibrium.
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The determination of the traffic carrying capacity of road network is of great significance to the scale control of urban vehicles and the control of transportation systems. Existing related works have proposed calculation models and solutions for different application environments. However, these studies have problems such as diversification of capacity definitions, incorrect analysis of factors, and excessive model constraints. In response to these problems, this paper aims to determine the connotation of traffic carrying capacity and put forward a novel calculation model for carrying capacity. Firstly, in-depth analysis found that the key factor affecting the number of vehicles is the service level of road network. Then, the connotation of traffic carrying capacity is clarified, that is, the maximum number of vehicles travelling simultaneously in the road network under a certain service level. Second, based on the definition of carrying capacity and the characterization relationship between average travel speed and service level, the calculation of carrying capacity is transformed into the establishment of relationship between average travel speed and maximum number of vehicles. The construction of this relationship includes five steps, which are proposal of equivalent lane, division of traffic basic units, construction of basic unit travel time model, calculation of basic unit carrying capacity, and calculation of road network carrying capacity. In particular, the proposal of equivalent lane achieves the conversion from intermittent flow to continuous flow, and the abstraction of traffic flow further unifies the operation process into a unified mode of free travel and stacked release. Finally, the VISSIM simulation software is employed to verify and evaluate the proposed models. The results show that the average relative error between the simulated data and the calculated data obtained from the model is -0. 46%. Findings from this study will provide an innovative idea for the evaluation of urban road network performance. It can also provide a basis for urban managers to improve service level of road network and optimize the design of transportation system.
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The urban traffic system is a complex dynamic system, and its state changes with the real-time traffic demand; correspondingly, the range of congested areas also continuously transforms spatiotemporally. Affected by the traffic congestion range, the dynamics of a road network and the macroscopic control model that describes the road network also change. The existing sub-region division methods divide sub-regions based on cluster algorithms, and their results cannot be directly used to establish a dynamic congested area model with varying ranges or to implement perimeter control because they fail to consider the continuity of congested area transfer. To achieve control of the dynamic entrance boundary of a continuously changing congested range, this paper carries out three related analyses. First, depending on the section data of the kernel congested area, a continuous division method for generating sub-regions is proposed on the basis of similarity theory to determine the dynamic boundary of the congested area. Then, after the boundary intersections of bottlenecks are categorized as output, input, or passing types, a congested area range estimation model is established using the density wave transfer speed to estimate the boundary range change trend caused by the influence of traffic congestion diffusion or dissipation. A three-dimensional macroscopic fundamental diagram (MFD) surface model with an independent section length, traffic flow density, and road network trip completion rate of the congested area is then established according to the changes in the congested area. On the basis of the three-dimensional MFD surface model, a sliding mode control with dynamic boundary (SMCDB) method is proposed to determine the entrance of the congested area. With a regional road network in Hefei taken as an example, numerical experiments are carried out, and the simulation results are compared with those of PI control with and without boundary changes, showing that the SMCDB method can track congested boundaries and adjust boundary flows according to the traffic state, protect the centre network from over-saturation, effectively improve the trip completion flow, and decrease the network travel delay.
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Multi-modal interactions at the network-level remain unexplored due to the lack of high-resolution data for all transportation modes involved. The current work investigates the effect of multi-modal interactions at space-mean network speed for each mode using the dataset from pNEUMA experiment that was carried out in a congested city centre network of Athens, Greece. Explanatory variables considered are the accumulation and the stopped fraction of vehicles of each mode. Firstly, a multi-modal mean speed MFD is considered by assuming that the mean speed of each mode can be expressed in terms of accumulations of all modes. The quality of multi-modal MFD fits is compared to the uni-modal ones, where the mean speed of a given mode is assumed to be a function of the accumulation of that mode only. Secondly, the classical two-fluid model is extended to multi-modal networks. An analysis on the ergodicity assumption in the context of stopped fraction is also presented. This work also introduces a network-level dynamic model that uses the stopped fraction of vehicles. This so-called extended trip-based model simulates the stop-and-go pattern of the vehicles thereby reproducing the evolution of network congestion. This work is the first to explore in this direction. The results from the classical trip-based and the extended trip-based models are compared and validated with the empirical data.
Article
Perimeter control is used to regulate transfer flows between urban regions. The greedy control (GC) method takes either the minimum or the maximum for the control inputs. Although it has the advantage of simplicity for real-time feasibility, a few existing studies have shown that it can sometimes have negative impacts because of unnecessary transfer flow restrictions. To reduce unnecessary restrictions, this study provides a method that gives flexibility to ease the strict conditions of the conventional GC. First, we propose a modification as a way of granting exceptions to the flow restriction under specific conditions. Second, we develop an algorithm to determine the threshold dynamically for accepting the exception, by comparing the possible outflow loss of the subject region and the possible outflow gain of its neighboring regions. The test results show that this flexible greedy control can handle the balance between the transfer demands and the greed of regions for securing the supply level, while increasing the performance in both vehicle hours traveled and trip completion.
Thesis
This Ph.D. thesis is done mainly in the context of the European Research Council's (ERC) Advanced Grant project Scale-FreeBack and partially in the context of Inria's COVID-19 Mission project Healthy-Mobility. The Scale-FreeBack project aims to develop a holistic, scale-free control approach to complex systems and to set new foundations for a theory dealing with complex physical networks with arbitrary dimensions. On the other hand, motivated by the onset of the COVID-19 pandemic, the Healthy-Mobility project aims to develop optimal control strategies for testing and urban human mobility to limit the epidemic spread. In relation to both projects, the contributions of the thesis are respectively divided into two parts.In the first part of the thesis, we develop a theory for monitoring large-scale clustered network systems with limited computational and sensing equipment through a projected network system, which is of tractable dimension and is obtained through the aggregation of clusters of a network system. We propose a minimum-order average observer and provide its design criteria. Then, the notions of average reconstructability, average observability, and average detectability are defined and their necessary and sufficient conditions are provided. We also provide graph-theoretic interpretations of these notions through inter-cluster and intra-cluster graph topologies of a clustered network system. When a clustered network system does not meet the design criteria of the average observer, we devise an optimal design methodology to minimize the average estimation error. On the other hand, if the clusters are not pre-specified in a network system, we develop clustering algorithms to achieve minimum average estimation error. Finally, we propose a K-means type clustering approach to estimate the state variance of network systems, which is a nonlinear functional of the state vector and measures the squared deviation of state trajectories from their average mean. We illustrate the results through application examples of a building thermal system and an SIS epidemic spread over large networks.In the second part of the thesis, we first study epidemic suppression through a testing policy. We develop a five-compartment epidemic model that incorporates the testing rate as a control input. We propose a best-effort strategy for testing (BEST), which is an epidemic suppression policy that provides a minimum testing rate from a certain day onward to stop the growth of the epidemic. The BEST policy is evaluated through its impact on the number of active intensive care unit (ICU) cases and the cumulative number of deaths for the COVID-19 case of France. Secondly, we develop a model of urban human mobility between residential areas and social destinations such as industrial areas, business parks, schools, markets, etc. for epidemic mitigation. We formulate two optimal control policies, the so-called optimal capacity control (OCC) and optimal schedule control (OSC), that aim to maximize the economic activity in an urban environment while keeping the number of active infected cases bounded. The OCC limits the epidemic spread by reducing the maximum number of people allowed at each destination category at any time of day, whereas the OSC limits the epidemic spread by reducing the daily business hours of each destination category.
Article
The problem of traffic state estimation for large-scale urban networks modeled with MFD dynamics is studied here. Given a network partitioned in a number of regions, aggregated traffic dynamics describe the vehicle accumulation in each region, as well as transfer flows to and from neighboring regions. Considering that MFD accumulation-based models have been integrated in perimeter control approaches, this work tackles the real-time estimation problem when limited data is available. An estimation engine is developed according to the Extended Kalman Filter (EKF) theory; it seeks to estimate the real state of the multi-region dynamic system based on traffic sensors’ measurements. First, a stochastic model is presented for the dynamics of the process (plant). Then, the EKF estimation scheme is described based on a simpler aggregated model of dynamics and some real-time measurements. Estimation accuracy is investigated through detailed micro-simulation of downtown Barcelona by studying a realistic configuration of real-time measurement availability through loop detector data; however, the developed methodology is generic. The state vector we seek to estimate, as well as the available measurements configuration, can be altered according to the application. The proposed methodology is tested both in macro- and micro-simulation; resulting estimated traffic states (i.e., regional accumulations, demands, and distribution of outflows) are compared to actual ones obtained from the stochastic plant. The developed algorithm can be utilized by closed-loop online urban traffic management strategies to feed the estimated traffic state back to the controller.
Conference Paper
This paper introduces a city scale realistic day-to-day assignment model augmented with a demand management policy and evaluates equilibrium conditions for a two-region urban network. Two macroscopic fundamental diagram based models are jointly implemented to explore the system performance and limited cooperation of travellers. The parsimonious accumulation-based model is implemented in the demand management strategy by solving a nonlinear optimization problem which minimizes the travel time spent in the network by manipulating travellers' departure times within a limited time window. The more detailed trip-based model is implemented to apply a day-to-day assignment which allowed travellers to shift departure time based on experienced and perceived generalized travel costs. The trip based model is conjugated with a network level detour ratio model to incorporate the route choice phenomenon at an aggregated level. The results confirm the resourcefulness of the model to address complex two-region traffic dynamics and increase overall performance while facilitating social welfare in the network.
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This paper quantifies the technology driving congestion in urban road networks. To do so, we estimate macroscopic fundamental relationships for homogeneously congested sub-networks (reservoirs) in thirty-four cities worldwide. We adopt a causal approach based on non-parametric instrumental variables to estimate the form of the reservoir-level flow-density relationship using large-scale traffic sensor data. Specifically, we apply a Bayesian non-parametric spline-based regression model with instrumental variables to adjust for potential confounding/endogeneity biases due to simultaneity and omitted variables such as vehicle interactions and traffic controls. Our estimates suggest that the provision of vehicular travel in cities is subject to decreasing returns to density and network size. Importantly, we find that increasing road network capacity is not an efficient solution to manage congestion because average travel speed does not change substantially with increase in capacity. As a by-product of the estimation, we also deliver estimates of important traffic control inputs such as capacity and critical occupancy for these reservoirs. Our results have implications for traffic flow modelling used by both economists and traffic engineers.
Preprint
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This paper presents an integrated cross-resolution framework for the traffic system state identification (TSSI) problem by simultaneously considering traffic state estimation (TSE), traffic flow model parameter estimation (MPE), and queue profile estimation (QPE) on transportation networks using heterogeneous data sources. Systematically considering the three tasks, that is, TSE, MPE, and QPE, in an integrated modeling framework helps to fully utilize information from different components and takes advantage of larger solution spaces, which is expected to improve the reliability and accuracy of system identification results. However, potential inconsistencies between different modeling components are introduced at the same time and should be carefully dealt with to ensure model feasibility. To minimize such inconsistencies, a novel nonlinear programming model was developed to formulate the TSSI problem by considering traffic flow models and observations from different resolutions. At the macroscopic level, we used a fluid queue approximation to model the traffic system of interest. Based on the assumption of polynomial arrival and departure rates, critical system measures such as time-dependent delay, travel time, and queue length were analytically derived. At the mesoscopic level, with the adoption of continuous space-time distribution (CSTD) functions, a continuous traffic state representation scheme is introduced to model traffic flow variables such as traffic volume, speed, and density. CSTD functions maintain the differentiability of traffic state variables such that partial differential equations in traffic flow models can be comprehensively considered in the proposed framework. A computational graph is constructed to represent the nonlinear programming model in a sequential propagation structure, which is then solved using a forward-backward method. Extensive numerical experiments based on real-world and hypothetical datasets were designed to demonstrate the effectiveness of the proposed framework.
Article
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Research on congestion propagation in large urban networks has been based mainly on microsimulations of link-level traffic dynamics. However, both the unpredictability of travel behavior and the complexity of accurate physical modeling present challenges, and simulation results may be time-consuming and unrealistic. This paper explores empirical data from large-scale urban networks to identify hidden information in the process of congestion formation. Specifically, the spatiotemporal relation of congested links is studied, congestion propagation is observed from a macroscopic perspective, and critical congestion regimes are identified to aid in the design of peripheral control strategies. To achieve these goals, the maximum connected component of congested links is used to capture congestion propagation in the city. A data set of 20,000 taxis with global positioning system (GPS) data from Shenzhen, China, is used. Empirical macroscopic fundamental diagrams of congested regions observed during propagation are presented, and the critical congestion regimes are quantified. The findings show that the proposed methodology can effectively distinguish congestion pockets from the rest of the network and efficiently track congestion evolution in linear time O(n).
Article
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Currently most optimization methods for urban transport networks (i) are suited for networks with simplified dynamics that are far from real-sized networks or (ii) apply decentralized control, which is not appropriate for heterogeneously loaded networks or (iii) investigate good-quality solutions through micro-simulation models and scenario analysis, which make the problem intractable in real time. In principle, traffic management decisions for different sub-systems of a transport network (urban, freeway) are controlled by operational rules that are network specific and independent from one traffic authority to another. In this paper, the macroscopic traffic modeling and control of a large-scale mixed transportation network consisting of a freeway and an urban network is tackled. The urban network is partitioned into two regions, each one with a well-defined Macroscopic Fundamental Diagram (MFD), i.e. a unimodal and low-scatter relationship between region density and outflow. The freeway is regarded as one alternative commuting route which has one on-ramp and one off-ramp within each urban region. The urban and freeway flow dynamics are formulated with the tool of MFD and asymmetric cell transmission model, respectively. Perimeter controllers on the border of the urban regions operating to manipulate the perimeter interflow between the two regions, and controllers at the on-ramps for ramp metering are considered to control the flow distribution in the mixed network. The optimal traffic control problem is solved by a Model Predictive Control (MPC) approach in order to minimize total delay in the entire network. Several control policies with different levels of urban-freeway control coordination are introduced and tested to scrutinize the characteristics of the proposed controllers. Numerical results demonstrate how different levels of coordination improve the performance once compared with independent control for freeway and urban network. The approach presented in this paper can be extended to implement efficient real-world control strategies for large-scale mixed traffic networks.
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The goal of this paper is to evaluate the data requirements for a possible implementation of a macroscopic fundamental diagram (MFD) control scheme in an urban area. Particularly, we have studied the accuracy of MFDs created using only a percentage of the links (i.e., streets). This is especially useful because monitoring resources are often scarce, and most cities do not have access to the large amount of information that is typically associated with the construction of an MFD. We evaluated several strategies that cities typically use to place fixed monitoring devices (e.g., loop detectors), and compared them with a quasi-optimal way to choose the links. The results show that independently of the strategy used for link selection, a minimum of 25 % of network coverage, according to our accuracy methodology, ensures an average error in density ratios below 15 percentage points (ppts). Based on the particular case of the city of Zurich, we also analyzed the feasibility of implementing an MFD control scheme with the links that are currently monitored. Results are very encouraging, showing an average error below 9 ppts. Although all results were obtained with a VISSIM microsimulation model of the inner city of Zurich, we believe the knowledge and methodology presented here can be transferred to other urban areas. In fact, we are hopeful that this research can contribute to making the implementation of an MFD control scheme feasible for many cities.
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Traffic management can prevent too many vehicles in a traffic network from reducing traffic performance. In particular, traffic can be routed so that the bottlenecks are not oversaturated. The macroscopic fundamental diagram provides a relationship between the number of vehicles and network performance. Traffic control can be applied on this level to overcome the computational complexity of networkwide control with traditional control levels of links or vehicles. The main questions are (a) how effective traffic control is with aggregate variables compared with full information and (b) whether the shape of the macroscopic fundamental diagram changes under traffic control. A grid network with periodic boundary conditions is used as an example and is split into several subnetworks. The following routing strategies are compared: the shortest paths in distance and time (dynamic due to congestion) and approximations of the path shortest in time but calculated with only variables aggregated for a subnetwork and of the path shortest in time but calculated with only subnetwork accumulation. For the third and fourth routing strategies, only information aggregated over the subnetwork is used. The results show improved traffic flow with detailed information. Effective control is also possible by using aggregated information, but only with the right choice of a subnetwork macroscopic fundamental diagram. Furthermore, when detailed information is used to optimize-and therefore in a subnetwork-the macroscopic fundamental diagram changes.
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A simple symmetric network that consists of two tangent rings on which vehicles obey the kinematic wave theory of traffic flow and can switch rings at the point of tangency is studied. An online adaptive simulation reveals that if there is any turning whatsoever, the two-ring system becomes unevenly loaded for densities greater than the optimal density, and reduces traffic flow. Furthermore, the two-ring system jams at significantly lower densities than the maximum density possible.
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The objective of this study was to characterize hysteresis and capacity drop phenomena in freeway networks with the use of commonly available loop detector data from three networks: Chicago, Illinois; Portland, Oregon; and Irvine, California. For exploration of the effects of variations in network topology and size on the network fundamental diagram, a comparison was made by using the observed flow-occupancy diagrams of the selected freeway networks. The results provide further confirmation that findings from the literature for a limited number of networks are also valid for freeway networks not previously studied. Freeway networks have been found more likely to exhibit an inconsistent hysteretic pattern in shape and size that depends on the spatial distribution of congestion over the network. On the basis of empirical observations, hysteresis loops were characterized by their shape and size. Two shapes of hysteresis loops, H1 and H2, were identified and characterized. The size of each hysteresis loop was believed to be characterized by its width, height, and the area covered by the hysteresis loop. The authors postulated that the capacity drop phenomenon existed in freeway networks in a manner similar to that in individual freeway sections. Two types of capacity drop were identified. Type 1 was associated with the inability of the freeway network to sustain its throughput at its peak value for a relatively long time, and therefore, capacity dropped while demand was still high and the network was loading. Type 2 was associated with the instability of network traffic when the network underwent reloading (e.g., afternoon peak period) after an incomplete recovery from the initial loading (e.g., morning peak period). In some cases, this reloading resulted in a lower capacity in the afternoon than in the morning. Empirical results showed that the observed phenomena were reproducible on different days and for different networks.
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Recent analysis of empirical data from cities showed that a macroscopic fundamental diagram (MFD) of urban traffic provides for homogenous network regions a unimodal low-scatter relationship between network vehicle density and network space-mean flow. In this paper, the optimal perimeter control for two-region urban cities is formulated with the use of MFDs. The controllers operate on the border between the two regions and manipulate the percentages of flows that transfer between the two regions such that the number of trips that reach their destinations is maximized. The optimal perimeter control problem is solved by model predictive control, where the prediction model and the plant (reality) are formulated by MFDs. Examples are presented for different levels of congestion in the regions of the city and the robustness of the controller is tested for different sizes of error in the MFDs and different levels of noise in the traffic demand. Moreover, two methods for smoothing the control sequences are presented. Comparison results show that the performances of the model predictive control are significantly better than a “greedy” feedback control. The results in this paper can be extended to develop efficient hierarchical control strategies for heterogeneously congested cities.
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The concept of the Macroscopic Fundamental Diagram (MFD) is elegant and attractive because it provides a global view of traffic behavior and performance at a network level. However, recent research shows that the MFD shape can be influenced by local traffic heterogeneities. Notably, route choices and heterogeneous local capacities may drive uneven (in space) or inconsistent (in time) distributions of congestion and then affect the shape and the scatter of the MFD. We are far from having a global understanding of the connections between local phenomena and the resulting MFD. This paper first aims to improve existing MFD estimation method for a succession of links with traffic signals. The new method overcomes previous limitations, notably regarding to the topology and signal settings regularities, by fully utilizing the receipts of the variational theory. Then, a single network with several parallel routes is investigated. MFDs on different routes are estimated with the variational method and then aggregated in a unified MFD for stationary and dynamic conditions and different sorts of equilibria (user and system optimum). It appears that the flow distribution among routes smoothly varies with respect to the total flow either in free-flow or congestion situations. Such a distribution is much more rough for system optimum, where it presents some discontinuities and is far from equity. This means that a control strategy able to lead such a network to the perfect system optimum would be hard to tune, especially in the congested regime. However, being able to determine the MFD corresponding to the system optimum provides a valuable reference to estimate the current efficiency of the considered network. Case studies for different simple networks and insights for generalization at the city level are proposed.
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This study explores the limiting properties of network-wide traffic flow relations under heavily congested conditions in a large-scale complex urban street network; these limiting conditions are emulated in the context of dynamic traffic assignment (DTA) experiments on an actual large network. The primary objectives are to characterize gridlock and understand its dynamics. This study addresses a gap in the literature with regard to the existence of exit flow and recovery period. The one-dimensional theoretical Network Fundamental Diagram (NFD) only represents steady-state behavior and holds only when the inputs change slowly in time and traffic is distributed homogenously in space. Also, it does not describe the hysteretic behavior of the network traffic when a gridlock forms or when network recovers. Thus, a model is proposed to reproduce hysteresis and gridlock when homogeneity and steady-state conditions do not hold. It is conjectured that the network average flow can be approximated as a non-linear function of network average density and variation in link densities. The proposed model is calibrated for the Chicago Central Business District (CBD) network. We also show that complex urban networks with multiple route choices, similar to the idealized network tested previously in the literature, tend to jam at a range of densities that are smaller than the theoretical average network jam density. Also it is demonstrated that networks tend to gridlock in many different ways with different configurations. This study examines how mobility of urban street networks could be improved by managing vehicle accumulation and re-distributing network traffic via strategies such as demand management and disseminating real-time traveler information (adaptive driving). This study thus defines and explores some key characteristics and dynamics of urban street network gridlocks including gridlock formation, propagation, recovery, size, etc.
Article
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Recently, some authors have provided experimental evidence of the existence of an urban-scale macroscopic fundamental diagram (MFD). Their convincing results were obtained on the basis of 500 urban fixed detectors placed 100 m upstream of most major intersections in the city of Yokohama, Japan. Those authors assume that the network in which data are collected is homogeneous in regard to congestion occurrence. This paper is devoted to exploring the impact of heterogeneity on the existence of an MFD. All data available for a medium-size French city are used. The data set encompasses measurements on highways, urban center streets (congested during business hours), and residential area streets. Data were collected by loop detectors with a distance from a downstream signal that can vary from 1,000 to 10 m. Heterogeneity is examined here in various aspects: differences between the surface and highway network, impact of the distance between the loop detector and the traffic signal in the surface network, and differences between penetrating roads and the ring road in the highway network. It is proved in this paper that heterogeneity has a strong impact on the shape of the macroscopic fundamental diagram.
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Observations of traffic pairs of flow vs. density or occupancy for individual locations in freeways or arterials are usually scattered about an underlying curve. Recent observations from empirical data in arterial networks showed that in some cases by aggregating the highly scattered plots of flow vs. density from individual loop detectors, the scatter almost disappears and well-defined macroscopic relations exist between space-mean network flow and network density. Despite these findings for the existence of well-defined relations with low scatter, these curves should not be universal. In this paper we investigate if well-defined macroscopic relations exist for freeway network systems, by analyzing real data from Minnesota's freeways. We show that freeway network systems not only have curves with high scatter, but they also exhibit hysteresis phenomena, where higher network flows are observed for the same average network density in the onset and lower in the offset of congestion. The mechanisms of traffic hysteresis phenomena at the network level are analyzed in this paper and they have dissimilarities to the causes of the hysteresis phenomena at the micro/meso level. The explanation of the phenomenon is dual. The first reason is that there are different spatial and temporal distributions of congestion for the same level of average density. Another reason is the synchronized occurrence of transitions from individual detectors during the offset of the peak period, with points remain beneath the equilibrium curve. Both the hysteresis phenomenon and its causes are consistently observed for different spatial aggregations of the network.
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Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far have been based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach, which facilitates a simple simulation of congestion spreading in cities. First, we show that a quantization of the macroscopic turning flows into units of single vehicles is necessary to obtain realistic fluctuations in the traffic variables, and how this can be implemented in a fluid-dynamic model. Then, we propose a new method to simulate destination flows without the requirement of individual route assignments. Combining both methods allows us to study a variety of different simulation scenarios. These reveal fundamental relationships between the average flow, the average density and the variability of the vehicle densities. Considering the inhomogeneity of traffic as an independent variable can eliminate the scattering of congested flow measurements. The variability also turns out to be a key variable of urban traffic performance. Our results can be explained through the number of full links of the road network, and approximated by a simple analytical formula.
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An area-wide traffic speed-flow model was developed for the Singapore CBD with the aim of providing an analytical framework for the evaluation of traffic management measures for the area (known as the Restricted Zone). A major survey of traffic speed and volume within the CBD was conducted in 1990. The speed data were collected using a fleet of floating cars which moved around two fixed survey circuits for 3 days. In the modelling process that followed, several approaches and mathematical models were studied. The final, recommended model relates journey speeds inside the Zone with the average traffic flow per lane inside the area which, in turn, is correlated with the cordon traffic volume. Thus, the model allows one to estimate average journey speed inside the Zone, based on the total traffic flow crossing the Zone cordon.
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Population-level analyses often use average quantities to describe heterogeneous systems, particularly when variation does not arise from identifiable groups. A prominent example, central to our current understanding of epidemic spread, is the basic reproductive number, R(0), which is defined as the mean number of infections caused by an infected individual in a susceptible population. Population estimates of R(0) can obscure considerable individual variation in infectiousness, as highlighted during the global emergence of severe acute respiratory syndrome (SARS) by numerous 'superspreading events' in which certain individuals infected unusually large numbers of secondary cases. For diseases transmitted by non-sexual direct contacts, such as SARS or smallpox, individual variation is difficult to measure empirically, and thus its importance for outbreak dynamics has been unclear. Here we present an integrated theoretical and statistical analysis of the influence of individual variation in infectiousness on disease emergence. Using contact tracing data from eight directly transmitted diseases, we show that the distribution of individual infectiousness around R(0) is often highly skewed. Model predictions accounting for this variation differ sharply from average-based approaches, with disease extinction more likely and outbreaks rarer but more explosive. Using these models, we explore implications for outbreak control, showing that individual-specific control measures outperform population-wide measures. Moreover, the dramatic improvements achieved through targeted control policies emphasize the need to identify predictive correlates of higher infectiousness. Our findings indicate that superspreading is a normal feature of disease spread, and to frame ongoing discussion we propose a rigorous definition for superspreading events and a method to predict their frequency.
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In this chapter we describe an iterative two-layer hierarchical approach to MPC of large-scale linear systems subject to coupled linear constraints. The algorithm uses constraint tightening and applies a primal-dual iterative averaging procedure to provide feasible solutions in every sampling step. This helps overcome typical practical issues related to the asymptotic convergence of dual decomposition based distributed MPC approaches. Bounds on constraint violation and level of suboptimality are provided. The method can be applied to large-scale MPC problems that are feasible in the first sampling step and for which the Slater condition holds (i.e., there exists a solution that strictly satisfies the inequality constraints). Using this method, the controller can generate feasible solutions of the MPC problem even when the dual solution does not reach optimality, and closed-loop stability is also ensured using bounded suboptimality.
Conference Paper
A new gating strategy based on the notion of the macroscopic or network fundamental diagram (MFD or NFD) and the feedback-based gating concept is introduced and tested successfully. Different regions of large-scale urban networks may experience congestion at different times during the peak period. In this paper, the zone including the initial core of congestion is considered as the first region which has to be protected from congestion via gating; eventually, as the congestion continues to expand, the border of an extended network part becomes the second perimeter for gating control. Extensions while distributing the ordered controller flow to the gated traffic signals in case of low demand or occurrence of spillback are also introduced. A greater part of the San Francisco urban network is used as test-bed within a microscopic simulation environment. Significant improvements in terms of average travel time and average delay are obtained compared to the single perimeter gating and non-gating cases.
Article
In this paper, we macroscopically describe the traffic dynamics in heterogeneous transportation urban networks by utilizing the Macroscopic Fundamental Diagram (MFD), a widely observed relation between network-wide space-mean flow and density of vehicles. A generic mathematical model for multi-reservoir networks with well-defined MFDs for each reservoir is presented first. Then, two modeling variations lead to two alternative optimal control methodologies for the design of perimeter and boundary flow control strategies that aim at distributing the accumulation in each reservoir as homogeneously as possible, and maintaining the rate of vehicles that are allowed to enter each reservoir around a desired point, while the system’s throughput is maximized. Based on the two control methodologies, perimeter and boundary control actions may be computed in real-time through a linear multivariable feedback regulator or a linear multivariable integral feedback regulator. Perimeter control occurs at the periphery of the network while boundary control occurs at the inter-transfers between neighborhood reservoirs. To this end, the heterogeneous network of San Francisco is partitioned into three homogeneous reservoirs and the proposed feedback regulators are compared with a pre-timed signal plan and a single-reservoir perimeter control strategy. Finally, the impact of the perimeter and boundary control actions is demonstrated via simulation by the use of the corresponding MFDs and other performance measures. A key advantage of the proposed approach is that it does not require high computational effort and future demand data if the current state of each reservoir can be observed with loop detector data.
Article
Macroscopic fundamental diagrams (MFDs) exist in large urban networks in which traffic conditions are homogenous. They can be used for estimation of the level of service on road networks, perimeter control, and macroscopic traffic modeling. However, before the MFD concept can be applied, the factors that influence the MFD shape should be identified and their effects investigated. A microscopic simulation model is used to change conditions, that is, to derive MFDs under different conditions and for different types of networks. Results indicate that a relationship indeed exists between production and accumulation for the whole network as well as for parts of the network focused on freeway or urban links. MFD shape is a property not only of the network itself but also of the applied traffic control measures. At the same time, congestion onset and resolution lead to heterogeneous traffic conditions with congestion at specific locations in the network, resulting in loops in congested parts of the MFD. Investigation of the effect of traffic demand on MFD also indicates that rapidly changing traffic demands drastically affect MFD shape.
Article
Real-time coordinated traffic management strategies that benefit from parsimonious models with aggregated network dynamics, provide a new generation of smart hierarchical strategies to improve network capacity and performance. However, this raises the question of route choice behavior in case of heterogeneous urban networks, where different parts of the city are subject to different types of control. Traffic equilibrium phenomena have not been thoroughly investigated in these models. Approximate traffic equilibrium conditions can be integrated within the parsimonious traffic models to develop regional routing strategies, while detailed route choice strategies can be incorporated at a later stage in a hierarchical framework. In this study, we develop an aggregated and approximate dynamic traffic assignment (DTA) procedure to be incorporated in the macroscopic fundamental diagram (MFD) dynamics, and establish dynamic stochastic user equilibrium (DSUE) conditions. The methodology consists of two main components; stochastic network loading and a fixed-point solution method. Loading procedure is designed to handle stochastic components in the model such as trip length uncertainty, variation of speeds across the links, perception error of travelers. The results taken from this procedure are averaged through the well-known method of successive averages (MSA) to reach fixed-point solution for the system. Real-time route guidance strategies can be revisited towards a “system of systems” approach.
Article
Recent works have introduced perimeter feedback-control strategies for a homogenous urban region and multiple urban regions with the help of the Macroscopic Fundamental Diagram (MFD) representation, that relates average flow and density (or accumulation) across the network. The perimeter controller is located on the region border, and manipulates the transfer flows across the border, while aiming at regulating around (nearby) the critical densities or accumulations, whereby the system throughput is maximized. While the desired state in the one urban region system is known in advance (given the MFD shape), for the system with multiple urban regions the desired accumulation points are not well known. Moreover, in some traffic scenarios the controller cannot regulate around the critical accumulations for both systems, e.g. because of high demand. In this paper, a robust perimeter controller for an urban region is designed. The controller aims at satisfying the control specifications and having a good performance for the whole accumulation set, uncongested and congested accumulations, and not necessary for a value range nearby the critical accumulation set-point. Moreover, unlike previous works, the robust controller is also designed to handle uncertainty in the MFD and the control constraints within the design level in a systematic way, where the constraints are explicitly integrated utilizing the so-called describing function. Comparison results show that the performances of the robust controller are significantly better than a “standard” feedback controller, for different traffic scenarios.
Article
This paper aims to investigate the likely thermal performance of a unique pre-1919 Victorian case study property by using both current and future projected weather data after a deep retrofit. The property is a re-construction within an environmental chamber using reclaimed materials designed to test housing retrofit solutions. Climate projections for Manchester from both UKCIP02 and UKCP09 programmes were used to assess the likely overheating in summer for this ‘Hard to Treat’ property judging by both single and adaptive comfort criteria from CIBSE Guide A and BS EN 15251. In the bedroom, where occupants have less ability to adapt, overheating could occur as early as 2020s; while in the living room, using the annually adaptive approach, overheating may not happen until 2080s. For high expectation occupants, however, short term overheating (weekly or monthly) can occur much earlier. The research highlights the discrepancies in predicting overheating using the two UK climate impact programmes; the inconsistencies of risk evaluation using different comfort criteria; and the differences between risk and severity of potential overheating.
Article
This paper aims to cross-compare existing estimation methods for the Macroscopic Fundamental Diagram. Raw data are provided by a mesoscopic simulation tool for two typical networks that mimic an urban corridor and a meshed urban center. We mainly focus on homogenous network loading in order to fairly cross-compare the different methods with the analytical reference. It appears that the only way to estimate the MFD without bias is to have the full information of vehicle trajectories over the network and to apply Edie's definitions. Combining information from probes (mean network speed) and loop detectors (mean network flow) also provides accurate results even for low sampling rate (<10%). Loop detectors fail to provide a good estimation for mean network speed or density because they cannot capture the traffic spatial dynamics over links. This paper proposes a simple adjustment technic in order to reduce the discrepancy when only loop detectors are available.
Article
It has been recently shown that a macroscopic fundamental diagram (MFD) linking space-mean network flow, density and speed exists in the urban transportation networks under some conditions. An MFD is further well defined if the network is homogeneous with links of similar properties. This collective behavior concept can also be utilized to introduce simple control strategies to improve mobility in homogeneous city centers without the need for details in individual links. However many real urban transportation networks are heterogeneous with different levels of congestion. In order to study the existence of MFD and the feasibility of simple control strategies to improve network performance in heterogeneously congested networks, this paper focuses on the clustering of transportation networks based on the spatial features of congestion during a specific time period. Insights are provided on how to extend this framework in the dynamic case. The objectives of partitioning are to obtain (i) small variance of link densities within a cluster which increases the network flow for the same average density and (ii) spatial compactness of each cluster which makes feasible the application of perimeter control strategies. Therefore, a partitioning mechanism which consists of three consecutive algorithms, is designed to minimize the variance of link densities while maintaining the spatial compactness of the clusters. Firstly, an over segmenting of the network is provided by a sophisticated algorithm (Normalized Cut). Secondly, a merging algorithm is developed based on initial segmenting and a rough partitioning of the network is obtained. Finally, a boundary adjustment algorithm is designed to further improve the quality of partitioning by decreasing the variance of link densities while keeping the spatial compactness of the clusters. In addition, both density variance and shape smoothness metrics are introduced to identify the desired number of clusters and evaluate the partitioning results. These results show that both the objectives of small variance and spatial compactness can be achieved with this partitioning mechanism. A simulation in a real urban transportation network further demonstrates the superiority of the proposed method in effectiveness and robustness compared with other clustering algorithms.
Article
Traffic signal control for urban road networks has been an area of intensive research efforts for several decades, and various algorithms and tools have been developed and implemented to increase the network traffic flow efficiency. Despite the continuous advances in the field of traffic control under saturated conditions, novel and promising developments of simple concepts in this area remains a significant objective, because some proposed approaches that are based on various meta-heuristic optimization algorithms can hardly be used in a real-time environment. To address this problem, the recently developed notion of network fundamental diagram for urban networks is exploited to improve mobility in saturated traffic conditions via application of gating measures, based on an appropriate simple feedback control structure. As a case study, the proposed methodology is applied to the urban network of Chania, Greece, using microscopic simulation. The results show that the total delay in the network decreases significantly and the mean speed increases accordingly.
Article
In this paper, stability analysis of traffic control for two-region urban cities is treated. It is known in control theory that optimality does not imply stability. If the optimal control is applied in a heavily congested system with high demand, traffic conditions might not change or the network might still lead to gridlock. A city partitioned in two regions with a Macroscopic Fundamental Diagram (MFD) for each of the regions is considered. Under the assumption of triangular MFDs, the two-region MFDs system is modeled as a piecewise second-order system. Necessary and sufficient conditions are derived for stable equilibrium accumulations in the undersaturated regimes for both MFDs. Moreover, the traffic perimeter control problem for the two-region MFDs system is formulated. Phase portraits and stability analysis are conducted, and a new algorithm is proposed to derive the boundaries of the stable and unstable regions. Based on these regions, a state-feedback control strategy is derived. Trapezoidal shape of MFDs are also addressed with numerical solutions.
Article
A recent study reported that the Macroscopic Fundamental Diagram of a medium size city exhibited a clockwise hysteresis loop on a day in which a major disturbance caused many drivers to use unfamiliar routes. It is shown below that, even in a perfectly symmetric network with uniform demand, clockwise loops are to be expected when there are disturbances, especially if the disturbances cause a significant fraction of the drivers to not change routes adaptively. It is also shown that when drivers are not adaptive networks are inherently more unstable as they recover from congestion than as they are loaded. In other words, during recovery congestion tends more strongly toward unevenness because very congested areas clear more slowly than less congested areas. Since it is known that uneven congestion distributions reduce network flows, it follows that lower network flows should arise during recovery, resulting in clockwise loops. Fortunately, the presence of a sufficient number of drivers that choose routes adaptively to avoid congested areas helps to even out congestion during recovery, increasing flow. Thus, clockwise loops are less likely to occur when driver adaptivity is high.
Article
A field experiment in Yokohama (Japan) revealed that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. It was observed that when the highly scattered plots of flow vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped along a well defined curve. Despite these and other recent findings for the existence of well-defined MFDs for urban areas, these MFDs should not be universally expected. In this paper we investigate what are the properties that a network should satisfy, so that an MFD with low scatter exists. We show that the spatial distribution of vehicle density in the network is one of the key components that affect the scatter of an MFD and its shape. We also propose an analytical derivation of the spatial distribution of congestion that considers correlation between adjacent links. We investigate the scatter of an MFD in terms of errors in the probability density function of spatial link occupancy and errors of individual links' fundamental diagram (FD). Later, using real data from detectors for an urban arterial and a freeway network we validate the proposed derivations and we show that an MFD is not well defined in freeway networks as hysteresis effects are present. The datasets in this paper consist of flow and occupancy measures from 500 fixed sensors in the Yokohama downtown area in Japan and 600 loop detectors in the Twin Cities Metropolitan Area Freeway network in Minnesota, USA.
Article
This paper describes an adaptive control approach to improve urban mobility and relieve congestion. The basic idea consists in monitoring and controlling aggregate vehicular accumulations at the neighborhood level. To do this, physical models of the gridlock phenomenon are presented both for single neighborhoods and for systems of inter-connected neighborhoods. The models are dynamic, aggregate and only require observable inputs. The latter can be obtained in real-time if the neighborhoods are properly instrumented. Therefore, the models can be used for adaptive control. Experiments should determine accuracy. Pareto-efficient strategies are shown to exist for the single-neighborhood case, and optimality principles are introduced for multi-neighborhood systems. The principles can be used without knowing the origin–destination table or the precise system dynamics.
Article
This paper shows that a macroscopic fundamental diagram (MFD) relating average flow and average density must exist on any street with blocks of diverse widths and lengths, but no turns, even if all or some of the intersections are controlled by arbitrarily timed traffic signals. The timing patterns are assumed to be fixed in time. Exact analytical expressions in terms of a shortest path recipe are given, both, for the street’s capacity and its MFD. Approximate formulas that require little data are also given.For networks, the paper derives an upper bound for average flow conditional on average density, and then suggests conditions under which the bound should be tight; i.e., under which the bound is an approximate MFD. The MFD’s produced with this method for the central business districts of San Francisco (California) and Yokohama (Japan) are compared with those obtained experimentally in earlier publications.
Article
Using a stochastic cellular automaton model for urban traffic flow, we study and compare Macroscopic Fundamental Diagrams (MFDs) of arterial road networks governed by different types of adaptive traffic signal systems, under various boundary conditions. In particular, we simulate realistic signal systems that include signal linking and adaptive cycle times, and compare their performance against a highly adaptive system of self-organizing traffic signals which is designed to uniformly distribute the network density. We find that for networks with time-independent boundary conditions, well-defined stationary MFDs are observed, whose shape depends on the particular signal system used, and also on the level of heterogeneity in the system. We find that the spatial heterogeneity of both density and flow provide important indicators of network performance. We also study networks with time-dependent boundary conditions, containing morning and afternoon peaks. In this case, intricate hysteresis loops are observed in the MFDs which are strongly correlated with the density heterogeneity. Our results show that the MFD of the self-organizing traffic signals lies above the MFD for the realistic systems, suggesting that by adaptively homogenizing the network density, overall better performance and higher capacity can be achieved.
Article
Recent experimental analysis has shown that some types of urban networks exhibit a low scatter reproducible relationship between average network flow and density, known as the macroscopic fundamental diagram (MFD). It has also been shown that heterogeneity in the spatial distribution of density can significantly decrease the network flow for the same value of density. Analytical theories have been developed to explore the connection between network structure and an MFD for urban neighborhoods with cars controlled by traffic signals. However these theories have been applied only in cities with deterministic values of topological and control variables for the whole network and by ignoring the effect of turns. In our study we are aiming to generate an MFD for streets with variable link lengths and signal characteristics and understand the effect of variability for different cities and signal structures. Furthermore, this variability gives the opportunity to mimic the effect of turning movements. Route or network capacity can be significantly smaller than the capacity of a single link, because of the correlations developed through the different values of offsets. The above analysis would not be possible using standard traffic engineering techniques. This will be a key issue in planning the signal regimes such a way that maximizes the network capacity and/or the density range of the maximum capacity.
Article
A field experiment in Yokohama (Japan) reveals that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. The experiment used a combination of fixed detectors and floating vehicle probes as sensors. It was observed that when the somewhat chaotic scatter-plots of speed vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped neatly along a smoothly declining curve. This evidence suggests, but does not prove, that an MFD exists for the complete network because the fixed detectors only measure conditions in their proximity, which may not represent the whole network. Therefore, the analysis was enriched with data from GPS-equipped taxis, which covered the entire network. The new data were filtered to ensure that only full-taxi trips (i.e., representative of automobile trips) were retained in the sample. The space-mean speeds and densities at different times-of-day were then estimated for the whole study area using relevant parts of the detector and taxi data sets. These estimates were still found to lie close to a smoothly declining curve with deviations smaller than those of individual links - and entirely explained by experimental error. The analysis also revealed a fixed relation between the space-mean flows on the whole network, which are easy to estimate given the existence of an MFD, and the trip completion rates, which dynamically measure accessibility.
Article
This paper presents a simple representation of traffic on a highway with a single entrance and exit. The representation can be used to predict traffic's evolution over time and space, including transient phenomena such as the bu