Simulation-based Dynamic Traffic Assignment Model Research Articles

Joint Routing and Pricing Control in Bimodal Mixed Autonomy Networks with Elastic Demand and Three-Dimensional Passenger Macroscopic Fundamental Diagram

The interaction between mixed autonomy traffic and public transport vehicles competing for limited road space is a less explored area of research. To evaluate the traffic dynamics in bimodal networks, a three-dimensional (passenger) network fundamental diagram, known as 3D-NFD (3D-pNFD), can be estimated that relates the accumulation of cars (autonomous and human-driven) and buses to the network vehicular (passenger) travel production. In this study, we propose a 3D-pNFD-based congestion pricing scheme considering three vehicle classes of buses, system-optimal (SO) seeking connected and automated vehicles (CAVs), and user-equilibrium (UE) seeking human-driven vehicles (HVs). We develop an iterative tri-level modeling framework for mode choice, pricing, and route choice in a mixed autonomy network. The lower level generates mixed equilibrium traffic flow through an integrated mixed equilibrium simulation-based dynamic traffic assignment model and a transit assignment model. The mid-level finds the optimal toll rates through a 3D-pNFD feedback-based controller. A nested logit-based mode choice model is also applied to capture travelers’ preferences toward three available modes and incorporates elastic demand. To encourage CAVs to follow the SO routing mode, they are provided with a discount on the congestion toll whereas UE-seeking HVs are subject to full price toll. Buses are also entirely exempt from the toll. We explore three scenarios with different discount rates on SO-seeking CAVs to investigate the effect of the incentive plans on the mode choice behaviors of road users in the pricing zone. The performance of the proposed model is evaluated in a large-scale network in Melbourne, Australia.

Managing network congestion with link-based incentives: A surrogate-based optimization approach

Incentive-based travel demand management (IBTDM) programs endow monetary incentives to encourage travel demand redistribution across space and time. They are more appealing than alternatives such as congestion charging because commuters do not need to pay out of pocket. However, such congestion-alleviation solutions are usually managed by small private companies with constrained incentive budgets. Thus, the incentive should be wisely determined so that a limited incentive budget can be effectively used to fulfill maximum social welfare while maintaining the financial health of the IBTDM program. It is essential to know whether IBTDM is financially sound—that is, whether financial investment in IBTDM will lead to more than the equivalent value in total system travel time reduction. However, optimizing the link-based endowment scheme in a large-scale network is challenging because 1) the objective function and the budget constraint are both characterized by expensive-to-evaluate functions without closed form, and 2) it is a large-scale optimization problem that contains massive amount of decision variables. In this study, a computationally efficient surrogate-based optimization framework that is suitable for high-dimensional problems is proposed. A simulation-based dynamic traffic assignment model is used to evaluate the performance of transportation systems, and a Kriging model with partial least squares acts as the surrogate to approximate the simulation model. The results show that the optimal network-wide link-based incentive scheme improves the performance of the system. The higher the incentive budget, the more effective the incentive and the lower the marginal utility of the incentive. Furthermore, in a well-designed incentive scheme, a $1M investment in IBTDM would lead to much more than the equivalent of $1M in total system travel time reduction, which proves the economic viability of IBTDM and provides support for its promotion. IBTDM implemented within smaller regions and tighter incentive budgets produces higher utility ratios.

A multiclass simulation-based dynamic traffic assignment model for mixed traffic flow of connected and autonomous vehicles and human-driven vehicles

Connected and Autonomous Vehicles (CAVs) may exhibit different driving and route choice behaviours compared to Human-Driven Vehicles (HDVs), which can result in a mixed traffic flow with multiple classes of route choice behaviour. Therefore, it is necessary to solve the Multiclass Traffic Assignment Problem (TAP) for mixed traffic flow. However, most existing studies have relied on analytical solutions. Furthermore, simulation-based methods have not fully considered all of CAVs’ potential capabilities. This study presents an open-source solution framework for the multiclass simulation-based TAP in mixed traffic of CAVs and HDVs. The proposed model assumes that CAVs follow system optimal with rerouting capabilities, while HDVs follow user equilibrium. It also considers the impact of CAVs on road capacity at both micro and meso scales. The proposed model is demonstrated through three case studies. This study provides a valuable tool that can consider several assumptions for better understanding the impact of CAVs on mixed traffic flow.

Dynamic pedestrian traffic assignment with link transmission model for bidirectional sidewalk networks

Planning assessment of urban walking infrastructure requires appropriate modeling methodologies that capture the time-dependent and unique microscopic characteristics of bidirectional pedestrian streams. In this paper, we develop a simulation-based dynamic pedestrian traffic assignment (DPTA) model specifically formulated for walking networks (e.g. sidewalks) with bidirectional links. The model consists of a dynamic user equilibrium (DUE) based walking route choice and a link transmission model (LTM) for network loading. The formulated DUE adopts a pedestrian volume delay function (pVDF) taking into account the properties of bidirectional pedestrian streams such as self-organization. The adopted LTM uses a three-dimensional triangular bidirectional fundamental diagram as well as a generalized first-order node model. The applicability and validity of the model is demonstrated in hypothetical small networks as well as a real-world large-scale network of sidewalks in Sydney. The model successfully replicates formation and propagation of shockwaves in walking corridors and networks due to bidirectional effects.

Deriving the Value of Time for Toll Revenue Forecasting using Multiple Criteria Decision-Making

Mathematical traffic models replicate travel decisions and driver behavior. These tools have become more sophisticated, yet they remain simplified representations of more complex systems, including associated toll forecasts. A literature review shows that a substantial amount of toll revenue forecasts has fallen short of accurately representing actual road usage—by as much as 50%. In recent years, simulation-based modeling tools have emerged as an innovative approach to regional traffic forecasting. They capture time-varying traffic conditions and represent more realistic traffic flow and congestion, but this type of travel forecasting new and complex. One key variable in these traffic modeling tools is the value of time (VoT). The VoT represents how drivers perceive their willingness to pay a toll to reduce their travel time. How to properly quantify the VoT is still not completely understood, but it is the governing factor in how toll revenue forecasts are calculated. We propose three different approaches for quantifying the VoT. The first approach uses socio-economic data in terms of median income per zone. The VoT is quantified based on income levels of each origin-zone that travelers depart from. The second approach uses a traveler’s destination zone—derived based on trip purpose. The second approach uses a multiple-criteria decision-making (MCDM) methodology known as the Analytical Hierarchy Process (AHP) to develop weighting for each trip purpose. A third approach also uses AHP (combined with departure time) to derive weights for each traveler’s VoT. The three approaches were tested using a simulation-based dynamic traffic assignment (DTA) model.

Distance-based time-dependent optimal ratio control scheme (TORCS) in congested mixed autonomy networks

Connected and automated vehicle technologies provide an opportunity for a more efficient distribution of traffic in urban networks through cooperative routing behavior. Controlling the route choice of a proportion of autonomous vehicles (AVs) to establish the system optimum (SO) condition has already been investigated in static networks. This study aims to develop a time-dependent optimal ratio control scheme (TORCS) in which an optimal ratio of AVs is identified and selected to seek SO routing. The objective of the control scheme is to achieve a reasonable compromise between the system efficiency (i.e., total travel time savings) and the control cost that is proportional to the total distance traveled by SO-seeking AVs. The proposed distance-based TORCS is formulated as a bi-level optimization problem. A mixed equilibrium simulation-based dynamic traffic assignment model (SBDTA) estimates time-dependent mixed traffic patterns in the lower level based on the time-dependent optimal ratios of SO-seeking AVs obtained from the upper level. We also introduce a new concept of frequency control within the TORCS application. The frequency-based TORCS enables the central agent to control the route choice of selected AVs only in the time periods with the most significant impact on system travel time reduction. This is formulated with a binary variable within the TORCS problem indicating an action/no action regarding controlling AVs at a given assignment interval. The applicability of the model is demonstrated on a real large-scale network of Melbourne, Australia.

A meso-to-macro cross-resolution performance approach for connecting polynomial arrival queue model to volume-delay function with inflow demand-to-capacity ratio

• Cross-resolution modelling approach for understanding the dynamic relationship between demand and supply and the resulting congestion. • Describe oversaturated system dynamics with parsimonious macroscopic analytical formulations with consistent mesoscopic queue vehicular fluid model. • Unified integration of multi-scale models provides city planners with a valid analytical framework to analyze queue saturation evolution process. • Estimate key model parameters from real-world data sets on heavily congested corridors. Although the macroscopic volume-delay function (VDF) has been widely used in static traffic assignment for transportation planning, the planning community has long recognized its deficiencies as a static function in capturing traffic flow dynamics and queue evolution process. In the existing literature, many queueing-based and simulation-based dynamic traffic assignment (DTA) models involving various traffic flow parameters have been proposed to capture traffic system dynamics on different spatial scales; however, how to calibrate these DTA models could still be a challenging task in its own right, especially for real-world congested networks with complex traffic dynamics. By extending the fluid-based polynomial arrival queue (PAQ) model with quadratic inflow rates proposed by Newell (1982) and cubic inflow rates by Cheng et al. (2022), this paper attempts to propose a cross-resolution Queueing-based Volume-Delay Function (QVDF) to explicitly establish a coherent connection between (a) the macroscopic average travel delay performance function in a long-term planning horizon and (b) the mesoscopic dynamic queuing model during a single oversaturated period. By introducing two types of elasticity functional forms, this paper develops a relationship from the macroscopic inflow demand-to-capacity (D/C) ratio to the congestion duration of a bottleneck, from the congestion duration to the magnitude of speed reduction. The QVDF can be directly utilized to provide closed-form expressions for both average travel delay performance and the time-dependent speed profiles. The proposed cross-resolution QVDF provides a numerically reliable and theoretically rigorous performance function to characterize oversaturated bottlenecks at both macroscopic and mesoscopic scales.

Joint routing and pricing control in congested mixed autonomy networks

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.

A link-to-link segment based metamodel for dynamic network loading

Dynamic network loading (DNL) is a core part of simulation-based dynamic traffic assignment (DTA) models, which describes how traffic propagates on a transportation network and usually maps a set of route departure rates to a set of route travel times. Due to the incorporation of different intra- and inter-link dynamics such as queuing, spillback, etc., DNL becomes complex, resulting in models with undesirable analytical properties (e.g., discontinuity, non-differentiability, and lack of closed-form) and requiring intensive computational efforts. Moreover, as DNL is applied repeatedly in simulation-based DTA algorithms, it often is the computational bottleneck of large-scale traffic assignment and related optimization problems. In this research, we address these problems by proposing a link-to-link segment-based Kriging metamodel for dynamic network loading. The proposed Kriging model calculates route travel time, link travel time, and link flow. It systematically approximates the traditional DNL model while being faster and maintaining some desirable analytical properties. Both temporal and spatial proximity information and the route segment incidence information are incorporated in the metamodel formulation. The models are trained using maximum likelihood estimation with different dataset sizes. In the experiments, the proposed Kriging metamodels performed better than a state-of-the-art neural network model, achieving an average error of 1.64% and 5.32% in the Nguyen Dupuis (ND) network and the Sioux Falls (SF) network, respectively, along with at least 43 times, sometimes as high as over 1300 times, improvement in computational speed. The results, however, suggest a tradeoff between efficiency and accuracy and the size of the training dataset. With balanced route demand, the model’s performance was reasonable even under congested traffic conditions. The MAPE values were at most 3% and 18% in the ND network and the SF network, respectively, for different level of congestion demonstrating the effectiveness of the proposed model.

Improving the accuracy and efficiency of online calibration for simulation-based Dynamic Traffic Assignment

Simulation-based Dynamic Traffic Assignment models have important applications in real-time traffic management and control. The efficacy of these systems rests on the ability to generate accurate estimates and predictions of traffic states, which necessitates online calibration. A widely used solution approach for online calibration is the Extended Kalman Filter (EKF), which – although appealing in its flexibility to incorporate any class of parameters and measurements – poses several challenges with regard to calibration accuracy and scalability, especially in congested situations for large-scale networks. This paper addresses these issues in turn so as to improve the accuracy and efficiency of EKF-based online calibration approaches for large and congested networks. First, the concept of state augmentation is revisited to handle violations of the Markovian assumption typically implicit in online applications of the EKF. Second, a method based on graph-coloring is proposed to operationalize the partitioned finite-difference approach that enhances scalability of the gradient computations.Several synthetic experiments and a real world case study demonstrate that application of the proposed approaches yields improvements in terms of both prediction accuracy and computational performance. The work has applications in real-world deployments of simulation-based dynamic traffic assignment systems.

Comparing Dynamic User Equilibrium and Noniterative Stochastic Route Choice in a Simulation-Based Dynamic Traffic Assignment Model: Practical Considerations for Large-Scale Networks

Simulation-based dynamic traffic assignment (DTA) models play a vital role in transportation planning and operations. While the widely studied equilibrium-seeking DTA including dynamic user equilibrium (DUE) often provides robust and consistent outcomes, their expensive computational cost for large-scale network applications has been a burden in practice. The noniterative stochastic route choice (SRC) model, as a nonequilibrium seeking DTA model, provides an alternative for specific transportation operations applications that may not require equilibrium results after all (e.g., evacuation and major network disruptions) and thus tend to be computationally less expensive, yet may suffer from inconsistent outcomes. While DUE is a widely accepted approach for many strategic planning applications, SRC has been increasingly used in practice for traffic operations purposes. This paper aims to provide a comparative and quantitative analysis of the two modeling approaches. Specifically, a comparison has been made at two levels: link-level flows and network-level congestion patterns. Results suggest that adaptive driving improves the quality of the SRC solution, but its difference from DUE still remains significant at the link level. Results have practical implications for the application of large-scale simulation-based DTA models for planning and operations purposes.

How does the value of time influence road user costs during work zone closures? A case study in El Paso, Texas, using simulation-based modeling methods

It is becoming standard practice for many departments of transportation (DOTs) to use incentive/disincentive clauses (also known as road user costs) with contractors to stay on or ahead of schedule. These road user costs are clauses that DOTs use to calculate a monetary amount to encourage contractors to complete work prior to milestone dates and/or limit the time specified on the contract. The monetary amounts are typically vehicle operating costs and vehicle delay costs encumbered by highway users resulting from construction, maintenance, or rehabilitation activity. In this paper, we propose an innovative way of calculating these costs using varied values of time based on trip purpose and departure time. In addition, we use advanced pre-trip and en route traveler information to determine the influence it has on route choice. Several scenarios are modeled using an advanced, simulation-based dynamic traffic assignment model. The goal of this paper is to identify the governing factors that contribute to road use costs by determining different approaches to derive the value one places on a trip. The approach to this study is twofold: first several research methods were used to derive the value of time. Second, the use of advanced traveler information is introduced to determine if it plays a critical role in route choice. The proposed methodology shows differences in road user cost calculations. Which approach would be more receptive to a contractor while proposing roadway construction? A case study of a roadway construction project in El Paso, Texas, is used to compare different approaches to calculate road user costs.

An Open GMNS Dataset of a Dynamic Multi-Modal Transportation Network Model of Melbourne, Australia

Simulation-based dynamic traffic assignment models are increasingly used in urban transportation systems analysis and planning. They replicate traffic dynamics across transportation networks by capturing the complex interactions between travel demand and supply. However, their applications particularly for large-scale networks have been hindered by the challenges associated with the collection, parsing, development, and sharing of data-intensive inputs. In this paper, we develop and share an open dataset for reproduction of a dynamic multi-modal transportation network model of Melbourne, Australia. The dataset is developed consistently with the General Modeling Network Specification (GMNS), enabling software-agnostic human and machine readability. GMNS is a standard readable format for sharing routable transportation network data that is designed to be used in multimodal static and dynamic transportation operations and planning models.

Estimating incident impacts on urban street travel time in the case of super saturation in traffic lights

Dynamic signal control strategies are effective in relieving congestions during nontypical days, such as those with high demands, incidents with different attributes, and adverse weather conditions. This research recognizes the need to model the impacts of dynamic signal controls for different days representing, different demand and incident levels. Methods are identified to calibrate the utilized tools for the patterns during different days based on demands and incident conditions utilizing combinations of real-world data with different levels of details. A significant challenge addressed in this study is to ensure that the mesoscopic simulation-based dynamic traffic assignment (DTA) models produces turning movement volumes at signalized intersections with sufficient accuracy for the purpose of the analysis. A new model is developed to estimate the drop in capacity at the incident location by considering the downstream signal control queue spillback effects. The developed capacity reduction models were used to estimate delay due to an urban street incident. The delay was calculated as a combination of the delay due to queuing on the incident link and the increase in upstream intersection control delays due the reduction in maximum throughputs resulting from queue spillback to the upstream intersection The HCS-based method estimated a reduction in delay resulting from the new signal timing plan to be around 3,404 vehicle-hours, whereas the VISSIM shows that the new signal timing saving in delay is 4,008 vehicle-hours. This confirms that the developed method and VISSIM estimation of the benefits are consistent.

Regional CO2 impact assessment of road infrastructure improvements

Transparent methods of estimating CO2 emissions from transportation sources are necessary to evaluate mitigation strategies. This study proposes a framework to assess the regional impact of roadway designs on CO2 emissions. First, three roadway infrastructure configurations were designed to improve the traffic flow at intersections and interchanges. Second, the economical and environmental life-cycle cost assessments of constructing and maintaining new infrastructures were developed. Then, the effects of infrastructure on regional vehicle CO2 emissions were modeled using a simulation-based dynamic traffic assignment model coupled with the U.S. Environmental Protection Agency's MOtor Vehicle Emission Simulator (MOVES) model. The case study estimated that converting 72 stop signs to roundabouts within El Paso, TX, reduced daily vehicular CO2 emissions by more than 50 tonnes, paying back the CO2 from construction and maintenance within 2.5 to 2.9 years. The roundabout modifications' cost-effectiveness ranged from $30 to $130 per tonne of CO2 over a 30-year assessment.

Simulation-based optimization of toll pricing in large-scale urban networks using the network fundamental diagram: A cross-comparison of methods

Simulation-based optimization (SO or SBO) has become increasingly important to address challenging transportation network design problems. In this paper, we propose to solve two toll pricing problems with different levels of complexity using the concept of the macroscopic or network fundamental diagram (MFD or NFD), where a large-scale simulation-based dynamic traffic assignment model of Melbourne, Australia is used. Four computationally efficient SBO methods are applied and compared, including the proportional-integral (PI) controller, regressing kriging (RK), DIviding RECTangles (DIRECT), and simultaneous perturbation stochastic approximation (SPSA). The comparison reveals that these methods work equally well on the simple problem without exhibiting significant performance differences. But, for the complex problem, RK manifests itself to be the best-performing method thanks to its capability of filtering out the numerical noise arising from computer simulations (i.e. allowing for non-smoothness of the objective function). While the PI controller is a more competitive solution to the simple problem given its faster rate of convergence, the poor scalability of the method in the complex problem results in limited applicability. Two caveats, however, deserve emphasis: (i) the chosen critical network density of the NFD does not necessarily represent a robust network control or optimization threshold, as it might shift in the presence of toll pricing; and (ii) re-interpolation is required as part of RK in order to achieve global convergence.

Hierarchical density-based clustering methods for tolling zone definition and their impact on distance-based toll optimization

Real-time network control strategies such as congestion pricing have been used in a number of metropolitan areas around the world for traffic congestion mitigation. Recent advances in Global Navigation Satellite System (GNSS) technology have led to increasing interest in distance- or usage-based road pricing as an effective alternative to traditional facility-, cordon- and area-based pricing that typically rely on fixed infrastructure. In this paper, we propose the use of feature-variant clustering methods, OPTICS and HDBSCAN*, as a systematic approach for tolling zone definition to operationalize distance-based tolling schemes. Subsequently, we develop a framework for predictive distance-based toll optimization to evaluate network performance for the various tolling zone definitions derived from the aforementioned feature-variant clustering methods. In this framework, for a specific tolling zone definition, tolling function parameters are optimized using a simulation-based Dynamic Traffic Assignment (DTA) model operating within a rolling horizon scheme. Predictive optimization is integrated with the guidance information generation. Behavioral models capture drivers’ responses to the tolls in terms of trip cancellation and choices of mode, route and departure time. Experiments on the real-world Expressway and Major Arterials network of Singapore demonstrate improved effectiveness of distance-based toll optimization given tolling zone definitions derived from feature-variant clustering, compared to fixed cordon-based pricing, adaptive cordon-based pricing, as well as distance-based pricing with ad hoc tolling zone definitions. Further, the results indicate that the use of the marginal link cost tolls as a clustering feature produces the most robust tolling zone definitions and yields significant improvements in social welfare over ad hoc zone definitions and cordon-pricing. Finally, experiments on the Boston CBD network also demonstrate the effectiveness of distance-based toll optimization schemes on urban traffic networks.

Providing optimal dynamic model of traffic lights in super saturated conditions with emphasis on ATM

Dynamic signal control strategies are effective in relieving congestions during nontypical days, such as those with high demands, incidents with different attributes, and adverse weather conditions. This research recognizes the need to model the impacts of dynamic signal controls for different days representing, different demand and incident levels. Methods are identified to calibrate the utilized tools for the patterns during different days based on demands and incident conditions utilizing combinations of real-world data with different levels of details. A significant challenge addressed in this study is to ensure that the mesoscopic simulation-based dynamic traffic assignment (DTA) models produces turning movement volumes at signalized intersections with sufficient accuracy for the purpose of the analysis. A new model is developed to estimate the drop in capacity at the incident location by considering the downstream signal control queue spillback effects. A second model is developed to estimate the reduction in the upstream intersection capacity due to the drop in capacity at These regression models are combined with the DTA model to estimate the volume at the incident location and alternative routes. The volumes with different demands and incident levels, resulting from DTA modeling are imported to a microscopic simulation model for more detailed analysis of dynamic signal control. The microscopic model shows that the implementation of special signal plans during incidents and different demand levels can improve mobility the midblock incident location as estimated by the first model measures.

Integration of Departure Time Choice Modeling and Dynamic Origin–Destination Demand Estimation in a Large-Scale Network

Time-dependent origin–destination (OD) demand estimation using link traffic data in a large-scale network is a highly underdetermined problem. As a result, providing an accurate initial solution is crucial for obtaining a more reliable estimated demand. In this paper, we discuss the necessity of having a comprehensive demand profiling model that considers the spatial differences of OD pairs and we demonstrate its application in the calibration of large-scale traffic assignment models. First, we apply a departure choice model that adds a time dimension to the OD demand flows concerning their spatial differences. The time-profiled demand is then fed into the time-dependent OD demand estimation problem for further adjustment. Results show that in addition to reducing the error between simulation outputs and the observed link counts, the estimated demand profile more accurately reflects the spatial correlation of the OD pairs in the large-scale network being studied. Results provide practical insights into deployment and calibration of simulation-based dynamic traffic assignment models.

A bi-partitioning approach to congestion pattern recognition in a congested monocentric city

This paper proposes a bi-partitioning approach using link density data to identify an optimal restricted zone (RZ) in a congested monocentric city to assist with the implementation of area-wide congestion management strategies. A composite similarity measure is developed for each link in the network as a weighted average of a density similarity measure (ensuring homogeneity) and a distance similarity measure (ensuring connectivity and compactness). The resulting similarity matrix is fed into a graph clustering method termed symmetric nonnegative matrix factorization (SNMF) to bi-partition the network. To determine the optimal weight as a hyperparameter, we propose a hierarchical search algorithm (HSA) based on the concept of “knee” that is used to find the most significant solution from the Pareto front. The proposed approach is demonstrated on the Melbourne network using a simulation-based dynamic traffic assignment model. Results show that the methodology (i) can effectively capture the spatial variations of the congestion pattern in the network; (ii) is robust to moderate parameter changes; (iii) can be extended to the time-dependent case and hence inform when to activate the area control; and (iv) can perform relatively well in the presence of missing data. When varying the distance threshold as a design parameter, we can observe how the optimal RZ evolves in space, a feature that is critical to devising a double- or multi-layered RZ for hierarchical control purposes.