Feedback perimeter control for multi-region large-scale congested networks

Perimeter and boundary flow control in multi-reservoir heterogeneous networks

Part I of the thesis investigates novel urban traffic state estimation methods utilizing probe vehicle data. Chapter 2 proposes a method to integrate the collective effect of dispersed probe data with traffic kinematic wave theory and data mining techniques to model the spatial and temporal dynamics of queue formation and dissipation in arterials. The queue estimation method captures interdependencies in queue evolutions of successive intersections, and moreover, the method is applicable in oversaturated conditions and includes a queue spillover statistical inference procedure. Chapter 3 develops a travel time reliability model to estimate arterial route travel times distribution (TTD) considering spatial and temporal correlations between traffic states in consecutive links. The model uses link-level travel time data and a heuristic grid clustering method to estimate the state structure and transition probabilities of a Markov chain. By applying the Markov chain procedure, the correlation between states of successive links is integrated and the route-level TTD is estimated. The methods in Part I are tested with various probe vehicle penetration rates on case studies with field measurements and simulated data. The methods are straightforward in implementation and have demonstrated promising performance and accuracy through numerous experiments. Part II studies network-level modeling and control of large-scale urban networks. Chapter 4 is the pioneer that introduces the urban perimeter control for two-region urban cities as an elegant control strategy to decrease delays in urban networks. Perimeter controllers operate on the border between the two regions, and manipulate the percentages of transfer flows between the two regions, such that the number of trips reaching their destinations is maximized. The optimal perimeter control problem is solved by the model predictive control (MPC) scheme, where the prediction model and the plant (reality) are formulated by macroscopic fundamental diagrams (MFD). Chapter 5 extends the perimeter control strategy and MFD modeling to mixed urban-freeway networks to provide a holistic approach for large-scale integrated corridor management (ICM). The network consists of two urban regions, each one with a well-defined MFD, and a freeway, modeled by the asymmetric cell transmission model, that is an alternative commuting route which has one on-ramp and one off-ramp within each urban region. The optimal traffic control problem is solved by the MPC approach to minimize total delay in the entire network considering several control policies with different levels of urban-freeway control coordination. Chapter 6 integrates traffic heterogeneity dynamics in large-scale urban modeling and control to develop a hierarchical control strategy for heterogeneously congested cities. Two aggregated models, region- and subregion-based MFDs, are introduced to study the effect of link density heterogeneity on the scatter and hysteresis of MFD. A hierarchical perimeter flow control problem is proposed to minimize the network delay and to homogenize the distribution of congestion. The first level of the hierarchical control problem is solved by the MPC approach, where the prediction model is the aggregated parsimonious region-based MFD and the plant is the subregion-based MFD, which is a more detailed model. At the lower level, a feedback controller tries to maximize the network outflow, by increasing regional homogeneity.

Traffic-responsive signal control is a cost-effective, easy-to-implement, network management strategy, bearing high potential to improve performance in heavily congested networks with dynamic traffic characteristics. Max Pressure (MP) distributed control gained significant popularity due to its theoretically proven ability of throughput maximization under specific assumptions. However, its effectiveness is questionable in over-saturated conditions, while network-scale implementation is often practically limited due to high instrumentation cost, which increases proportionally to the number of controlled intersections. Perimeter control (PC) based on the concept of Macroscopic Fundamental Diagram (MFD) is a state-of-the-art aggregated control strategy that regulates exchange flows between homogeneously congested regions, with the objective of maximizing traffic system performance and prevent over-saturation. However, homogeneity assumption is hardly realistic under congested conditions, which can compromise PC effectiveness. In this paper, network-wide parallel application of PC and MP strategies embedded in a two-layer control framework is evaluated in a macroscopic simulation environment. With the aim of reducing implementation cost of network-wide MP without significant performance drop, we propose a critical node identification algorithm that is based on node traffic characteristics and assess partial MP deployment to the most critical nodes. An enhanced version of Store-and-forward dynamic traffic paradigm incorporating finite queues and spill-back consideration is used to test different configurations of the two-layer framework, as well as each layer individually, for a real large-scale network, in moderate and highly congested conditions. Results show that: (i) combination of MP and PC outperforms individual layer application in almost all cases for both demand scenarios tested; (ii) MP control in critical node sets formed by the proposed strategy leads to similar or even better performance compared to full-network implementation, thus allowing for significant cost reduction; iii) the proposed control schemes improve system performance even under stochastic demand fluctuations of up to 20% of mean.

Macroscopic fundamental diagram (MFD) that describes traffic flow in an urban road network can be used to design perimeter control method to regulate the traffic flow from a macroscopic level. Most of the perimeter control algorithms are regarded as a kind of model-based feedback control method, whose performance is hardly to improve in practice due to the model uncertainty. By noticing the repetitive nature of urban traffic flow, an iterative learning control (ILC) based perimeter control method is proposed for an urban region. Since the repetitive information of the controlled system is fully utilized, an improved tracking performance is guaranteed by theoretical analysis, and simulation results verify the effectiveness of the proposed perimeter control method.

Urban traffic networks are highly vulnerable to external disturbances such as heavy rainfall, which can induce capacity degradation, non-periodic congestion, and delayed system recovery. To address the limitations of existing perimeter control strategies that primarily focus on demand-side fluctuations and assume fixed network capacity, this study proposes a distributed coordinated perimeter control framework that explicitly incorporates rainfall-induced capacity degradation into system feedback. The proposed framework adopts a two-layer control structure, in which a main controller regulates global network accumulation near the critical macroscopic fundamental diagram (MFD) state, while sub-controllers dynamically adjust perimeter control rates in response to localized traffic conditions and water accumulation. A case study based on real taxi trajectory data from Wuhan City, combined with SUMO-based microscopic traffic simulation, is conducted to evaluate the proposed approach under heavy rainfall conditions. The results show that the distributed coordinated control framework reduces peak network accumulation by 39.6%, increases average vehicle speed by 35.28%, and significantly accelerates post-disturbance recovery. These findings indicate that integrating environmental disturbances into distributed perimeter control can effectively enhance the stability and resilience of urban traffic systems under adverse weather conditions.

Macroscopic fundamental diagram (MFD) describes a unimodal, low-scatter relationship between network vehicle density and network space mean flow for homogenous network regions, and provides a possible solution to traffic signal control for urban road networks. Transfer between multiple states has been ignored in a few control methods, despite continuous advances in the areas of congestion perimeter control because different states should have different control objectives. This paper proposes a boundary hybrid control for two-region urban cities based on three network states: free flow, critical flow, and congestion flow as characterized by MFD. The hybrid perimeter control for two-region urban cities with different states can be set up according to different control objectives by analyzing the control adaptation characteristics for the single-control method of Bang-Bang, PI feedback control, and nonlinear PI control based on the MFD curve at a single-boundary entrance under different conditions. Furthermore, the confirmation of rapid reduction in the saturation, traffic distribution, and signal timing of the boundary intersection is derived. An urban center network located approximately 20 km <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in Hefei is taken as an example. Comparison results show that the hybrid control performs significantly better than the single-control scheme in completing vehicle travel, decreasing travel delay, and preventing network oversaturation.

In this paper, we improve the effect of perimeter control for Urban Traffic Sub-region by optimizing signal timing in traffic sub-region. Firstly, we verify the influence of different signal timing on the shape of macroscopic fundamental diagram(MFD) by simulation. Then, we use BP neural network to model the mapping relationship between signal timing and MFD maximum volume(saturated traffic volume of sub-region). In perimeter control based on MFD, the larger the saturated traffic volume, the more vehicles passing through the sub-area. When the output of the BP neural network model reaches the maximum value, the signal timing of the road network is the best one. Comparing the perimeter control effects of different signal timings, we find that the larger the saturation traffic, the larger the traffic in the boundary control and the smaller the vehicle delay.

Modeling, estimation, and control in large-scale urban road networks with remaining travel distance dynamics

Recent research has demonstrated that the Macroscopic Fundamental Diagram (MFD) is reliable and practical tool for modeling traffic dynamics and network performance in single-mode (cars only) urban road networks. In this paper, we first extend the modeling of the single-mode MFD to a bi-modal (bus and cars) one. Based on simulated data, we develop a three-dimensional MFD (3D-MFD) relating the accumulation of cars and buses, and the total circulating flow in the network. We propose an exponential function to capture the shape of the 3D-MFD, which shows a good fit to the data. We also propose an elegant estimation for passenger car equivalent of buses (PCU), which has a physical meaning and depends on the bi-modal traffic in the network. Moreover, we analyze a 3D-MFD for passenger network flows and derive its analytical function. Finally, we investigate an MFD for networks with dedicated bus lanes and the relationship between the shape of the MFD and the operational characteristics of buses. The output of this paper is an extended 3D-MFD model that can be used to (i) monitor traffic performance and, (ii) develop various traffic management strategies in bi-modal urban road networks, such as redistribution of urban space among different modes, perimeter control, and bus priority strategies.

Perimeter control schemes proposed to alleviate congestion in large-scale urban networks usually assume perfect knowledge of the accumulation state together with current and future inflow demands, requiring information about the origins and destinations (OD) of drivers. Such assumptions are problematic for practice due to: (i) Measurement noise, (ii) difficulty of measuring OD-based accumulation states and inflow demands. To address these, we propose a nonlinear moving horizon estimation (MHE) scheme for large-scale urban road networks with dynamics described via macroscopic fundamental diagram. Furthermore, we consider various measurement configurations likely to be encountered in practice, such as measurements on regional accumulations and transfer flows without OD information, and provide results of their observability tests. Simulation studies, considering joint operation of the MHE with a model predictive perimeter control scheme, indicate substantial potential towards practical implementation of MFD-based perimeter control.

Perimeter control for urban traffic system based on macroscopic fundamental diagram

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To alleviate regional traffic congestion in large areas of the urban zonal road network, an extensible perimeter control strategy based on the macroscopic fundamental diagram is proposed to improve the effectiveness of the entire urban network. The proposed strategy considers the fleet storage capacity of the links, avoids over queuing, and establishes a constraint of perimeter control and a regional feedback control model. A new extended boundary is formed by dynamically adjusting the control boundary of the protected area in real time, and a feedback gate is set at the junction of extended boundary to restrict the traffic flow in the road network of the congested area. To verify the effectiveness of the proposed strategy, a Sioux Falls test network is used as the research area, and the effect of the proposed strategy is evaluated in Vissim. Simulation results show that the implementation of the scalable perimeter control strategy improves the operation index of the road network, and a wide range of congestion is obviously alleviated.

Traffic flow control has motivated many researchers since early decades of the 19th century. Recently, the concept of a perimeter traffic control for an urban region has been strengthened by a series of works, which have shown that a perimeter controller, located at a region border, can manipulate the transfer flows across the border to maximize the total outflow of the region. The macroscopic fundamental diagram (MFD), that relates average flow with accumulation, is used to model the traffic flow dynamics in the region. Assuming that the control inputs of the cross-border flows are coupled, i.e. the border is always utilized over time for transferring flows by one of the two directions (from and towards the region), and that the urban region has two traffic flow demands generated inside the region with internal and external destinations, and a generated traffic flow outside the region with a destination to the region, the explicit formulation of the optimal feedback control policy and a proof of optimality are provided. The proof is based on the modified Krotov-Bellman sufficient conditions of optimality, where the upper and lower bounds of state variables are calculated.

Cooperative traffic signal and perimeter control in semi-connected urban-street networks