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Distributed Optimization and Coordination Algorithms for Dynamic Traffic Metering in Urban Street Networks
Abstract
Previous research has shown that proper metering of entry traffic to urban street networks, similar to metering traffic on on-ramps in freeway facilities, reduces traffic congestion especially in oversaturated flow conditions. Building on the previous research, this paper presents a real-time and scalable methodology for finding near-optimal metering rates dynamically in urban street networks. The problem is formulated into a Mixed-Integer Linear Program (MILP) based on the cell transmission model. We propose a distributed optimization scheme that decomposes the network level MILP into several link-level MILPs to reduce the complexity of the problem. We convert the link-level MILPs to linear programs to reduce the computational complexity further. Moreover, we create distributed coordination between the link-level linear programs to push the solutions towards optimality. The distributed optimization and coordination solution algorithm is incorporated into a rolling horizon technique to account for the time-varying demand and capacity and to reduce the computational complexity further. We applied the proposed solution technique to a number of case studies and observed that it was scalable and real-time, and found solutions that were at most 2.2% different from the optimal solution of the problem. Like the previous studies, we found significant improvements in network operations as a result of traffic metering.
... This oversight can lead to inconsistencies between expected and actual performances of perimeter controls. Furthermore, solution algorithms based on the CTM are challenged by the model's complexity, which makes real-time, large-scale application and adjustment to changing conditions difficult, even with the adoption of more recent decomposition techniques Mohebifard and Hajbabaie, 2018a). The reliance on accurate traffic predictions, which are often elusive, further limits the practicality of these strategies. ...
... This method leverages data from loop detectors and connected vehicles to estimate the flow of traffic between sub-intersections. Mohebifard and Hajbabaie (2018a) suggested that this transmission flow could also be determined through iterative optimization. ...
... Although their theoretical foundation has been established, these methods are still in the nascent stages of development. The complexity of optimizing road metering rates with CTM poses significant computational challenges for online control in large-scale networks, even with the network decomposition techniques proposed by Mohebifard and Hajbabaie (2018a). Moreover, these techniques often do not adequately consider traffic flow from interior network generation sites and typically assume a centralized decision-maker for both interior and perimeter metering. ...
Perimeter control is a traffic management approach aimed at regulating vehicular accumulation within urban regional networks by managing flows on all border-crossing roads. Methods based on the macroscopic fundamental diagram (MFD) fall short in providing specific metering for individual roads. Recent advancements in the cell transmission model (CTM) have attempted to address this limitation but are hindered by their reliance on centralized control, which requires the availability of full information and authority over traffic generation sites. Our study proposes an innovative decentralized, game-theoretical framework for perimeter control to address these practical challenges. It is structured around two key groups of agents: perimeter agents, tasked with managing border roads, and interior agents, focused on traffic within generation sites. The framework also incorporates mechanisms for interactions between these agents and the road network, aiming to optimize their individual utilities. Additionally, we have developed a multi-agent reinforcement learning (RL) algorithm, extending the mean-field theory concept, to address the complexity of simultaneous learning by multiple agents.
... However, the different techniques in the literature to simulate AVs have limitations. Several researchers proposed different algorithms and assigned an Application Programming Interface (API) of micro-simulation software (VISSIM) to create an AV environment and assessed the safety benefits (Deluka Tibljaš et al., 2018;Tajalli and Hajbabaie, 2018;Wan et al., 2016). Furthermore, fewer studies calibrated the carfollowing model parameters without any ground truth to create an AV environment (Bansal et al., 2017;Genders and Razavi, 2016). ...
... Furthermore, fewer studies calibrated the carfollowing model parameters without any ground truth to create an AV environment (Bansal et al., 2017;Genders and Razavi, 2016). Moreover, most studies assessed the safety benefits using the default driving behavior implemented in car-following model, which may not estimate real-world AV behavior (Tajalli and Hajbabaie, 2018;Mirheli et al., 2018;Letter and Elefteriadou, 2017;Mousavi et al., 2021). ...
... Traffic conflicts were identified using TTC and Post-encroachment Time (PET) thresholds in SSAM software. For safety assessment, several studies examined at a default TTC criterion of 1.5 s Papadoulis et al., 2019;Rahman et al., 2019;Tajalli and Hajbabaie, 2018). Similar to that, the default TTC criterion of 1.5 s was taken into account in this study. ...
Several past studies showed that Autonomous Vehicles (AVs) can reduce crash risk, stop-and-go traffic, and travel time. To analyze the safety benefits of AVs, most of the researchers proposed algorithms and simulation-based techniques. However, these studies have not assessed the safety benefits of AVs for different vehicle types under heterogeneous conditions. With this opportunity, this study focuses on the benefits of AVs in terms of safety for different penetration rates under heterogeneous conditions. This study considered three driving logics during peak hour conditions to assess the performance of AVs in terms of safety. In VISSIM, default driving behavior models for AVs were adopted to consider cautious and all-knowing driving logic and the third driving logic (Atkins) was modeled in VISSIM using parameters adopted from the previous studies. To this end, using VISSIM, the travel time output results were obtained. Also, using Surrogate Safety Assessment Model (SSAM), conflicts were extracted from output trajectory files (VISSIM). The results suggest that “cautious driving logic” reduced travel time and crash risk significantly when compared to the other two driving logics during peak hour conditions. Furthermore, the statistical analysis clearly demonstrated that “cautious driving logic” differs significantly from the other two driving logics. When Market Penetration Rates (MPR) were 50% or greater, the “cautious driving logic” significantly outperforms the other two driving logics. The results highlight that adopting “cautious driving logic” at an expressway may significantly increase safety at higher AV penetration rates (above 50%).
... The distributed convex optimization (DCO) has attracted significant attention and brings many applications for multiagent systems (MASs), for example, reliable communications in wireless networks [1], collision avoidance among multiple robots [2], economic dispatch in power systems [3], [4], distributed optimal power flow [5], traffic management for large-scale railway networks [6], traffic metering in urban street networks [7]. In a DCO problem, each agent has a local cost function only known to itself and there is a global cost function takes the sum of local cost functions. ...
... where α,ᾱ,α are K ∞ functions and µ is denoted in (5).α(µ) is called prescribed-time convergent gain. The inequalities in (7) are simplified as V (x) ∼ {α,ᾱ,α|ẋ = f (x, µ)}. The continuously differentiable function V (x) : R n → R ≥0 is called the prescribed-time input-to-state stable (ISS) Lyapunov function for the systemẋ = f (x, d, µ) with d ∈ R n d being the external input, if V (x) and its derivative along the trajectory of the system satisfy, for all x ∈ R n and t ∈ T p , ...
In this paper, we address the distributed prescribed-time convex optimization (DPTCO) problem for a class of nonlinear multi-agent systems (MASs) under undirected connected graph. A cascade design framework is proposed such that the DPTCO implementation is divided into two parts: distributed optimal trajectory generator design and local reference trajectory tracking controller design. The DPTCO problem is then transformed into the prescribed-time stabilization problem of a cascaded system. Changing Lyapunov function method and time-varying state transformation method together with the sufficient conditions are proposed to prove the prescribed-time stabilization of the cascaded system as well as the uniform boundedness of internal signals in the closed-loop systems. The proposed framework is then utilized to solve robust DPTCO problem for a class of chain-integrator MASs with external disturbances by constructing a novel variables and exploiting the property of time-varying gains. The proposed framework is further utilized to solve the adaptive DPTCO problem for a class of strict-feedback MASs with parameter uncertainty, in which backstepping method with prescribed-time dynamic filter is adopted. The descending power state transformation is introduced to compensate the growth of increasing rate induced by the derivative of time-varying gains in recursive steps and the high-order derivative of local reference trajectory is not required. Finally, theoretical results are verified by two numerical examples.
... Under the assumption of fully-penetrated CV environment, this method predicted the network dynamics through an improved model similar to the cell transmission model (CTM) (Daganzo, 1994) and reduced computational complexity by network decomposition. Similar ideas were carried through to network speed harmonization and signal-vehicle cooperative optimization (Tajalli and Hajbabaie, 2018;Tajalli et al., 2021). By integrating different data sources, the method also took effect under low CV penetration rates (Islam et al., 2020). ...
... Computational The problem provides a real-time centralized solution over the network, which makes it time consuming to optimize large-scale networks with long predicted horizons. Therefore, network partitioning (Islam et al., 2020;Tajalli and Hajbabaie, 2018;Zhang and Su, 2021) is necessary to obtain small-scale networks (containing several intersections) before implementing an efficient real-time network control. In addition, a decentralized solution approach is introduced in the following section to address this problem and acquire a sub-optimal solution with acceptable time costs. ...
This paper presents a framework for signalized road network predictive optimization using real-time routing information from connected vehicles (CVs). An important feature of the real-time routing information is the ability of CVs to broadcast the target routes they expect to travel through to the infrastructure in real time while assuming that a majority of the CVs can provide their target routes. A fully movement-level network representation model is proposed to easily describe the traffic state and demand of the signalized network. The problem is formulated as a mixed integer linear programming model to predict the movement-level network dynamics, which is solved in real time to optimize phase-free movement signal timings. The objective is to maximize the network throughput within the prediction horizon while avoiding queue spillbacks. A decentralized solution algorithm is developed to decompose the network-level problem into intersection-level subproblems, thereby reducing computational complexity. Simulation experiments validate the advantages of the proposed framework over TRANSYT schemes and max pressure-based control strategy in various scenarios. Sensitivity analysis shows the control performance under different traffic demand levels and penetration rates of the target route information. Comparisons in prediction accuracy, control performance, and computational efficiency between centralized and decentralized solutions of the proposed model are also conducted. This study explores the application of real-time routing information as a potential type of data for the network-level predictive signal optimization in the future CV environment.
... In addition, CAVs can improve traffic mobility without sacrificing safety. For instance, controlling the trajectory of CAVs upstream of signalized intersections based on advanced knowledge of signal phase and timing (SPaT) increases intersection throughput and reduces the experienced delay and risk of collisions among vehicles (25,(33)(34)(35)(36)(37)(38). Moreover, the trajectory of CAVs can be managed to avoid stops at the intersection and minimize fuel consumption (12,34,39). ...
... While many studies have examined the possible effects of connected and automated vehicles on traffic operations on uninterrupted flow facilities (16)(17)(18)(19)(20), the impacts of connectivity and automation on interrupted flow facilities, especially signalized intersections, are not thoroughly studied. Existing studies focus on either using signal timing information to plan the arrival of CAVs (33)(34)(35), jointly optimizing signal timing parameters and CAV trajectories (11,(40)(41)(42)(43)(44), or designing a signal-free environment with a fleet of 100% CAVs (45)(46)(47)(48)(49)(50)(51)(52)(53)(54)(55). The effects of different market penetration levels of connectivity and automation on the saturation headway and capacity at signalized intersections are unknown. ...
This paper analyzes the potential effects of connected and automated vehicles on saturation headway and capacity at signalized intersections. A signalized intersection is created in Vissim as a testbed, where four vehicle types are modeled and tested: (I) human-driven vehicles (HVs), (II) connected vehicles (CVs), (III) automated vehicles (AVs), and (IV) connected automated vehicles (CAVs). Various scenarios are defined based on different market penetration rates of these four vehicle types. AVs are assumed to move more cautiously compared to human drivers. CVs and CAVs are supposed to receive information about the future state of traffic lights and adjust their speeds to avoid stopping at the intersection. As a result, their movements are expected to be smoother with a lower number of stops. The effects of these vehicle types in mixed traffic are investigated in terms of saturation headway, capacity, travel time, delay, and queue length in different lane groups of an intersection. A Python script code developed by Vissim is used to provide the communication between the signal controller and CVs and CAVs to adjust their speeds accordingly. The results show that increasing CV and CAV market penetration rate reduces saturation headway and consequently increases capacity at signalized intersections. On the other hand, increasing the AV market penetration rate deteriorates traffic operations. Results also indicate that the highest increase (80%) and decrease (20%) in lane group capacity are observed, respectively, in a traffic stream of 100% CAVs and 100% AVs.
... Since the compliance rate of CAVs is 100 percent, the obedience problem associated with conventional VSL is overcome. A number of studies on speed harmonization with CAVs have been conducted [11][12][13][14][15][16]. In most studies, CAVs are merely information providers for improved traffic state estimation and prediction [12,17]. ...
... A number of studies on speed harmonization with CAVs have been conducted [11][12][13][14][15][16]. In most studies, CAVs are merely information providers for improved traffic state estimation and prediction [12,17]. Only three studies take one step further and actually take advantage of the proactive control of CAVs. ...
This research aims to model system dynamics for mixed traffic flow consisting of Connected and Automated Vehicles (CAVs) and Human-driven Vehicles (HVs). It quantifies the impact of CAVs’ speed change on the overall traffic state on a real-time basis. The model describes the impedance of CAVs’ speed reduction on traffic flow and considers the impact of potential additional lane change induced by the speed reduction. To validate the effectiveness of the proposed model, a VISSIM based microscopic simulation evaluation is performed. The results confirm that the accuracy of the proposed model is generally over 80% with the CAVs’ speed reduction constrained within 20 km/h. Sensitivity analysis is conducted in terms of various CAV penetration rates and congestion levels. The proposed model demonstrates consistently good performance across all CAV penetration rates and congestion levels. A showcase is presented to show the effect of the system dynamics in active traffic management. The proposed model could serve as the foundation of CAV based traffic management applications, such as variable speed limit and speed harmonization.
... e purpose of road planning is to solve the driving problem of driverless vehicles on the road. Relevant achievements include lane planning (e.g., Liu and Song [8] and and Xia et al. [9]), traffic signal control planning (e.g., Domínguez and Sanguino [10] and Jiang [11]), and speed limit planning (e.g., Tajalli and Hajbabaie [12] and Liu et al. [13]). e purpose of parking planning is to solve the parking problem of driverless vehicles, and relevant achievements include parking lot design (e.g., Nourinejad et al. [14] and Estepa et al. [15]) and parking lot management (e.g., Yamashita and Takami [16] and Wang et al. [17]). ...
... Let the supply-demand deviation Z(k) � D(k) − S(k), we can obtain the following equation according to formulas (12) and (13). ...
To study the guidance method of driverless travel mode choice from the perspective of traffic supply-demand, we assume that all vehicles are driverless and establish a multimodal travel market model to depict the supply-demand relationship of multimodal driverless transportation network. To regulate the disequilibrium multimodal travel market, an optimal price regulation law is proposed, which aims to minimize the supply-demand deviation and the amplitude of price regulation. Then, the existence, uniqueness, and stability of the optimal price regulation law are confirmed. In the calculation process of a numerical example, the travel prices of driverless car and driverless subway are realized by congestion fee and subway fare, respectively. The results indicate that the optimal price regulation law can reduce the supply-demand deviation of the multimodal travel market and guide travelers to choose a reasonable travel mode to travel in the driverless transportation network.
... Distributed optimization has been widely applied to a wide application scenario, especially for large-scale networks [1][2][3][4][5][6]. Estrin et al. [7] showed that distributed optimization offers greater robustness and scalability advantages compared to centralized ones. ...
With the rise in computational complexity and network scale, distributed optimization problems have gained increasing interest due to their robustness and scalability advantages over centralized approaches. It has been widely applied in various scenarios. However, privacy concerns can deter participants from sharing their sensitive data in such networks. To address this issue, we introduce methods to preserve privacy in distributed optimization problems, particularly over unbalanced directed communication networks, in this chapter. Two algorithms, namely, PP-DOAGT and SD-Push-Pull, are introduced in detail to balance the tradeoff between performance and privacy. PP-DOAGT ensures privacy over infinite iterations and highlights two fundamental impossibility results concerning privacy and performance. Due to the second dilemma, the tradeoff between ε-DP and performance analysis is studied under summable stepsize sequences in PP-DOAGT. In contrast, SD-Push-Pull focuses on guaranteeing privacy over finite iterations. Through state decomposition, this algorithm attains linear convergence with an unchanged stepsize, approaching neighborhood of optimum under certain conditions. With the proposed methods, privacy can be guaranteed in real application scenarios such as machine learning, allowing participants to confidently share their data within distributed optimization frameworks.
... Problem (P1) represents a generalized DER control problem formulation, containing coupled objective functions and constraints (e.g., (9)-(12) and (4), (6)), and separable objective functions and constraints (e.g., (13), (14), and (7)). Additionally, it has also been broadly applied in other industrial cyber-physical system applications, such as rate control in communication networks [107], coordination of connected and autonomous vehicles [108], path tracking of unmanned aerial vehicles [109], control of nonlinear systems [110], and congestion management in transportation systems [111]. ...
Distributed energy resources (DERs) are gaining prominence due to their advantages in improving energy efficiency, reducing carbon emissions, and enhancing grid resilience. Despite the increasing deployment, the potential of DERs has yet to be fully explored and exploited. A fundamental question restrains the management of numerous DERs in large-scale power systems, "How should DER data be securely processed and DER operations be efficiently optimized?" To address this question, this paper considers two critical issues, namely privacy for processing DER data and scalability in optimizing DER operations, then surveys existing and emerging solutions from a multi-agent framework perspective. In the context of scalability, this paper reviews state-of-the-art research that relies on parallel control, optimization, and learning within distributed and/or decentralized information exchange structures, while in the context of privacy, it identifies privacy preservation measures that can be synthesized into the aforementioned scalable structures. Despite research advances in these areas, challenges remain because these highly interdisciplinary studies blend a wide variety of scalable computing architectures and privacy preservation techniques from different fields, making them difficult to adapt in practice. To mitigate this issue, this paper provides a holistic review of trending strategies that orchestrate privacy and scalability for large-scale power system operations from a multi-agent perspective, particularly for DER control problems. Furthermore, this review extrapolates new approaches for future scalable, privacy-aware, and cybersecure pathways to unlock the full potential of DERs through controlling, optimizing, and learning generic multi-agent-based cyber-physical systems.
... Such a distributed paradigm facilitates breaking large-scale problems into sequences of smaller ones. That is why it has been widely adopted in several applications, such as power grids [1], sensor networks [2] and vehicular networks [3]. ...
This paper addresses the problem of distributed optimization, where a network of agents represented as a directed graph (digraph) aims to collaboratively minimize the sum of their individual cost functions. Existing approaches for distributed optimization over digraphs, such as Push-Pull, require agents to exchange explicit state values with their neighbors in order to reach an optimal solution. However, this can result in the disclosure of sensitive and private information. To overcome this issue, we propose a state-decomposition-based privacy-preserving finite-time push-sum (PrFTPS) algorithm without any global information such as network size or graph diameter. Then, based on PrFTPS, we design a gradient descent algorithm (PrFTPS-GD) to solve the distributed optimization problem. It is proved that under PrFTPS-GD, the privacy of each agent is preserved and the linear convergence rate related to the optimization iteration number is achieved. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed approach.
... In recent decades, the issue of distributed controlling of the Multi-Agent Systems (MAS) has received more attention due to their useful potential and theatrical tasks. MAS can be used in many applications such as distributed sensor networks (Meesookho et al., 2002), autonomous vehicles (Di Vaio et al., 2019;Ilie et al., 2020;Tajalli & Hajbabaie, 2018), and power grids (Fishov et al., 2015;Hommelberg et al., 2007;Pipattanasomporn et al., 2009). In many practical applications, the number of agents can grow vastly; this yields computational load and massive communication in the system. ...
This paper addresses distributed nonlinear model predictive controller design for formation control of agents with fractional-order dynamics (DNMPC-FCFO) in the presence of obstacles. By introducing new constraints, the collisions between non-neighboring agents are avoided while there is no need to use the information of non-neighboring agents. Moreover, by applying contractive constraints in our optimization problem the Lyapunov stability is guaranteed. Since in parallel DMPC method contraction occurred only on first two steps, the use of terminal components that are essential parts of conventional MPC to create stability is eliminated. These components usually complicate the design and are often used for low-end systems. Using fractional-order equations often leads to mathematical models capable of better describing experimental behavior, but due to memory effects, the controller design is usually more complex. The mathematical stability proof is provided in this regard. In the proposed scheme, considering limited communication range in mobile robots, the controller is designed to preserve the network connectivity. Simulation results show the effectiveness of the proposed method.
... The purpose of coordinated control of urban traffic is to ensure traffic safety. Due to the continuous development and progress of the times, various contradictions in urban transportation are emerging one after another, people's living standards are constantly improving, and the requirements for transportation are getting higher and higher (Mohebifard and Hajbabaie, 2018). This will enable researchers to apply new scientific and technological achievements to the traffic control system, thereby accelerating the development of coordinated control for urban traffic and promoting traffic intelligence. ...
... The purpose of coordinated control of urban traffic is to ensure traffic safety. Due to the continuous development and progress of the times, various contradictions in urban transportation are emerging one after another, people's living standards are constantly improving, and the requirements for transportation are getting higher and higher (Mohebifard and Hajbabaie, 2018). This will enable researchers to apply new scientific and technological achievements to the traffic control system, thereby accelerating the development of coordinated control for urban traffic and promoting traffic intelligence. ...
... The entering vehicle does not require a complete stop to wait for the green light. As a result, traffic delays are reduced, and traffic capacity is improved [4], [5]. Therefore, connected and automated driving techniques are a favorable vantage point for addressing the issue of traffic congestion and conflict at This work was supported in part by the A*STAR Grant (No.1922500046), and the SUG-NAP Grant (No.M4082268.050) of Nanyang Technological University, Singapore. ...
To address the coordination issue of connected automated vehicles (CAVs) at urban scenarios, a game-theoretic decision-making framework is proposed that can advance social benefits, including the traffic system efficiency and safety, as well as the benefits of individual users. Under the proposed decision-making framework, in this work, a representative urban driving scenario, i.e. the unsignalized intersection, is investigated. Once the vehicle enters the focused zone, it will interact with other CAVs and make collaborative decisions. To evaluate the safety risk of surrounding vehicles and reduce the complexity of the decision-making algorithm, the driving risk assessment algorithm is designed with a Gaussian potential field approach. The decision-making cost function is constructed by considering the driving safety and passing efficiency of CAVs. Additionally, decision-making constraints are designed and include safety, comfort, efficiency, control and stability. Based on the cost function and constraints, the fuzzy coalitional game approach is applied to the decision-making issue of CAVs at unsignalized intersections. Two types of fuzzy coalitions are constructed that reflect both individual and social benefits. The benefit allocation in the two types of fuzzy coalitions is associated with the driving aggressiveness of CAVs. Finally, the effectiveness and feasibility of the proposed decision-making framework are verified with three test cases.
... Regional partitioning is used in [7] for static traffic assignment and in [43] for SODTA with route and departure time variables. More general regional partitioning examples can be found in [44]- [46]. The boundary of each intersection should be selected such that each intersection (subproblem) has more or less the same number of decision variables to balance out the run time and reduce overhead delays. ...
This study presents a distributed gradient-based approach to solve system optimal dynamic traffic assignment (SODTA) formulated based on the cell transmission model. The algorithm distributes SODTA into local sub-problems, who find optimal values for their decision variables within an intersection. Each sub-problem communicates with its immediate neighbors to reach a consensus on the values of common decision variables. A sub-problem receives proposed values for common decision variables from all adjacent sub-problems and incorporates them into its own offered values by weighted averaging and enforcing a gradient step to minimize its objective function. Then, the updated values are projected onto the feasible region of the sub-problems. The algorithm finds high quality solutions in all tested scenarios with a finite number of iterations. The algorithm is tested on a case study network under different demand levels and finds solutions with at most a 5% optimality gap.
... A number of studies on speed harmonization with CAVs have been conducted (Ma et al., 2016). In most studies, CAVs are merely information providers for improving traffic state estimation and prediction (Abdelghaffar et al., 2020;Han and Ahn, 2018a, b;Learn et al., 2017;Li et al., 2019;Tajalli and Hajbabaie, 2018;Talebpour et al., 2013;Wang et al., 2016). Only few studies actually take advantage of the proactive control of CAVs. ...
... The occupied length is found by multiplying the average vehicle length L m by the difference of the number of vehicles x t,m i in cell i ∈ C n and the total number of vehicles j ∈(i) y t,m i j exited that cell towards cell j ∈ (i ) at time step t ∈ T . Constraints (11) show this concept. ...
Existing multi-class cell transmission model (CTM) based methodologies for signal timing or traffic assignment may transfer prioritized transit vehicles from one cell to the next one before processing their preceding passenger cars. In addition, existing CTM-based methodologies process a proportion of a slow-moving transit vehicle in each time step. As such a portion of each transit vehicle remains in each cell and it never clears them. This paper presents constraints to project the position of transit vehicles based on the speed and cell occupancy variations between different classes of vehicles and incorporates them into the CTM. The resulting optimization program is a mixed-integer nonlinear problem. We used a distributed receding horizon control framework to solve it in real-time. The proposed formulation is executed in a simulated arterial street with four signalized intersections in Springfield, IL with different traffic volume levels and transit vehicle frequencies. The results showed that the proposed algorithm addressed the mentioned issues of the existing multi-class CTM, and yielded more efficient network performance than the conventional transit signal priority-based (CTSP) systems. The proposed formulation reduced average bus delay by 1% to 70% and car delay by 52% to 76% compared to CTSP.
... Compared with centralized ones, distributed algorithms allow more flexibility and scalability due to its capability of breaking large-scale problems into sequences of smaller ones. In view of this, distributed algorithms are inherently robust to environment uncertainties and communication failures and are widely adopted in power grids [1], sensor networks [2] and vehicular networks [3]. ...
In this paper, we study the problem of consensus-based distributed optimization where a network of agents, abstracted as a directed graph, aims to minimize the sum of all agents' cost functions collaboratively. In existing distributed optimization approaches (Push-Pull/AB) for directed graphs, all agents exchange their states with neighbors to achieve the optimal solution with a constant stepsize, which may lead to the disclosure of sensitive and private information. For privacy preservation, we propose a novel state-decomposition based gradient tracking approach (SD-Push-Pull) for distributed optimzation over directed networks that preserves differential privacy, which is a strong notion that protects agents' privacy against an adversary with arbitrary auxiliary information. The main idea of the proposed approach is to decompose the gradient state of each agent into two sub-states. Only one substate is exchanged by the agent with its neighbours over time, and the other one is kept private. That is to say, only one substate is visible to an adversary, protecting the privacy from being leaked. It is proved that under certain decomposition principles, a bound for the sub-optimality of the proposed algorithm can be derived and the differential privacy is achieved simultaneously. Moreover, the trade-off between differential privacy and the optimization accuracy is also characterized. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed approach.
... ADMM is based on the classical Lagrangian decomposition approach (Fisher, 1985;Hajibabai & Ouyang, 2013) with improved convergence properties (Boyd et al., 2011) and the added possibility of utilizing distributed optimization techniques (Islam & Hajbabaie, 2017;Mohebifard & Hajbabaie, 2019b). In ADMM, a complicating constraint whose relaxation allows decomposing the problem into easier sub-problems is identified and penalized in the objective function with a penalty parameter > 0. This modification regularizes the errors of solving the sub-problems iteratively and hence results in faster convergence rates (Boyd et al., 2011). ...
This paper presents a methodology to control the trajectory of cooperative connected automated vehicles (CAVs) at roundabouts with a mixed fleet of CAVs and human-driven vehicles (HVs). We formulate an optimization program in a two-dimensional space for this purpose. A model predictive control-based solution technique is developed to optimize the trajectories of CAVs at discretized time steps based on the estimated driving behavior of HVs, while the actual behavior of HVs is controlled by a microscopic traffic simulator. At each time step, the location and speed of vehicles are collected, and a decomposition-based methodology optimizes CAV trajectories for a few time steps ahead of the system time. The optimization methodology has convexification, alternating direction method of multipliers, and cutting plane decomposition components to tackle the complexities of the problem. We tested the solution technique in a case study roundabout with different traffic demand flow rates and CAV market penetration rates. The results showed that increasing the CAV market penetration rate from 20% to 100% reduced total travel times by 2.8% to 35.8%. The analyses indicate that the presence of cooperative CAVs in roundabouts can lead to considerable improvements.
... To improve the computation efficiency, Tajalli and Hajbabaie [18] decomposed AV-based network-level speed optimization problem into several sub-problems and developed a distributed algorithm for parallel computing. ...
This paper studies an optimal dynamic lane reversal and traffic control (DLRTC) strategy in the presence of autonomous vehicles (AVs). A centralized controller is set to change lane directions dynamically and regulate traffic flow on a motorway network. Through vehicle to infrastructure (V2I) communication, the roadside sensors can send lane reversal information and flow control actions to the AVs which can perform lane-changing behaviors and adjust travel speed. To model the traffic dynamics under DLRTC, we propose a novel multi-lane cell transmission model (CTM). A logit model is used to characterize the lane-changing behaviors under uncontrolled cases. A mixed integer linear programming model (MILP) is formulated for DLRTC, and optimal control actions are implemented in a framework of model predictive control (MPC). The numerical experiments based on the Ayer Rajah Expressway (AYE) in Singapore are conducted to demonstrate the effectiveness of the proposed methods. The results show that the DLRTC strategy can effectively reduce road congestion and achieve better system performance compared to the benchmark method.
... Then, the centralized controller guides the vehicle to pass through the intersection according to an optimized passing sequence [12]. In [13], a distributed coordination algorithm is developed for dynamic speed optimization of CAVs in the urban street networks for improving the efficiency of network operations. However, the turning behavior of CAV is not considered in the traffic networks. ...
To improve the safety and efficiency of the intelligent transportation system, particularly in complex urban scenarios, in this paper a game theoretic decision-making framework is designed for connected automated vehicles (CAVs) at unsignalized roundabouts considering their personalized driving behaviours. Within the decision-making framework, a motion prediction module is designed and optimized using model predictive control (MPC) to enhance the effectiveness and accuracy of the decision-making algorithm. Besides, the payoff function of decision making is defined with the consideration of vehicle safety, ride comfort and travel efficiency. Additionally, the constraints of the decision-making problem are constructed. Based on the established decision-making model, Stackelberg game and grand coalition game approaches are adopted to address the decision making of CAVs at an unsignalized roundabout. Three testing cases considering personalized driving behaviours are carried out to verify the performance of the developed decision-making algorithms. The testing results show that the proposed game theoretic decision-making framework is able to make safe and reasonable decisions for CAVs in the complex urban scenarios, validating its feasibility and effectiveness. Stackelberg game approach shows its advantage in guaranteeing personalized driving objectives of individuals, while the grand coalition game approach is advantageous regarding the efficiency improvement of the transportation system.
... e realization of spatiotemporal trajectory optimization mainly includes two parts: (1) realizing the dynamic speed control of multiple vehicles in the longitudinal direction; (2) achieving the cooperative lane-changing control of multiple vehicles in the horizontal direction. In the intelligent traffic system (ITS) strategic plan published by the US Department of Transportation in 2010, dynamic speed coordination based on spatiotemporal trajectory was denoted as one of the important methods for traffic flow optimization of road network [3]. Grumert and Tapani [4] established a variable speed limit (VSL) algorithm based on the traffic occupancy. ...
It is agreed that connected vehicle technologies have broad implications to traffic management systems. In order to alleviate urban congestion and improve road capacity, this paper proposes a multilane spatiotemporal trajectory optimization method (MSTTOM) to reach full potential of connected vehicles by considering vehicular safety, traffic capacity, fuel efficiency, and driver comfort. In this MSTTOM, the dynamic characteristics of connected vehicles, the vehicular state vector, the optimized objective function, and the constraints are formulated. The method for solving the trajectory problem is optimized based on Pontryagin’s maximum principle and reinforcement learning (RL). A typical scenario of intersection with a one-way 4-lane section is measured, and the data within 24 hours are collected for tests. The results demonstrate that the proposed method can optimize the traffic flow by enhancing vehicle fuel efficiency by 32% and reducing pollutants emissions by 17% compared with the advanced glidepath prototype application (GPPA) scheme.
... e underlying concept of most hierarchical approaches is to make network level decisions at the upper (or central) level and the real-time, small-area computations in the lower (or intersection) level. e exchange of information is a crucial aspect [13][14][15][16][17]. ...
This paper suggests the adoption of a spatial decomposition method to solve the signal synchronization problem. A good signal setting maximizes the number of vehicles passing through intersections, while minimizing gas emissions and possible delays experienced by drivers. The signals synchronization issue can be defined as the problem of finding the offsets, the green timings, and the cycle length for a series of controlled intersections, minimizing the total delay of the network subject to admissibility constraints. In this paper, the authors optimized the signal setting through a new Surrogate Method calculating the objective function via the CTMUT model while performing a simulation. A spatial decomposition approach is here suggested with a simultaneous analysis of different levels of cooperation among subnetworks. This study tries to identify a subnetwork that might be representative of the entire network while taking into consideration two factors: efficiency and efficacy. A comparison between centralized and decentralized control is performed.
... The problem of interfacing and coordinating arterial intersections and freeways (through the control of freeway ramp operations) is an issue serious enough without the complexity that is brought by the AGI operations. Several studies have addressed similar issues and proposed how RM should be set to avoid adverse feedback between arterials and freeways and vice versa [12,18,29]. When AGI is added to this complex interaction, the problem becomes even tougher to resolve. ...
Traffic congestion is a global problem that cannot be solved by continuing to add new roads and extra capacity, which is accentuated in the areas where roads of unlimited-access (e.g. arterial streets) interface those of limited-access (e.g. freeways). Many researchers have addressed this problem but we present here a novel method to utilize a fuzzy logic model to reduce traffic congestion in such interfacing areas during saturated traffic conditions. More specifically this paper presents a control method for a complex traffic control system: Diverging Diamond Interchange (DDI) - Ramp Metering (RM), under oversaturated traffic conditions. The DDI is a relatively new concept of an alternative intersection geometry where two intersections serve left-turn movements without conflicts. However, such DDI left-turn movements, along with the right-turn movements from the opposite direction, put additional ‘pressure’ on the on-ramp of the freeways or multilane highways that intersect with DDIs. If freeway operations are saturated or near saturation, which may be the result of RM operations, this type of traffic control system can lead to a fully jammed condition with a potential spillback. The purpose of the proposed fuzzy-logic control is to prevent such a queue spillback from the metering ramp to the DDI. After presenting the fuzzy-logic control (FLC) model, we compare it to the conventional fixed time control (FTC) to evaluate potential benefits. To assess the quality of proposed analytical solutions in the real-traffic-like environment we evaluated the two logics in a VISSIM microsimulation model. The results show that, when compared to FTC, the FLC method improves traffic conditions moderately but in the oversaturated environment where there is very little room for improvement.
... Distributed algorithms are suitable to solve complex traffic control problems that have a large number of decision variables (Wongpiromsarn et al., 2014;Timotheou, Panayiotou and Polycarpou, 2015;Tajalli and Hajbabaie, 2018;Mirheli et al., 2019;Mohebifard and Hajbabaie, 2019a). The algorithm solves the distributed mathematical program at each intersection controller over a prediction horizon. ...
This paper presents two algorithms to estimate traffic state in urban street networks with a mixed traffic stream of connected and unconnected vehicles and incorporates them in a real-time and distributed traffic signal control methodology. The first algorithm integrates connected vehicles (CV) and loop detector data to estimate the trajectory of unconnected vehicles based on car-following concepts. The second algorithm converts the temporal point vehicle detections to a spatial vehicle distribution on a link. The signal control methodology utilizes either algorithm to estimate traffic state on all network links at a time, optimizes the signal timing parameters over a prediction period constituting several time steps, implements the optimal decisions in the next time step, and continues this process until the end of the study period. We applied the methodology to a real-world case study network simulated in Vissim. The results show that both algorithms are effective under a wide range of CV market penetration rates in all tested demand patterns: at 0% market penetration rate, the proposed methodology reduced travel time by 2% to 10% and average delay by 7% to 20% compared to the existing signal timing parameters and traffic demand. At a 40% penetration rate, the proposed algorithms reduced travel time by 27% to 33% and average delay by 50% to 61% compared to the existing signal and demand pattern in the case study network. Similar trends were found for all other demand patterns tested in this study.
... We linearize the non-linear terms in the formulation similar to our previous work [34]- [38]. In addition, we use a receding horizon control, similar to our previous work in [39]- [42], to reduce the complexity of the problem and capture the dynamic nature of the signal and trajectory optimization by repeatedly solving the problem over a planning horizon ̂, which is shorter than the study period . ...
This study investigates the effects of the "white phase" on the performance of isolated signalized intersections. During the white phase, connected automated vehicles (CAV) control traffic flow through an intersection, and connected human-driven vehicles (CHV) follow their front vehicle (either CAV or CHV). The traffic controller ensures collision-free movement of vehicles through the intersection by determining 1) the sequence and duration of phases (green and white) and 2) trajectory of CAVs during white phases. White phases can be assigned to conflicting movements simultaneously. We have formulated this problem as a mixed-integer non-linear program (MINLP) and solved it using a receding horizon algorithm. Two demand patterns with five different CAV market penetration rates are used to evaluate the effects of the white phase on mobility and safety in an isolated intersection. Each case study is tested with three different control scenarios: 1) No-white-phase, 2) white-phase-only, and 3) optimal-white-phase activation (combination of white, green, and red phases). The results indicate that the white phase yields significant improvement in intersection performance while maintaining the same safety level.
... The characteristics of heterogeneous traffic flow significantly differ with the original traffic flow; many studies have carried out in heterogeneous traffic flow. The research includes road capacity [26][27][28][29], traffic safety [30][31][32][33], control optimization [34][35][36], and stability analysis [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. This study focuses on the stability analysis of heterogeneous traffic flow. ...
With the development of connected automated vehicles (CAVs) technologies, traffic flow on the road is converting into the heterogeneous traffic flow, which consists of CAVs and human-driven vehicles (HDVs). Considering the function of CAVs would degrade when following HDVs in heterogeneous traffic flow. Moreover, the reaction time of degraded CAVs would be different with CAVs or HDVs. This paper deduces and analyzes the linear stability of such heterogeneous traffic flow based on CAVs degradations and reaction time diversity. Firstly, considering the degradations of CAVs, the vehicle types and their ratios in heterogeneous traffic flow are analyzed. Secondly, the car-following model and the reaction time of three types of vehicles are discussed. Then, the linear stability condition of heterogeneous traffic flow is proposed. Finally, the impact factors on the stability condition are illustrated through numerical analysis. The results show that the high penetration rate of CAVs and the short reaction time can improve the linear stability of heterogeneous traffic flow. Besides, when the penetration rate of CAVs increases to 65%, the stability of heterogeneous traffic flow is not affected by speed. Furthermore, the analysis shows that CAVs degradations also has a negative effect on linear stability.
... In recent years, distributed cooperative optimization over networks has attracted extensive attentions, such as the economic dispatch in power grids [1,2], the traffic flow control in intelligent transportation networks [3,4], and the cooperative source localization by sensor networks [5,6], et al. For these networked systems, each node is a local optimizer with certain capabilities of data collection, storage, calculation and communication. ...
We study distributed stochastic optimization by networked nodes to cooperatively minimize a sum of convex cost functions. The network is modeled by a sequence of time-varying random digraphs with each node representing a local optimizer and each edge representing a communication link. We consider the distributed subgradient optimization algorithm with noisy measurements of local cost functions' subgradients, additive and multiplicative noises among information exchanging between each pair of nodes. By stochastic Lyapunov method, convex analysis, algebraic graph theory and martingale convergence theory, it is proved that if the local subgradient functions grow linearly and the sequence of digraphs is conditionally balanced and uniformly conditionally jointly connected, then proper algorithm step sizes can be designed so that all nodes' states converge to the global optimal solution almost surely.
Macroscopic link-based flow models are efficient for simulating flow propagation in urban road networks. Existing link-based flow models described traffic states of a link with two state variables of link inflow and outflow and assumed homogeneous traffic states within a whole link. Consequently, the turn-level queue length change within the link cannot be captured accurately, resulting in underrepresented queue spillback. Moreover, a constant link free-flow speed was assumed to formulate models, restricting their applicability in modeling phenomena involving time-varying free-flow speed. This study proposed a new link-based flow model by introducing an additional state variable of link queue inflow and adapting the link outflow to be free-flow speed-dependent. In our model, the vehicle propagation within each link is described by the link inflow, queue inflow, and outflow, which depends on the link free-flow speed changes and signal control. A node model is further defined to capture the presence of potential queue spillback, which estimates the constrained flow propagation between adjacent road segments. Simulation experiments were conducted on a single intersection and on networks to verify the proposed model performance. Results demonstrate the predictive power of the proposed model in simulating traffic proppagations for networks with multiple turning movements and time-varying free-flow speed. Our model outperforms the baseline link-based flow model while preserving the computational tractability property of link-based flow models.
This study introduces a distributed methodology for system optimal dynamic traffic assignment formulated using the cell transmission model (CTM). Using CTM increases the methodology’s accuracy in predicting link flows and its dynamics; however, it increases the computational complexity significantly. Our methodology is specifically designed to address this challenge and provide a balance between the quality of the solution and computational complexity while ensuring first-in-first-out (FIFO) queuing discipline. The methodology follows a receding horizon framework and distributes the network-level traffic assignment into several intersection-level sub-problems and solves them in parallel. Therefore, this heuristic significantly reduces the computational complexity and finds solutions in real-time. The distribution is achieved by relaxing coupling constraints among different sub-problems. The sub-problems coordinate their decisions with each other by sharing information and implementing it in the re-introduced constraints that were previously relaxed. This process was used to avoid infeasible solutions, reduce the likelihood of finding local solutions, and promote system-level optimality. The information that needs to be exchanged is estimated using CTM simulation runs. All optimal sub-problem solutions are implemented in network-level CTM simulations, and cell occupancies and flows are obtained. The FIFO discipline is also approximated in CTM. We have tested the methodology in networks of 20 and 40 intersections with 15 and 25 origin-destination pairs, respectively, under various demand levels, and compared the performance with a benchmark approach capable of finding the optimal solutions. The maximum observed optimality gap in case studies with 20 and 40 intersections was 3.1%, and the solutions were found in real-time in all scenarios.
Proper metering can improve traffic operations in congested urban street networks. The available approaches either (a) use macroscopic fundamental diagrams to model traffic dynamics or (b) use numerical time–space discretization of the hydrodynamic traffic flow model with high computational requirements. Therefore, they either (a) do not represent traffic dynamics accurately or (b) are not suitable for online applications. This study introduces a deep reinforcement learning (DRL) methodology to capture traffic dynamics on a micro-level scale with the capability of capturing detailed traffic dynamics with low computational time. The DRL methodology employs two neural networks that map the location of connected vehicles in a network to traffic metering signal indications and estimate the objective function of the traffic metering problem. The outputs of the neural networks are used to construct a loss function, whose optimization provides the optimal parameters for the neural networks. Because of the complexity of the loss function, the gradient descent optimization technique with Monte Carlo simulation is used to optimize the loss function. The proposed methodology was tested on a simulated case study network in Vissim software with 20 intersections. The numerical results showed that the methodology increased throughput by 41.2% and 21.3% and reduced the total travel time of vehicles by 3.4% and 15.5% compared to a no-metering strategy. Comparing the computational time of the proposed methodology with one of the existing traffic metering approaches also showed the potential of the methodology for online applications.
This paper studies the optimization problem of heterogeneous networks under a time-varying topology. Each agent only accesses to one local objective function, which is nonsmooth. An improved algorithm with noisy measurement of local objective functions’ sub-gradients and additive noises among information exchanging between each pair of agents is designed to minimize the sum of objective functions of all agents. To weaken the effect of these noises, two step sizes are introduced in the control protocol. By graph theory, stochastic analysis and martingale convergence theory, it is proved that if the sub-gradients are uniformly bounded, the sequence of digraphs is balanced and the union graph of all digraphs is joint strongly connected, then the designed control protocol can force all agents to find the global optimal point almost surely. At last, the authors give some numerical examples to verify the effectiveness of the stochastic sub-gradient algorithms.
This paper formulates a cooperative traffic control methodology that integrates traffic signal timing and ramp metering decisions into an optimization model to improve traffic operations in a corridor network. A mixed integer linear model is formulated and is solved in real time within a model predictive controller framework, where the cell transmission model is used as the system state predictor. The methodology is benchmarked in a case study corridor in San Mateo, CA, in VISSIM with two optimization scenarios, namely, optimal metering and optimal signal control, and two simulation scenarios with a preset metering plan and no metering. The numerical results show that integrated traffic signal and ramp metering control reduces delays, stops, and travel times of the corridor by up to 33.1%, 36%, and 16.4%, respectively, compared to existing benchmark conditions. With appropriate weights prioritizing freeway or arterial street operations, the integrated control balances traffic congestion between the arterial street and the freeway.
In recent years, there has been a growing interest in distributed optimization, which collaboratively attains an optimum by exchanging information with neighbours. Among the various distributed algorithms available, optimization with gradient tracking is particularly notable for its superior convergence results, especially in the context of directed graphs. However, privacy concerns arise when gradient information is transmitted directly which would induce more information leakage. Surprisingly, the literature has not adequately addressed the associated privacy issues. In response to the gap, our paper proposes a privacy-preserving distributed optimization algorithm with gradient tracking by adding noises to transmitted messages, namely, the decision variables and the estimate of the aggregated gradient. We prove two dilemmas for this kind of algorithm. In the first dilemma, we reveal that this distributed optimization algorithm with gradient tracking cannot achieve
-differential privacy (DP) and exact convergence simultaneously. Building on this, we subsequently highlight that the algorithm fails to achieve
-DP when employing non-summable stepsizes in the presence of Laplace noises. It is crucial to emphasize that these findings hold true regardless of the size of the privacy metric
. After that, we rigorously analyse the convergence performance and privacy level given summable stepsize sequences under Laplace distribution since it is only with summable stepsizes that is meaningful for us to study. We derive sufficient conditions that allow for the simultaneous stochastically bounded accuracy and
-DP. Recognizing that several options can meet these conditions, we further derive an upper bound of the mean error's variance and specify the mathematical expression of
under such conditions. Numerical simulations are provided to demonstrate the effectiveness of our proposed algorithm.
This paper addresses the problem of distributed optimization, where a network of agents represented as a directed graph (digraph) aims to collaboratively minimize the sum of their individual cost functions. Existing approaches for distributed optimization over digraphs, such as Push-Pull, require agents to exchange explicit state values with their neighbors in order to reach an optimal solution. However, this can result in the disclosure of sensitive and private information. To overcome this issue, we propose a state-decomposition-based privacy-preserving finite-time push-sum (PrFTPS) algorithm without any global information, such as network size or graph diameter. Then, based on PrFTPS, we design a gradient descent algorithm (PrFTPS-GD) to solve the distributed optimization problem. It is proved that under PrFTPS-GD, the privacy of each agent is preserved and the linear convergence rate related to the optimization iteration number is achieved. Finally, numerical simulations are provided to illustrate the effectiveness of the proposed approach.
In this paper, we study the problem of consensus-based distributed optimization, where a network of agents, abstracted as a directed graph, aims to minimize the sum of all agents' cost functions collaboratively. In existing distributed optimization approaches (Push-Pull/AB) for directed graphs, all agents exchange their states with neighbors to achieve the optimal solution with a constant stepsize, which may lead to the disclosure of sensitive and private information. For privacy preservation, we propose a novel state-decomposition based gradient tracking approach (SD-Push-Pull) for distributed optimization over directed networks that preserves differential privacy, which is a strong notion that protects agents' privacy against an adversary with arbitrary auxiliary information. The main idea of the proposed approach is to decompose the gradient state of each agent into two sub-states. Only one substate is exchanged by the agent with its neighbours over time, and the other one is not shared. That is to say, only one substate is visible to an adversary, protecting the sensitive information from being leaked. It is proved that under certain decomposition principles, a bound for the sub-optimality of the proposed algorithm can be derived and the differential privacy is achieved simultaneously. Moreover, the trade-off between differential privacy and the optimization accuracy is also characterized. Finally, a numerical simulation is provided to illustrate the effectiveness of the proposed approach.
This paper studies a novel distributed optimization problem that aims to minimize the sum of the non-convex objective functionals of the multi-agent network under privacy protection, which means that the local objective of each agent is unknown to others. The above problem involves complexity simultaneously in the time and space aspects. Yet existing works about distributed optimization mainly consider privacy protection in the space aspect where the decision variable is a vector with finite dimensions. In contrast, when the time aspect is considered in this paper, the decision variable is a continuous function concerning time. Hence, the minimization of the overall functional belongs to the calculus of variations. Traditional works usually aim to seek the optimal decision function. Due to privacy protection and non-convexity, the Euler-Lagrange equation of the proposed problem is a complicated partial differential equation. Hence, we seek the optimal decision derivative function rather than the decision function. This manner can be regarded as seeking the control input for an optimal control problem, for which we propose a centralized reinforcement learning (RL) framework. In the space aspect, we further present a distributed reinforcement learning framework to deal with the impact of privacy protection. Finally, rigorous theoretical analysis and simulation validate the effectiveness of our framework.
This paper presents robust cooperative tracking control in camera sensor networks. We consider a camera sensor network with a Pan-Tilt (PT) mechanism whose dynamics is expressed as the Euler–Lagrange equation. We propose a distributed control law based on sliding mode control to achieve cooperative target tracking. The stability of the closed-loop system is conducted by Lyapunov's stability theory considering discontinuities of the control input. We also verify the effectiveness of the proposed method with a numerical example of synchronization of a PT camera sensor network under external disturbance.
This study presents a distributed gradient-based approach to solve system optimal dynamic traffic assignment (SODTA) formulated based on the cell transmission model. The algorithm distributes SODTA into local sub-problems, who find optimal values for their decision variables within an intersection. Each sub-problem communicates with its immediate neighbors to reach a consensus on the values of common decision variables. A sub-problem receives proposed values for common decision variables from all adjacent sub-problems and incorporates them into its own offered values by weighted averaging and enforcing a gradient step to minimize its objective function. Then, the updated values are projected onto the feasible region of the sub-problems. The algorithm finds high quality solutions in all tested scenarios with a finite number of iterations. The algorithm is tested on a case study network under different demand levels and finds solutions with at most a 5% optimality gap.
In order to solve the problem of traffic congestion and emission optimization of urban multi-class expressways, a robust dynamic nondominated sorting multi-objective genetic algorithm DFCM-RDNSGA-III based on density fuzzy c-means clustering method is proposed in this paper. Considering the three performance indicators of travel time, ramp queue and traffic emissions, the ramp metering and variable speed limit control schemes of an expressway are optimized to improve the main road and ramp traffic congestion, therefore achieving energy conservation and emission reduction. In the VISSIM simulation environment, a multi-on-ramp and multi-off-ramp road network is built to verify the performance of the algorithm. The results show that, compared with the existing algorithm NSGA-III, the DFCM-RDNSGA-III algorithm proposed in this paper can provide better ramp metering and variable speed limit control schemes in the process of road network peak formation and dissipation. In addition, the traffic congestion of expressways can be improved and energy conservation as well as emission reduction can also be realized.
This paper introduces a methodology to optimize the trajectory of connected automated vehicles (CAVs) in roundabouts using a two-dimensional point-mass model. We formulate an optimization problem that includes vehicle dynamics and collision-avoidance constraints with explicit representation of vehicle paths. The objective function of the problem minimizes the distance of CAVs to their destinations and their acceleration magnitudes. The methodology also involves a customized solution technique that convexifies the collision-avoidance constraints and employs the alternating direction method of multipliers to decompose the convexified problem into two sub-problems. The first sub-problem only includes vehicle dynamics constraints while the second sub-problem projects the solutions of the first sub-problem onto a collision-free region. The first sub-problem is then transformed into a quadratic problem by redefining its decision variables along vehicle paths. The transformation allows solving this sub-problem with several vehicle-level problems in a distributed architecture. Moreover, we show that iterating between the two sub-problems leads to convergence to the optimal solutions of the convexified problem. The methodology is applied to a case study roundabout with different demand levels. The results show that the trajectory optimization reduced the total travel times and average delays respectively by 9.1% to 36.8% and 95.8% to 98.5% compared to a scenario with human-driven vehicles.
This study introduces a methodology for cooperative signal timing and trajectory optimization at intersections with a mix of connected automated vehicles (CAVs) and human-driven vehicles (HVs). We represent joint signal timing and trajectory control as a mixed-integer non-linear program, which is computationally complex. The developed methodology provides a balance between computational efficiency and solution quality by (a) linearizing the nonlinear constraints and reformulating the problem with a tight convex hull of the mixed-integer solutions and (b) decomposing the intersection-level program into several lane-level programs. Hence, a unique controller jointly optimizes the trajectories of CAVs on a lane and the signal timing parameters associated with that lane. This setting will allow finding near-optimal solutions with small duality gaps for complex intersections with different demand levels. Case study results show that the proposed methodology finds solutions efficiently with at most 0.1% duality gap. We compared the developed methodology with an existing signal timing and trajectory control approach and found 13% to 41% reduction in average travel time and 1% to 31% reduction in fuel consumption under different scenarios.
This study evaluates the effects of various market penetration rates of connected autonomous vehicles (CAV) on traffic operations at roundabouts. We have utilized a simulation-and an optimization-based approach for this purpose. The simulation-based approach included calibrated car following models with different driving behavior parameters for a mixed fleet of conventional vehicles and CAVs with various penetration rates ranging from 0% to 100%. We also used an optimization-based approach for the 100% CAV market penetration rate case to evaluate operations while trajectories of CAVs were optimized by a central controller. The simulation results showed that CAVs improved traffic operations in under-and semi-saturated flow conditions. Nevertheless, the optimization of CAV trajectories resulted in significant delay reductions and improvements in the roundabout performance. These results indicate that CAVs have great potentials for improving traffic operations once an effective control algorithm is available.
In this paper, we develop a model to plan energy-efficient speed trajectories of electric trucks in real-time by taking into account the information of topography and traffic ahead of the vehicle. In this real time control model, a novel state-space model is first developed to capture vehicle speed, acceleration, and state of charge. We then formulate an energy minimization problem and solve it by an alternating direction method of multipliers (ADMM) method that exploits the structure of the problem. A model predictive control framework is then employed to deal with topographic and traffic uncertainties in real-time. An empirical study is conducted on the performance of the proposed eco-driving algorithm and its impact on battery degradation. The experimental results show that the energy consumption by using the developed method is reduced by up to 5.05%, and the battery life extended by as high as 35.35% compared to benchmarking solutions.
Recent studies demonstrated the efficiency of feedback-based gating control in mitigating congestion in urban networks by exploiting the notion of macroscopic or network fundamental diagram (MFD or NFD). The employed feedback regulator of proportional-integral (PI)-type targets an operating NFD point of maximum throughput to enhance the mobility in the urban road network during the peak period, under saturated traffic conditions. In previous studies, gating was applied directly at the border of the protected network (PN), i.e. the network part to be protected from over-saturation. In this work, the recently developed feedback-based gating concept is applied at junctions located further upstream of the PN. This induces a time-delay, which corresponds to the travel time needed for gated vehicles to approach the PN. The resulting extended feedback control problem can be also tackled by use of a PI-type regulator, albeit with different gain values compared to the case without time-delay. Detailed procedures regarding the appropriate design of related feedback regulators are provided. In addition, the developed feedback concept is shown to work properly with very long time-steps as well. A large part of the Chania, Greece, urban network, modelled in a microscopic simulation environment under realistic traffic conditions, is used as test-bed in this study. The reported results demonstrate a stable and efficient behaviour and improved mobility of the overall network in terms of mean speed and travel time.
The objective of this paper is the regulation of freeway traffic by means of optimal control techniques. A first innovative aspect of the proposed approach is the adopted objective function in which, besides the reduction of traffic congestion (which is typically considered in traffic control schemes), the minimization of traffic emissions is also included. Moreover, a multi-class framework is defined in which two classes of vehicles (cars and trucks) are explicitly modelled, and specific control actions for each vehicle class are sought. This results in the formulation of a multi-objective optimal control problem which is described in the paper and for which a specific solution algorithm is developed and used. The algorithm exploits a specific version of the feasible direction algorithm whose effectiveness is demonstrated in the paper by means of simulation results.
Optimal control problems on dynamical systems are concerned with finding a control policy, which minimizes a desired objective, where the objective value depends on the future evolution of the system (the state of the system), which, in turn, depends on the control policy. For systems which contain subsystems that are disjoint across the state variables, distributed optimization techniques exist, which iteratively update subsystems concurrently and then exchange information between subsystems with shared control variables. This article presents a method, based on the asynchronous alternating directions method of multiplier algorithm, which extends these techniques to subsystems with shared control and state variables, while maintaining similar communication structure. The method is used as the basis for splitting network flow control problems into many subnetwork control problems with shared boundary conditions. The decentralized and parallel nature of the method permits high scalability with respect to the size of the network. For highly nonconvex applications, an efficient method, based on adjoint gradient computations, is presented for solving subproblems with shared state. The method is applied to decentralized, coordinated ramp metering and variable speed limit control on a realistic freeway network model using distributed model predictive control.
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.
The operation of traffic signals is currently limited by the data available from traditional point sensors. Point detectors can provide only limited vehicle information at a fixed location. The most advanced adaptive control strategies are often not implemented in the field because of their operational complexity and high-resolution detection requirements. However, a new initiative known as connected vehicles allows the wireless transmission of the positions, headings, and speeds of vehicles for use by the traffic controller. A new traffic control algorithm, the predictive microscopic simulation algorithm, which uses these new, more robust data, was developed. The decentralized, fully adaptive traffic control algorithm uses a rolling-horizon strategy in which the phasing is chosen to optimize an objective function over a 15-s period in the future. The objective function uses either delay only or a combination of delay, stops, and decelerations. To measure the objective function, the algorithm uses a microscopic simulation driven by present vehicle positions, headings, and speeds. The algorithm is relatively simple, does not require point detectors or signal-to-signal communication, and is completely responsive to immediate vehicle demands. To ensure drivers’ privacy, the algorithm does not store individual or aggregate vehicle locations. Results from a simulation showed that the algorithm maintained or improved performance compared with that of a state-of the-practice coordinated actuated timing plan optimized by Synchro at low and midlevel volumes, but that performance worsened under saturated and oversaturated conditions. Testing also showed that the algorithm had improved performance during periods of unexpected high demand and the ability to respond automatically to year-to-year growth without retiming.
J. F. Benders devised a clever approach for exploiting the structure of mathematical programming problems withcomplicating variables (variables which, when temporarily fixed, render the remaining optimization problem considerably more tractable). For the class of problems specifically considered by Benders, fixing the values of the complicating variables reduces the given problem to an ordinary linear program, parameterized, of course, by the value of the complicating variables vector. The algorithm he proposed for finding the optimal value of this vector employs a cutting-plane approach for building up adequate representations of (i) the extremal value of the linear program as a function of the parameterizing vector and (ii) the set of values of the parameterizing vector for which the linear program is feasible. Linear programming duality theory was employed to derive the natural families ofcuts characterizing these representations, and the parameterized linear program itself is used to generate what are usuallydeepest cuts for building up the representations.In this paper, Benders'' approach is generalized to a broader class of programs in which the parametrized subproblem need no longer be a linear program. Nonlinear convex duality theory is employed to derive the natural families of cuts corresponding to those in Benders'' case. The conditions under which such a generalization is possible and appropriate are examined in detail. An illustrative specialization is made to the variable factor programming problem introduced by R. Wilson, where it offers an especially attractive approach. Preliminary computational experience is given.
A nonlinear model-predictive hierarchical control approach is presented for coordinated ramp metering of freeway networks. The utilized hierarchical structure consists of three layers: the estimation/prediction layer, the optimization layer and the direct control layer. The previously designed optimal control tool AMOC (Advanced Motorway Optimal Control) is incorporated in the second layer while the local feedback control strategy ALINEA is used in the third layer. Simulation results are presented for the Amsterdam ring-road. The proposed approach outperforms uncoordinated local ramp metering and its efficiency approaches the one obtained by an optimal open-loop solution. It is demonstrated that metering of all on-ramps, including freeway-to-freeway intersections, with sufficient ramp storage space leads to the optimal utilization of the available infrastructure.
Recently, Daganzo introduced the cell transmission model--a simple approach for modeling highway traffic flow consistent with the hydrodynamic model. In this paper, we use the cell transmission model to formulate the single destination System Optimum Dynamic Traffic Assignment (SO DTA) problem as a Linear Program (LP). We demonstrate that the model can obtain insights into the DTA problem, and we address various related issues, such as the concept of marginal travel time in a dynamic network and system optimum necessary and sufficient conditions. The model is limited to one destination and, although it can account for traffic realities as they are captured by the cell transmission model, it is not presented as an operational model for actual applications. The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA. A numerical example illustrates the simplicity and applicability of the proposed approach.
Recurrent and non-recurrent congestion on freeways may be alleviated if today's `spontaneous' infrastructure utilization is replaced by an orderly, controllable operation via comprehensive application of ramp metering and freeway-to-freeway control, combined with powerful optimal control techniques. This paper first explains why ramp metering can lead to a dramatic amelioration of traffic conditions on freeways. An overview of ramp metering algorithms is provided next, ranging from early fixed-time approaches to traffic-responsive regulators and to modern sophisticated nonlinear optimal control schemes. Finally, a large-scale example demonstrates the high potential of advanced ramp metering approaches.
Dynamic speed harmonization has shown great potential to smoothen the flow of traffic and reduce travel time in urban street networks. The existing methods, while providing great insights, are neither scalable nor real-time. This paper develops Distributed Optimization and Coordination Algorithms (DOCA) for dynamic speed optimization of connected and autonomous vehicles in urban street networks to address this gap. DOCA decomposes the nonlinear network-level speed optimization problem into several sub-network-level nonlinear problems thus, it significantly reduces the problem complexity and ensures scalability and real-time runtime constraints. DOCA creates effective coordination in decision making between each two sub-network-level nonlinear problems to push solutions towards optimality and guarantee attaining near-optimal solutions. DOCA is incorporated into a model predictive control approach to allow for additional consensus between sub-network-level problems and reduce the computational complexity further. We applied the proposed solution technique to a real-world network in downtown Springfield, Illinois and observed that it was scalable and real-time while finding solutions that were at most 2.7% different from the optimal solution of the problem. We found significant improvements in network operations and considerable reductions in speed variance as a result of dynamic speed harmonization. 2
Traffic metering offers great potential to reduce congestion and enhance network performance in oversaturated urban street networks. This paper presents an optimization program for dynamic traffic metering in urban street networks based on the Cell Transmission Model (CTM). We have formulated the problem as a Mixed-Integer Linear Program (MILP) capable of metering traffic at network gates with given signal timing parameters at signalized intersections. Due to the complexities of the MILP model, we have developed a novel and efficient solution approach that solves the problem by converting the MILP to a linear program and several CTM simulation runs. The solution algorithm is applied to two case studies under different conditions. The proposed solution technique finds solutions that have a maximum gap of 1% of the true optimal solution and guarantee the maximum throughput by keeping some vehicles at network gates and only allowing enough vehicles to enter the network to prevent gridlocks. This is confirmed by comparing the case studies with and without traffic metering. The results in an adapted real-world case study network show that traffic metering can increase network throughput by 4.9–38.9% and enhance network performance.
Connected vehicle technology, the Internet of Things, and other advanced communication technologies create possibilities to facilitate the movement of vehicles through transportation networks and reduce their travel time. Harmonizing the speed of vehicles in different network links not only yields a more efficient network capacity utilization, but also regulates the movement of vehicles to achieve a “smoother” flow of traffic. This study develops a mathematical nonlinear formulation for dynamic speed harmonization in urban street networks aiming at improving traffic operations. We have converted the nonlinear problem into a linear program utilizing the fundamental flow–density relationship and developed a model predictive control approach to account for stochastic changes in traffic demand and further improve the efficiency of the developed solution algorithm. Results showed that the algorithm efficiently found dynamic optimal advisory speeds on various network links, and speed harmonization significantly reduced the travel time (up to 5.4%), speed variance (19.8%–29.4%), and the number of stops (8.3%–18.5%), while increasing the average speed (up to 5.9%) and the number of completed trips (up to 4%) in our case study network under all tested demand patterns.
Local traffic control schemes fall short of achieving coordination with other parts of the urban road network, whereas a centralized controller based on the detailed traffic models would suffer from excessive computational burden. State estimation for detailed traffic models with limited observations and unpredictability of individual driver behavior create additional complications in the applicability of these models for large-scale traffic control. This point toward the need for designing network-level controllers building on aggregated traffic models, which have recently attracted attention through the macroscopic fundamental diagram (MFD) of urban traffic. Under some conditions, the MFD provides a unimodal, low-scatter, and demand-insensitive relationship between vehicle accumulation and travel production inside an urban region. In this paper, we propose MFD-based economic model predictive control (MPC) schemes to improve mobility in heterogeneously congested large-scale urban road networks. For more realistic simulations of urban networks with route guidance actuation-based control, a new model with cyclic behavior prohibition is developed. This paper extends upon earlier works on perimeter control-based MPC schemes with MFD modeling by integrating route guidance type actuation, which distributes flows exiting a region over its neighboring regions. Performance of the proposed schemes is evaluated via simulations of congested scenarios with noise in demand estimation and measurement errors. Results show the possibility of substantial improvements in urban network performance, in terms of network delays and traveled distance, even for low levels of driver compliance to route guidance.
This article develops an efficient methodology to optimize the timing of signalized intersections in urbanstreetnetworks.Ourapproachdistributesanetworklevel mixed-integer linear program (MILP) to intersection level. This distribution significantly reduces the complexity of the MILP and makes it real-time and scalable. We create coordination between MILPs to reduce the probability of finding locally optimal solutions. The formulationaccountsforoversaturatedconditionsbyusing an appropriate objective function and explicit constraints on queue length. We develop a rolling-horizon solution algorithm and apply it to several case-study networks under various demand patterns. The objective function of the optimization program is to maximize intersection throughput. The comparison of the obtained solutions to an optimal solution found by a central optimization approach (whenever possible) shows a maximum of 1% gap on a number of performance measures over different conditions.
This paper presents a Distributed-Coordinated methodology for signal timing optimization in connected urban street networks. The underlying assumption is that all vehicles and intersections are connected and intersections can share information with each other. The novelty of the work arises from reformulating the signal timing optimization problem from a central architecture, where all signal timing parameters are optimized in one mathematical program, to a decentralized approach, where a mathematical program controls the timing of only a single intersection. As a result of this distribution, the complexity of the problem is significantly reduced thus, the proposed approach is real-time and scalable. Furthermore, distributed mathematical programs continuously coordinate with each other to avoid finding locally optimal solutions and to move towards global optimality. We proposed a real-time and scalable solution technique to solve the problem and applied it to several case study networks under various demand patterns. The algorithm controlled
queue length and maximized intersection throughput (between 1% and 5% increase compared to the actuated coordinated signals optimized in VISTRO) and reduced travel time (between 17% and 48% decrease compared to actuated coordinated signals) in all cases.
Perimeter traffic control for large-scale urban road networks has been studied by several researchers during the last decade. Recently, the initial steps towards taking into account model’s uncertainties under control synthesis were made in Haddad and Shraiber (2014) and Haddad (2015), where by considering one- and multi- region control problem, respectively, a robust perimeter control has been designed to systematically take into account uncertainties in MFD-based dynamics, e.g. the MFD scatter. The robust control design can provide a fixed controller with constant gains to compensate all uncertainties, following the worst case scenario concept. In this paper, an adaptive control scheme is developed. Similarly to robust control, the developed adaptive control scheme postulates one controller structure, however, the controllers’ gains vary with time to adapt themselves against the model parameter uncertainties.
In this paper, in order to accommodate uncertainties and take into consideration the restrictions on the available information, we deal with the adaptive perimeter control problem for multi-region MFD systems, which have an interconnected structure composing several homogeneous regions. Unlike previous works that assume centralized approach, where feedback informations are needed from all urban regions, in this paper we follow a coordinated distributed control approach, where regional control laws are developed depending on (i) real on-line local information of the region, i.e. regional accumulation and its perimeter control input only, and (ii) reference signal information forwarded to all distributed perimeter controllers by a high level coordinator controller.
Most feedback perimeter control approaches that are based on the Macroscopic Fundamental Diagram (MFD) and are tested in detailed network structures restrict inflow from the external boundary of the network. Although such a measure is beneficial for the network performance, it creates virtual queues that do not interact with the rest of the traffic and assumes small unrestricted flow (i.e. almost zero disturbance). In reality, these queues can have a negative impact to traffic conditions upstream of the protected network that is not modelled. In this work an adaptive optimization scheme for perimeter control of heterogeneous transportation networks is developed and the aforementioned boundary control limitation is dropped. A nonlinear model is introduced that describes the evolution of the multi-region system over time, assuming the existence of well-defined MFDs. Multiple linear approximations of the model (for different set-points) are used for designing optimal multivariable integral feedback regulators. Since the resulting regulators are derived from approximations of the nonlinear dynamics, they are further enhanced in real-time with online learning/adaptive optimization, according to performance measurements. An iterative data-driven technique is integrated with the model-based design and its objective is to optimize the gain matrices and set-points of the multivariable perimeter controller based on real-time observations. The efficiency of the derived multi-boundary control scheme is tested in microsimulation for a large urban network with more than 1500 roads that is partitioned in multiple regions. The proposed control scheme is demonstrated to achieve a better distribution of congestion (by creating “artificial” inter-regional queues), thus preventing the network degradation and improving total delay and outflow.
Results of an exploratory study of network-level relationships in an isolated network with a fixed number of vehicles circulating according to the microscopic rules embedded in the NETSIM traffic simulation model are presented. The primary concern was to assess the usefulness of such simulation-based approaches in the investigation of macroscopic network-level traffic relationships. Three specific objectives were addressed: identification of network-level descriptors that are related in operationally useful and simple ways, exploration of some aspects of the two-fluid theory of town traffic, and examination of the traffic flow distribution over the network components.
A new gating strategy for concentric cities based on the notion of the macroscopic or network fundamental diagram and the feedback-based gating concept is introduced and successfully tested. Different regions of large-scale urban networks may experience congestion at different levels and 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. Remarkable extensions while distributing the ordered controller flow to the gated traffic signals in case of low demand or occurrence of spillback are also considered. A greater part of the San Francisco urban network is used as test-bed within a microscopic simulation environment. Significant improvements in terms of network-wide mean speed and average delay per kilometer are obtained compared to the single perimeter gating and non-gating simulation scenarios.
This paper formulates a scenario-based stochastic programming model to optimize the timing of pretimed signals along arterials under day-to-day demand variations or future uncertain traffic growth. Demand scenarios and their corresponding probabilities of occurrence are introduced to represent the demand uncertainty. On the basis of a cell-transmission representation of traffic dynamics, cycle length, green splits, phase sequences, and offsets are determined to minimize the expected delay incurred by high-consequence demand scenarios. A simulation-based genetic algorithm is proposed to solve the model, and a numerical example is presented to verify and validate the model.
Choosing an appropriate objective function in optimizing traffic signals in urban transportation networks is not a simple and straightforward task because the choice likely will affect the set of constraints, modeling variables, obtained outputs, and necessary computer and human resources. A methodology for selection of an appropriate objective function for the problem of signal timing optimization was developed. The methodology was applied to a realistic case study network under four demand patterns (symmetric, asymmetric, undersaturated, oversaturated). Selection is made from a pool of five candidates: minimizing the delay, minimizing the travel time, maximizing the throughput-minus-queue, maximizing the
number of completed trips (or trip maximization), and maximizing the weighted number of completed trips (or weighted trip maximization). Findings indicate that for all demand patterns, weighted trip maximization
improved network performance compared with the other objective functions. Weighted trip maximization reduced system total delay by 0.1% to 5.2% in symmetric undersaturated demand, by 1.0% to 2.4%
in asymmetric undersaturated demand, by 1.2% to 16.6% in symmetric oversaturated demand, and by 11.7% to 27.4% in asymmetric partially oversaturated demand. These figures indicate that the weighted trip
maximization objective function is the most suitable of the candidates in oversaturated conditions, especially when demand is not symmetric. Throughput-minus-queue and trip maximization were the second most
suitable objective functions for oversaturated conditions, and trip maximization was slightly more suitable when demand was asymmetric.
This study formulates a program for simultaneous traffic signal optimization and system optimal traffic assignment for urban transportation networks with added degree of realism. The formulation presents a new objective function, i.e., weighted trip maximization, and explicit constraints that are specifically designed to address oversaturated conditions. This formulation improves system-wise performance while locally prevents queue spillovers, de-facto reds, and gridlocks. A meta-heuristic algorithm is developed that incorporates microscopic traffic flow models and system optimal traffic assignment in genetic algorithms. This solution technique efficiently optimizes signal timing parameters, at the same time solves system optimal traffic assignment, and accounts for oversaturated conditions and different driver’s behaviors. This study also proposes a framework to calculate an upper bound on the value of the objective function by solving the problem while several constraints (i.e., network loading and traffic assignment) are relaxed. An empirical case study for a portion of downtown Springfield, Illinois has been conducted under four demand patterns. Findings indicate that our solution approach can solve the problem effectively. Several managerial insights have also been drawn.
One challenge in dynamic traffic assignment (DTA) modeling is estimating the finely disaggregated trip matrix required by such models. In previous work, an exogenous time distribution profile for trip departure rates is applied uniformly across all origin-destination (O-D) pairs. This article develops an endogenous departure time choice model based on an arrival time penalty function incorporated into trip distribution, which results in distinct demand profiles by O-D pair. This yields a simultaneous departure time and trip choice making use of the time-varying travel times in DTA. The required input is arrival time preferences, which can be disaggregated by O-D pair and may be easier to collect through surveys than the demand profile. This model is integrated into the four-step planning process with feedback, creating an extension of previous frameworks which aggregate over time. Empirical results from a network representing Austin, Texas indicate variation in departure time choice appropriate to the arrival time penalties and travel times. Our model also appears to converge faster to a dynamic trip table prediction than a time-aggregated coupling of DTA and planning, potentially reducing the substantial computation time of combined planning models that solve DTA as a subproblem of a feedback process.
Traffic signal control is a key ingredient in intelligent transportation systems to increase the capacity of existing urban transportation infrastructure. However, to achieve optimal system-wide operation, it is essential to coordinate traffic signals at various intersections. In this paper, we model the multiple-intersection traffic signal control problem using the cell transmission model as a mixed-integer linear program. The solution of the problem is facilitated by its special structure, which allows both temporal and spatial decomposition. Temporal decomposition is employed to reduce the problem size by solving subproblems of a smaller time window compared to the original problem. Temporal subproblems can be further spatially decomposed into subproblems associated with different intersections, which are jointly solved by exchanging messages between neighboring intersections. The proposed distributed solution strategy is comprised of two phases. First, the relaxed linear problem is reformulated and distributedly solved via the alternating direction method of multipliers. Second, two distributed rounding schemes are developed to solve the original problem. Simulation results indicate that the proposed solution strategy is scalable to large transportation topologies, which is suitable for online execution, and provides close-to-optimal results.
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.
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.
This paper proposes a non-holding back linear programming (NHBLP) model with an embedded cell transmission model (CTM), to account for the system optimum dynamic traffic assignment.
Traffic metering at on-ramps in interstate highways has been widely used and led to desirable results. In urban transportation networks when demand reaches network capacity level, traffic metering may also increase network performance efficiency. In this paper, we apply different metering strategies to a case study network to see if they result in a different network operation and potentially a more efficient performance. To make sure if any observed differences in network performance efficiency is due to metering strategies and not due to an inappropriate signal timing, we determine near optimal signal timing of the network by using our Intelligent Dynamic Signal Timing Optimization Program (IDSTOP). IDSTOP incorporates Genetic Algorithms (GAs) with microscopic traffic simulation to find near-optimal signal timing parameters of the network. Our results showed that letting all traffic enter the network or metering a large portion of the traffic are not the best options. Instead metering around 20% of the traffic resulted in the best network performance in terms of average delay (16% reduction compared to no metering and 17% reduction compared to extremely heavy metering strategies), network throughput (18% increase compared to heavy metering), and average travel time (14% reduction compared to no metering and 10% reduction compared to heavy metering). Our findings suggested that in an urban network, there is an optimal point that sending more vehicles into the network than that deteriorates network performance efficiency.
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.
The cell-based system optimal dynamic traffic assignment (SO-DTA) model has recently been applied to study emergency evacuation by a handful of authors. It is recognized that an optimal solution to this model may contain a phenomenon called traffic holding, which discharges flow at a lower rate than what can be achieved under the given traffic conditions. Mathematically, this is caused by the relaxation of traffic flow propagation constraints. In this paper, an optimal traffic pattern that contains no holding is always proved to exist in the context of evacuation planning. An optimal traffic pattern without holding is much easier and less costly to implement in emergency response. A dynamic network simplex method for solving the simplified SO-DTA model that represents traffic flow propagation by a point-queue model is proposed. By making full use of the network structure, the algorithm is able to identify an optimal solution without holding. For the original cell-based SO-DTA, an iterative procedure is suggested that can effectively eliminate holding in a solution obtained from a conventional linear programming algorithm.
The paper characterizes the behavior of the cell transmission model of a freeway, divided into N sections or cells, each with one on-ramp and one off-ramp. The state of the dynamical system is the N-dimensional vector n of vehicle densities in the N sections. A feasible stationary demand pattern induces a unique equilibrium flow in each section. However, there is an infinite set—in fact a continuum—of equilibrium states, including a unique uncongested equilibrium n u in which free flow speed pre-vails in all sections, and a unique most congested equilibrium n con . In every other equilibrium n e one or more sections are con-gested, and n u 6 n e 6 n con . Every equilibrium is stable and every trajectory converges to some equilibrium state. Two implications for ramp metering are explored. First, if the demand exceeds capacity and the ramps are not metered, every trajectory converges to the most congested equilibrium. Moreover, there is a ramp metering strategy that increases discharge flows and reduces total travel time compared with the no-metering strategy. Second, even when the demand is feasible but the freeway is initially congested, there is a ramp metering strategy that moves the system to the uncongested equilibrium and reduces total travel time. The two conclusions show that congestion invariably indicates wastefulness of freeway resources that ramp metering can eliminate.
A novel concept for a decentralized adaptive traffic signal control in urban networks using in future available vehicle to infratructure (V2I) communication data is presented. The phase-based strategy takes advantage of the improved detection data and optimizes each time interval of 5 seconds the phase sequence in order to reduce the total queue length within a forecast horizon of 20 seconds. For optimization the methods of dynamic programming and complete enumeration are used. The methods are embedded in the simulation environment of the microscopic traffic simulator AIMSUN NG. The market penetration level is the critical factor that impacts the quality of the new signal control. Hence, various penetration levels are modelled. For reference TRANSYT-7F is used.
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.
This paper discusses the optimal coordination of variable speed limits and ramp metering in a freeway traffic network, where the objective of the control is to minimize the total time that vehicles spend in the network. Coordinated freeway traffic control is a new development where the control problem is to find the combination of control measures that results in the best network performance. This problem is solved by model predictive control, where the macroscopic traffic flow model METANET is used as the prediction model. We extend this model with a model for dynamic speed limits and for main-stream origins. This approach results in a predictive coordinated control approach where variable speed limits can prevent a traffic breakdown and maintain a higher outflow even when ramp metering is unable to prevent congestion (e.g., because of an on-ramp queue constraint). The use of dynamic speed limits significantly reduces congestion and results in a lower total time spent.Since the primary effect of the speed limits is the limitation of the main-stream flow, a comparison is made with the case where the speed limits are replaced by main-stream metering. The resulting performances are comparable. Since the range of flows that main-stream metering and dynamic speed limits can control is different, the choice between the two should be primarily based on the traffic demands.
The onramp metering control problem is posed using a cell transmission-like model called the asymmetric cell transmission model (ACTM). The problem formulation captures both freeflow and congested conditions, and includes upper bounds on the metering rates and on the onramp queue lengths. It is shown that a near-global solution to the resulting nonlinear optimization problem can be found by solving a single linear program, whenever certain conditions are met. The most restrictive of these conditions requires the congestion on the mainline not to back up onto the onramps whenever optimal metering is used. The technique is tested numerically using data from a severely congested stretch of freeway in southern California. Simulation results predict a 17.3% reduction in delay when queue constraints are enforced.
This article shows how the evolution of multi-commodity traffic flows over complex networks can be predicted over time, based on a simple macroscopic computer representation of traffic flow that is consistent with the kinematic wave theory under all traffic conditions. The method does not use ad hoc procedures to treat special situations. After a brief review of the basic model for one link, the article describes how three-legged junctions can be modeled. It then introduces a numerical procedure for networks, assuming that a time-varying origin-destination (O-D) table is given and that the proportion of turns at every junction is known. These assumptions are reasonable for numerical analysis of disaster evacuation plans. The results are then extended to the case where, instead of the turning proportions, the best routes to each destination from every junction are known at all times. For technical reasons explained in the text, the procedure is more complicated in this case, requiring more computer memory and more time for execution. The effort is estimated to be about an order of magnitude greater than for the static traffic assignment problem on a network of the same size. The procedure is ideally suited for parallel computing. It is hoped that the results in the article will lead to more realistic models of freeway flow, disaster evacuations and dynamic traffic assignment for the evening commute.
Measurements taken downstream of freeway/on-ramp merges have previously shown that discharge flow diminishes when a merge becomes an isolated bottleneck. By means of observation and experiment, we show here that metering an on-ramp can recover the higher discharge flow at a merge and thereby increase the merge capacity. Detailed observations were collected at a single merge using video. These data revealed that the reductions in discharge flow are triggered by a queue that forms near the merge in the freeway shoulder lane and then spreads laterally, as drivers change lanes to maneuver around slow traffic. Our experiments show that once restrictive metering mitigated this shoulder lane queue, high outflows often returned to the median lane. High merge outflows could be restored in all freeway lanes by then relaxing the metering rate so that inflows from the on-ramp increased. Although outflows recovered in this fashion were not sustained for periods greater than 13 min, the findings are the first real evidence that ramp metering can favorably affect the capacity of an isolated merge. Furthermore, these findings point to control strategies that might generate higher outflows for more prolonged periods and increase merge capacity even more. Finally, the findings uncover details of merge operation that are essential for developing realistic theories of merging traffic.
The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon. In this paper we present a network flow algorithm for this problem. We show that the problem is equivalent to the earliest arrival flow and then solve the earliest arrival flow on a time-expanded network. In particular, a scaled flow scheme is proposed to deal with the situation in which the ratio of backward wave speed to forward wave speed is less than one. The proposed algorithm produces path-based flows exhibiting realistic nonvehicle-holding properties. Complexity and numerical analyses show that the algorithm runs more efficiently than LP.
The modeling of traffic control systems for solving such problems as surface street signalization, dynamic traffic assignment, etc., typically results in the appearance of a conditional function. For example, the consistent representation of the outflow discharge at an approach of a signalized intersection implies a function that is conditional on the signal indication and the prevailing traffic conditions. Representing such functions by some sort of constraint(s), ideally linear, so as to be considered in the context of a mathematical programming problem, is a nontrivial task, most often resolved by adopting restrictive assumptions regarding real-life process behavior. To address this general problem, we develop two methodologies that are largely based on analogies from mathematical logic that provide a practical device for the transformation of a specific form of a linear conditional piecewise function into a mixed integer model (MIM), i.e., a set of mixed-integer linear inequality constraints. We show the applicability of these methodologies to transforming into a MIM virtually every possible conditional piecewise function that can be found when one is modeling transportation systems based on the widely adopted dispersion-and-store and cell transmission traffic flow models, as well as to analyzing existing MIMs for identifying and eliminating redundancies.