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Dynamic traffic metering in urban street networks: Formulation and solution algorithm
Abstract
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.
... However, challenges arise in obtaining a stable MFD for urban settings due to varying network dynamics influenced by factors such as traffic signal settings or the presence of reversible lanes (Ji and Geroliminis, 2012). Additionally, MFD-based perimeter control strategies face practical limitations due to their inability to set specific metering levels for each border-crossing road (Mohebifard and Hajbabaie, 2018b). To overcome this, recent studies Hajbabaie, 2018b, 2019) have introduced mixed integer linear programming (MILP) models based on the cell transmission model (CTM), enabling optimal metering without relying on an MFD. ...
... In essence, only one decision maker (agent) can execute the metering action, necessitating the centralized manager to accurately forecast the traffic status of the road network and anticipate the future demand of incoming traffic. Subsequently, the manager adjusts the metering levels to prevent congestion within the protected area Mohebifard and Hajbabaie, 2018b). However, such a configuration may prove impractical, as it requires a highly centralized control structure and a unified communication protocol to facilitate control over all metering gates. ...
... Hence, CTM-based approaches allow for setting specific metering levels for each road, independently of the MFD. The first application of CTM to perimeter control in urban road networks was by Mohebifard and Hajbabaie (2018b), who formulated a Mixed Integer Linear Programming (MILP) model for the traffic metering problem and developed a solution algorithm based on the generalized Benders decomposition technique. This technique, involving multiple CTM simulations to obtain duals of decision variables, can be time-consuming and challenging for realworld network implementation, despite recent acceleration attempts by Gu et al. (2021) and Kim et al. (2018). ...
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.
... Mohebifard and Hajbabaie [11] formulated dynamic traffic metering in urban street networks into a Mixed to find near-optimal solutions. While the approach works well in medium size networks, due to problem complexities, it does not scale well to large urban street networks. ...
... As a result, these approaches determine distinct metering rates for each gate without the need to derive an MFD. Mohebifard and Hajbabaie [11] proposed an MILP formulation based on the CTM for dynamic metering in urban street networks. Their approach dynamically optimized metering rates at each gate and yielded significant improvements in network performance compared to a no-metering strategy. ...
... The problem formulation is adopted from Mohebifard and Hajbabaie [11], which is based on the CTM [31], [32], and finds the optimal traffic volume level that should enter the network through its entry links. We used the CTM network loading concept since it provides a good balance between accuracy and computational complexity: it is a macroscopic traffic flow model and at the same time disaggregates network links to shorter cells as such, can predict traffic flow conditions and back of the queue location more accurately than the linklevel macroscopic traffic models or approaches that are based on the MFD. ...
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.
... where u i (t) ∈ Z ≥0 is the inlet flow which is defined as the number of vehicles entering the traffic network through inlet i during the time interval [t, t + 1). The computed optimal inflows can be implemented by means of network gates, i.e., ramp meters [37], [38] for highways and metering gates [39] for urban streets). In (4), q j,i λ(t) is the fraction of outflow of lane j directed toward lane i during the time interval [t, t + 1), which is ...
... A different method [19] to ensure that vehicles will not be blocked is to constrain the total boundary inflow to be equal to a certain amount, i.e., i∈Nin u i (t) =ū, ∀t, whereū can be determined based upon prior traffic data. It is noteworthy that the computed optimal inflows can be implemented by means of network gates, i.e., ramp meters [37], [38] for highways and metering gates [39] for urban streets). ...
This paper proposes a traffic control scheme to alleviate traffic congestion in a network of interconnected signaled lanes/roads. The proposed scheme is emergency vehicle-centered, meaning that it provides an efficient and timely routing for emergency vehicles. In the proposed scheme, model predictive control is utilized to control inlet traffic flows by means of network gates, as well as configuration of traffic lights across the network. Two schemes are considered in this paper: i) centralized; and ii) decentralized. In the centralized scheme, a central unit controls the entire network. This scheme provides the optimal solution, even though it might not fulfil real-time computation requirements for large networks. In the decentralized scheme, each intersection has its own control unit, which sends local information to an aggregator. The main responsibility of this aggregator is to receive local information from all control units across the network as well as the emergency vehicle, to augment the received information, and to share it with the control units. Since the decision-making in decentralized scheme is local and the aggregator should fulfil the above-mentioned tasks during a traffic cycle which takes a long period of time, the decentralized scheme is suitable for large networks, even though it may provide a sub-optimal solution. Extensive simulation studies are carried out to validate the proposed schemes, and assess their performance. Notably, the obtained results reveal that traveling times of emergency vehicles can be reduced up to ~50% by using the centralized scheme and up to ~30% by using the decentralized scheme, without causing congestion in other lanes.
... function. The min(.) operator can be linearized with the big-M technique (Lo, 2001;Mohebifard and Hajbabaie, 2018b). This technique requires adding many auxiliary binary variables to the problem and hence increases the complexity of the problem. ...
... operator. Note that four binary variables are required to represent a min (.) operator that includes four expressions for each link and time step, similar to the case of Constraint (9) with the big-M technique, please see (Mohebifard and Hajbabaie, 2018b) for more details). Thus, (P1) is a large optimization program even for a small network. ...
This paper formulates the network-level traffic signal timing optimization problem as a Mixed-Integer Non-Linear Program (MINLP) and presents a customized methodology to solve it with a tight optimality gap. The MINLP is based on the Cell Transmission Model (CTM) network loading concept and captures the fundamental flow-density diagram of the CTM explicitly by considering closed-form constraints in the model and thus, eliminates the flow holding-back problem. The proposed solution algorithm is based on the Benders decomposition technique and decomposes the original MINLP to an equivalent Integer Program (IP) (Master problem), and a new MINLP (Primal problem). We will show that the new MINLP has only one optimal non-holding-back solution that can be found by a CTM simulation run. We will prove that the proposed solution technique guarantees convergence to optimal solutions with a finite number of iterations. Furthermore, we propose a dual estimation algorithm for the new MINLP (the Primal problem), which utilizes a simulation-based approach to generate Benders cuts instead of solving a complex optimization program. We applied the proposed solution technique to a simulated network of 20 intersections under various demand patterns and observed an optimality gap of at most 2% under all tested conditions. We compared the solutions of the proposed algorithm with two benchmark algorithms and found reductions in total travel time ranging from 7.0% to 35.7%.
... Additionally, four virtual gates (red bars) are set up at the boundary of the buffer zone corresponding to the four approaches to hold excessive traffic and prevent it from proceeding to the buffer zone. The mechanism of the virtual gate is similar to ramp metering (Kotsialos et al., 2001;Kotsialos and Papageorgiou, 2004) applied to the highway entrance, and traffic metering in urban street networks (Mohebifard and Hajbabaie, 2018). For implementation in the future pure CAV environment, the virtual gate is a location at the boundary of the buffer zone where the intersection controller informs approaching vehicles whether to proceed forward (through V2I communications). ...
The emerging technologies of connectivity and automation enable the potential for signal-free intersection control. In this context, virtual platooning is posited to be an innovative, decentralized control strategy that maps two-dimensional vehicle movements onto a one-dimension virtual platoon to enable intersection operations. However, the effectiveness of virtual platooning-based control can be limited or degraded by parametric inaccuracies and unparameterized disturbances in vehicle dynamics, heavy traffic congestion, and/or uncoordinated platoons in multi-lane intersections. To explicitly address these limitations, this study proposes a hybrid cooperative intersection control framework consisting of microscopic-level virtual platooning control and macroscopic-level traffic flow regulation for traffic environments with connected autonomous vehicles. In virtual platooning control, vehicles approaching an intersection are organized into coordinated independent virtual platoons to avoid potential conflicts triggered by platoon formation changes. Through coordination, vehicles in a platoon are grouped into compatible passing sets to maintain desired safe spacing when proceeding through the intersection. We propose a distributed adaptive sliding mode controller (DASMC) which uses the backstepping control method and model reference adaptive control method to address parametric inaccuracies, and the sliding mode control method to consistently suppress the negative effects of the unparameterized disturbances. Each vehicle approaching the intersection utilizes the kinematic information from neighboring vehicles to implement the DASMC in a distributed manner such that vehicles within the same virtual platoon can achieve consensus safely. However, virtual platooning control cannot preclude excessive traffic from approaching the intersection, which can cause undesired spillbacks and degrade intersection control performance. To address this issue, traffic flow regulation is integrated with the virtual platooning control using an iterative feedback loop mechanism. In each iteration of the iterative feedback loop, a constrained finite-time optimal control (CFTOC) problem is solved to determine the optimal input flow permitted to proceed through the intersection, and the virtual platooning control provides feedback on the queue status to the CFTOC to initiate the next iteration. The effectiveness of the proposed intersection control framework is evaluated through numerical experiments. The results indicate that the proposed virtual platooning DASMC controller can mitigate the effects of parametric inaccuracies and unparameterized disturbances to achieve consensus for approaching vehicles, as well as guarantee string stability. Further, the proposed framework can alleviate traffic spillbacks and travel delays effectively through traffic flow regulation.
... Note that CTM relates flow and density in each cell using non-linear equations. Some examples of formulations based on CTM can be found in [36]- [39]. We used the linearized form of the CTMbased SODTA formulation introduced by Beard and Ziliaskopoulos [5] and modified the set of OD pairs to reduce the computational complexity. ...
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.
... Note that , is the dual value of the added constraints =̂in R-subproblem 1. The values of this dual value can be found by simulating the case study and measuring the sensitivity of the objective function to the values of̂ (Mohebifard & Hajbabaie, 2018). ...
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.
... The formulation introduced in section II is intractable due to non-linear terms and the large number of binary variables. 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 algorithm iterates between the two sub-problems until the convergence criteria is met. For more details see Mohebifard and Hajbabaie [46]. ...
This study develops a methodology for coordinated speed optimization and traffic light control in urban street networks. We assume that all vehicles are connected and automated. The signal controllers collect vehicle data through vehicle to infrastructure communications and find optimal signal timing parameters and vehicle speeds to maximize network throughput while harmonizing speeds. Connected and automated vehicles receive these dynamically assigned speeds, accept them, and implement them. The problem is formulated as a mixed-integer non-linear program and accounts for the trade-offs between maximizing the network throughput and minimizing speed variations in the network to improve the network operational performance and at the same time smoothen the traffic flow by harmonizing the speed and reducing the number of stops at signalized intersections. A distributed optimization scheme is developed to reduce the computational complexity of the proposed program, and effective coordination ensures near-optimality of the solutions. The case study results show that the proposed algorithm works in real-time and provide near-optimal solutions with a maximum optimality gap of 5.4%. The proposed algorithm is implemented in Vissim. The results show that coordinated signal timing and speed optimization improved network performance in comparison with cases that either signal timing parameters or average speed of vehicles are optimized. The coordinated approach reduced the travel time, average delay, average number of stops, and average delay at stops by 1.9%, 5.3%, 28.5%, and 5.4%, respectively compared to the case that only signal timing parameters are optimized.
... The CTM [44], [45] is a discrete approximation of the continuum traffic flow model that can describe traffic dynamics according to hydrodynamic theory [53], [54]. CTM has been extensively used in traffic control problems [55]- [60]. Each link in the network is divided into homogeneous sections called cells that are connected to each other by connectors. ...
This paper develops a stochastic gradient-based optimization model for traffic signal control with bounds on network-level vehicular energy consumption. The signal control problem is formulated as a mixed-integer linear mathematical program, which incorporates inequality constraints to limit the total energy consumption in the network. The developed stochastic gradient approximation algorithm provides a near-optimal solution to the non-convex optimization problem. To account for the energy consumption constraints, a penalty function method leveraging the pseudo gradient estimation technique is developed. Empirical results from a signalized arterial street show that it is possible to achieve optimized signal settings at the desired energy consumption bound without compromising delay. Further, we report the sensitivity of the energy bounds to the mobility metrics--system delay. Our novel gradient-approximation-based solution technique offers a functional and feasible way to accommodate non-convex energy consumption bounds within a signal control optimization model to achieve maximal mobility with minimal energy consumption.
... However, we will focus on gating, also referred to as perimeter control. There are gating solutions to reduce congestion, travel time, and delay, some of which are based on the NFD and others that are not [20][21][22][23][24][25][26][27][28]. This paper focuses on methods that rely, in one form or another, R on the NFD. ...
Urban traffic congestion is a chronic problem faced by many cities in the US and worldwide. It results in inefficient infrastructure use as well as increased vehicle fuel consumption and emission levels. Congestion is intertwined with delay, as road users waste precious hours on the road, which in turn reduces productivity. Researchers have developed, and continue to develop, tools and systems to alleviate this problem. Network perimeter control is one such tool that has been studied extensively. It attempts to control the flow of vehicles entering a protected area to ensure that the congested regime predetermined by the Network Fundamental Diagram (NFD) is not reached. In this paper, an approach derived from sliding mode control theory is presented. Its main advantages over proportional-integral controllers include (1) minimal tuning, (2) no linearization of the governing equations, (3) no assumptions with regard to the shape of the NFD, and (4) ability to handle various demand profiles without the need to retune the controller. A sliding mode controller was implemented and tested on a congested grid network. The results show that the proposed controller produces network-wide delay savings and disperses congestion effectively.
... However, we will focus on gating, also referred to as perimeter control. There are gating solutions to reduce congestion, travel time, and delay, some of which are based on the NFD and others that are not [20][21][22][23][24][25][26][27][28]. ...
Urban traffic congestion is a chronic problem faced by many cities in the US and worldwide. It results in inefficient infrastructure use as well as increased vehicle fuel consumption and emission levels. Congestion is intertwined with delay, as road users waste precious hours on the road, which in turn reduces productivity. Researchers have developed, and continue to develop, tools and systems to alleviate this problem. Network perimeter control is one such tool that has been studied extensively. It attempts to control the flow of vehicles entering a protected area to ensure that the congested regime predetermined by the Network Fundamental Diagram (NFD) is not reached. In this paper, an approach derived from sliding mode control theory is presented. Its main advantages over proportional-integral controllers include (1) minimal tuning, (2) no linearization of the governing equations, (3) no assumptions with regard to the shape of the NFD, and (4) the ability to handle various demand profiles without the need to re-tune the controller. An SMC controller was implemented and tested on a congested grid network. The results show that the proposed controller produces network-wide delay savings and disperses congestion effectively.
... This section presents a linearized formulation for the SODTA problem based on the CTM network loading concept. We have used the CTM in our previous work for signal timing optimization (Mehrabipour & Hajbabaie, 2017;Mehrabipour, 2018), speed harmonization (Tajalli & Hajbabaie, 2018a, 2018b, and traffic metering (Mohebifard & Hajbabaie, 2018, 2019aMohebifard, Islam, & Hajbabaie, in press). We first define the temporal and spatial distribution of the problem. ...
This paper presents a decomposition scheme to find near-optimal solutions to a cell transmission model-based system optimal dynamic traffic assignment problem with multiple origin-destination pairs. A linear and convex formulation is used to define the problem characteristics. The decomposition is designed based on the Dantzig-Wolfe technique that splits the set of decision variables into subsets through the construction of a master problem and subproblems. Each subproblem includes only a single origin-destination pair with significantly less computational burden compared to the original problem. The master problem represents the coordination between subprob-lems through the design of interactive flows between the pairs. The proposed methodology is implemented in two case study networks of 20 and 40 intersections with up to 25 origin-destination pairs. The numerical results show that the decomposition scheme converges to the optimal solution, within 2.0% gap, in substantially less time compared to a benchmark solution, which confirms the computational efficiency of the proposed algorithm. Various network performance measures have been assessed based on different traffic state scenarios to draw managerial insights.
... However, improvements are achieved at the expense of delaying vehicles at the boundaries of the network. Moreover, traffic metering can be applied only to locations where there exists enough capacity to hold vehicles Kouvelas, Saeedmanesh, & Geroliminis, 2017;Mohebifard & Hajbabaie, 2018b, 2018a, 2018c. ...
Signal controllers are key components of transportation networks that manage traffic congestion by minimizing travelers’ delay and travel time. Controllers also contribute to managing environmental pollutants and fuel consumption. This contribution has social and economic effects. Signal settings of controllers can be determined by optimizing signal timing variables of formulated problems based on real-world transportation networks.
Approaches to solving signal timing optimization problems can be categorized into centralized, decentralized, hierarchical, and distributed-coordinated control approaches. These categories of approaches are neither tractable nor real-time for large-scale networks. Some of the approaches place restrictive assumptions on network topology and movements at intersections or they generate low-quality solutions.
In this thesis, a Distributed Optimization and Coordination Algorithm for a Signal Timing Optimization (DOCA-STO) problem is proposed. DOCA-STO is real-time and finds near-optimal values of signal timing variables by solving a mixed integer linear problem formulated based on the Cell Transmission Model (CTM). DOCA-STO distributes a network-level problem to several intersection-level sub-problems. Each sub-problem is an autonomous
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agent that is optimized separately and in a parallel architecture. This distribution increases the computational efficiency of DOCA-STO. The sub-problems broadcast several pieces of information to their neighbors to create a coordination scheme. The information includes the available capacity of receiving cells and the number of vehicles dispatched from each intersection. This coordination scheme is created using outputs of a CTM simulation for an entire network. The rolling horizon technique is also adopted to provide the possibility of quick responses to network changes and events and increase the efficiency of DOCA-STO by discretizing a study period.
The algorithm was tested on various test networks including those of 2, 6 and 20 intersections, and its results were compared with a centralized control system, a decentralized control system, and theoretical upper-bounds. The results are promising and show the capability of DOCA-STO for real-world case studies. The differences between the solutions of the proposed algorithm from globally optimal solutions were at most 1%, a result which validates the accurate performance of the proposed algorithm.
... For instance, Feng et al., (2015) and He et al., (2014) developed strategies to control the timing of signalized intersections using connected vehicle information and technology. Letter and Elefteriadou (2017), Ntousakis et al. (2016), and Mohebifard and Hajbabaie (2018b) developed metering strategies based on connected vehicle information. Moreover, Levin and Boyles (2016) and Zhu and Ukkusuri (2015) developed dynamic traffic assignment methods for connected vehicle environments, and Zhu and Ukkusuri (2014) developed a method for speed harmonization for connected vehicles. ...
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
... Connected vehicles, the internet of things, and smart infrastructure technologies facilitate the exchange of real-time, highly granular information between individual transportation system users, operators, and infrastructures. Harnessing the emergent ubiquitous connectivity and the consequential data stream opens unprecedented opportunities for congestion management strategies such as traffic metering (Marinescu et al. 2012;Mohebifard and Hajbabaie 2017), signal timing (Islam and Hajbabaie 2017;Mehrabipour and Hajbabaie 2017) Li et al. 2011;Feng et al. 2015;He et al. 2012), dynamic traffic assignment (Bagloee et al., 2017;Melson et al., 2017;Levin and Boyles, 2015), and speed harmonization (Li et al. 2016). Advisory speeds can be transmitted to connected vehicles to harmonize the flow of vehicles and consequently reduce unnecessary accelerations, decelerations, and stops. ...
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.
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 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.
This study presents a vehicle-level distributed coordination strategy to control a mixed traffic stream of connected automated vehicles (CAVs) and connected human-driven vehicles (CHVs) through signalized intersections. We use CAVs as mobile traffic controllers during a newly introduced “white phase”, during which CAVs will negotiate the right-of-way to lead a group of CHVs while CHVs must follow their immediate front vehicle. The white phase will not be activated under low CAV penetration rates, where vehicles must wait for green signals. We have formulated this problem as a distributed mixed-integer non-linear program and developed a methodology to form an agreement among all vehicles on their trajectories and signal timing parameters. The agreement on trajectories is reached through an iterative process, where CAVs update their trajectory based on shared trajectory of other vehicles to avoid collisions and share their trajectory with other vehicles. Additionally, the agreement on signal timing parameters is formed through a voting process where the most voted feasible signal timing parameters are selected. The numerical experiments indicate that the proposed methodology can efficiently control vehicle movements at signalized intersections under various CAV market shares. The introduced white phase reduces the total delay by 3.2% to 94.06% compared to cooperative trajectory and signal optimization under different CAV market shares in our tests. In addition, our numerical results show that the proposed technique yields reductions in total delay, ranging from 40.2% -98.9%, compared to those of a fully-actuated signal control obtained from a state-of-practice traffic signal optimization software.
This study presents a vehicle-level distributed coordination strategy to control a mixed traffic stream of connected automated vehicles (CAVs) and connected human-driven vehicles (CHVs) through signalized intersections. We use CAVs as mobile traffic controllers during a newly introduced white phase, during which CAVs will negotiate the right-of-way to lead a group of CHVs while CHVs must follow their immediate front vehicle. The white phase will not be activated under low CAV penetration rates, where vehicles must wait for green signals. We have formulated this problem as a distributed mixed-integer non-linear program and developed a methodology to form an agreement among all vehicles on their trajectories and signal timing parameters. The agreement on trajectories is reached through an iterative process, where CAVs update their trajectory based on shared trajectory of other vehicles to avoid collisions and share their trajectory with other vehicles. Additionally, the agreement on signal timing parameters is formed through a voting process where the most voted feasible signal timing parameters are selected. The numerical experiments indicate that the proposed methodology can efficiently control vehicle movements at signalized intersections under various CAV market shares. The introduced white phase reduces the total delay by 3.2% to 94.06% compared to cooperative trajectory and signal optimization under different CAV market shares in our tests. In addition, our numerical results show that the proposed technique yields reductions in total delay, ranging from 40.2% - 98.9%, compared to those of a fully-actuated signal control obtained from a state-of-practice traffic signal optimization software.
This study presents a methodology for optimal control of connected automated vehicles (CAVs) in freeway segments with a lane drop. Lane drops can create bottlenecks with a considerable number of mandatory and discretionary lane-changing maneuvers when traffic volume is high, which can eventually lead to stop-and-go conditions. Proper motion planning aligned with optimal lane changing upstream of a lane drop can increase capacity and reduce the number of stops and the risk of collision. This paper introduces a vehicle-level mixed-integer program to control longitudinal and lateral movement of CAVs, provide a smooth flow of traffic, and avoid congestion in freeway segments with lane drops. To ensure the feasibility of vehicle-level decisions and promote system-level optimality, a cooperative distributed algorithm is established, where CAVs coordinate their decisions to find the optimal longitudinal and lateral maneuvers that avoid collisions among all vehicles. The proposed coordination scheme lets CAVs find their optimal trajectories based on predictive information from surrounding vehicles (i.e., future locations and speeds) and coordinate their lane-changing decisions to avoid collisions. The results show that optimal lane changing of CAVs smoothens the traffic flow and increases freeway capacity in congested traffic conditions. Compared with all-knowing CAVs simulated in Vissim, the proposed methodology reduced the average travel time by up to 86.4%. It increased the number of completed trips by up to 134.3% based on various traffic demands and lane drop layout combinations.
This article proposes a traffic control scheme to alleviate traffic congestion in a network of interconnected signaled lanes/roads. The proposed scheme is emergency vehicle-centered, meaning that it provides an efficient and timely routing for emergency vehicles. In the proposed scheme, model predictive control is utilized to control inlet traffic flows by means of network gates, as well as the configuration of traffic lights across the network. Two schemes are considered in this article: 1) centralized and 2) decentralized. In the centralized scheme, a central unit controls the entire network. This scheme provides the optimal solution even though it might not fulfill real-time computation requirements for large networks. In the decentralized scheme, each intersection has its own control unit, which sends local information to an aggregator. The main responsibility of this aggregator is to receive local information from all control units across the network and the emergency vehicle, augment the received information, and share it with the control units. Since the decision-making in a decentralized scheme is local and the aggregator should fulfill the abovementioned tasks during a traffic cycle, which takes a long period of time, the decentralized scheme is suitable for large networks even though it may provide a suboptimal solution. Extensive simulation studies are carried out to validate the proposed schemes and assess their performance. Notably, the obtained results reveal that traveling times of emergency vehicles can be reduced up to
% by using the centralized scheme and up to
% by using the decentralized scheme without causing congestion in other lanes.
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.
Ramp metering offers great potential to mitigate traffic congestion and improve freeway management efficiency under traffic congestion conditions. This paper proposes an optimization program for freeway dynamic ramp metering based on Cell Transmission Model (CTM). This problem has been formulated as a discrete time optimal control problem with smooth state equations and constraints to meter traffic inflow from on-ramps. In the proposed model, the 'min' operators in the primal CTM are non-differentiable and thus, the corresponding optimal control problem cannot be solved directly using conventional gradient based methods. In this paper, we introduce a smooth approximation to approximate the 'min' operators and then a unified computational approach is developed to solve the problem. Theoretical analysis is carried out, showing that the optimal solution obtained from the approximated problem converges to the optimal solution of the primal CTM. Compared to the classical inequality relaxation method, our method can resolve the flow holding-back problem and reduce under fundamental diagram phenomenon. Compared with the Big-M method, our method has better efficiency. To achieve the desired traffic response control in real application, a series of online optimal control problems are solved using Model Predictive Control (MPC). Simulation studies show that our method can significantly improve freeway traffic management efficiency.
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.
This paper presents an integrated formulation and a distributed solution technique for cooperative signal control and perimeter traffic metering in urban street networks with various market penetration rates of connected vehicles. The problem is formulated as a mixed integer nonlinear program thus, does not scale well with the size of the network in a centralized optimization framework due to the presence of many mixed integer decision variables and constraints. To address this limitation, we will develop a distributed model predictive control that distributes the network-level cooperative problem into several intersection-level sub-problems and coordinates their decisions. Our numerical analyses show that the proposed distributed methodology finds solutions to the problem in real-time with the optimality gap of at most 3.6% in our case studies. We have implemented the distributed methodology in Vissim and observed that cooperative signal timing and perimeter control yielded significant improvements in traffic operations. Our case study results show that the cooperative approach increases the number of completed trips by 6.0%-12.8% and 10.9%-11.0% and reduces the total travel times by 8.1%-9.0% and 23.6%-24.2% compared to independent signal control and independent perimeter control, respectively.
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.
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.
Due to the complexity of the traffic flow dynamics in urban road networks, most quantitative descriptions of city traffic so far have been based on computer simulations. This contribution pursues a macroscopic (fluid-dynamic) simulation approach, which facilitates a simple simulation of congestion spreading in cities. First, we show that a quantization of the macroscopic turning flows into units of single vehicles is necessary to obtain realistic fluctuations in the traffic variables, and how this can be implemented in a fluid-dynamic model. Then, we propose a new method to simulate destination flows without the requirement of individual route assignments. Combining both methods allows us to study a variety of different simulation scenarios. These reveal fundamental relationships between the average flow, the average density and the variability of the vehicle densities. Considering the inhomogeneity of traffic as an independent variable can eliminate the scattering of congested flow measurements. The variability also turns out to be a key variable of urban traffic performance. Our results can be explained through the number of full links of the road network, and approximated by a simple analytical formula.
This paper analyzes the effects of different traffic metering levels at the entry points of a simulated signalized network to maintain efficient vehicle processing. Metering signals were placed along the network perimeter in advance of the bordering intersections to reduce the vehicle arrival rate and prevent oversaturation. In the simulation environment, traffic signals were externally controlled by independent agents using a learning algorithm based on approximate dynamic programming. Agents operated the signals in a cycle-free mode, reacting in real time to current demands and occupancy estimated from detectors placed at the entry and exit points of all links. The metering strategies were analyzed for delay, throughput, network congestion, and queue management. Results indicate that metering have a significant effect on network performance. Metering to levels just below the maximum throughput capacity of an intersection resulted in increased network throughput (up to 5%); reduced delay (up to 10.9%), including vehicles inside and those metered outside of the network; and queue lengths inside the network that allowed efficient use of green time. However, metering to points well below or above the capacity of an intersection did not always provide network improvements. This finding suggests that an optimal congestion level exists inside the network that can be achieved by a metering strategy. An analysis of the metering effects is presented in a case study, and field implementations and scenarios in which metering can be applied are discussed.
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.
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.
This study explores the limiting properties of network-wide traffic flow relations under heavily congested conditions in a large-scale complex urban street network; these limiting conditions are emulated in the context of dynamic traffic assignment (DTA) experiments on an actual large network. The primary objectives are to characterize gridlock and understand its dynamics. This study addresses a gap in the literature with regard to the existence of exit flow and recovery period. The one-dimensional theoretical Network Fundamental Diagram (NFD) only represents steady-state behavior and holds only when the inputs change slowly in time and traffic is distributed homogenously in space. Also, it does not describe the hysteretic behavior of the network traffic when a gridlock forms or when network recovers. Thus, a model is proposed to reproduce hysteresis and gridlock when homogeneity and steady-state conditions do not hold. It is conjectured that the network average flow can be approximated as a non-linear function of network average density and variation in link densities. The proposed model is calibrated for the Chicago Central Business District (CBD) network. We also show that complex urban networks with multiple route choices, similar to the idealized network tested previously in the literature, tend to jam at a range of densities that are smaller than the theoretical average network jam density. Also it is demonstrated that networks tend to gridlock in many different ways with different configurations. This study examines how mobility of urban street networks could be improved by managing vehicle accumulation and redistributing network traffic via strategies such as demand management and disseminating real-time traveler information (adaptive driving). This study thus defines and explores some key characteristics and dynamics of urban street network gridlocks including gridlock formation, propagation, recovery, size, etc.
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.
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.
This paper analyzes the effects of different traffic metering levels at the entry points of a simulated signalized network to maintain efficient vehicle processing. Metering signals were placed along the network perimeter in advance of the bordering intersections to reduce the vehicle arrival rate and prevent oversaturation. In the simulation environment, traffic signals were externally controlled by independent agents using a learning algorithm based on approximate dynamic programming. Agents operated the signals in a cycle-free mode, reacting in real time to current demands and occupancy estimated from detectors placed at the entry and exit points of all links. The metering strategies were analyzed for delay, throughput, network congestion, and queue management. Results indicate that metering have a significant effect on network performance. Metering to levels just below the maximum throughput capacity of an intersection resulted in increased network throughput (up to 5%); reduced delay (up to 10.9%), including vehicles inside and those metered outside of the network; and queue lengths inside the network that allowed efficient use of green time. However, metering to points well below or above the capacity of an intersection did not always provide network improvements. This finding suggests that an optimal congestion level exists inside the network that can be achieved by a metering strategy. An analysis of the metering effects is presented in a case study, and field implementations and scenarios in which metering can be applied are discussed.
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.
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.
Recent works have introduced perimeter feedback-control strategies for a homogenous urban region and multiple urban regions with the help of the Macroscopic Fundamental Diagram (MFD) representation, that relates average flow and density (or accumulation) across the network. The perimeter controller is located on the region border, and manipulates the transfer flows across the border, while aiming at regulating around (nearby) the critical densities or accumulations, whereby the system throughput is maximized. While the desired state in the one urban region system is known in advance (given the MFD shape), for the system with multiple urban regions the desired accumulation points are not well known. Moreover, in some traffic scenarios the controller cannot regulate around the critical accumulations for both systems, e.g. because of high demand. In this paper, a robust perimeter controller for an urban region is designed. The controller aims at satisfying the control specifications and having a good performance for the whole accumulation set, uncongested and congested accumulations, and not necessary for a value range nearby the critical accumulation set-point. Moreover, unlike previous works, the robust controller is also designed to handle uncertainty in the MFD and the control constraints within the design level in a systematic way, where the constraints are explicitly integrated utilizing the so-called describing function. Comparison results show that the performances of the robust controller are significantly better than a “standard” feedback controller, for different traffic scenarios.
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.
This paper develops a formulation for the network level dynamic traffic equilibrium model with departure time choice and route choice. The embedded network loading procedure follows the cell transmission model without the holding-back issues by using detailed representations of flows at merges and diverges. The problem is modeled using a complementarity approach. The existence of the equilibrium solution is discussed using techniques from generalized variational inequalities. Computational results are performed using state of the art solvers. Since these solvers fail to solve any reasonable size networks, a specialized projection algorithm is developed to solve the problem. Numerical results are presented to demonstrate the performance of the algorithm in various starting with simple networks and extending to reasonable size networks with different traffic parameters. It is shown that the solution procedure produces good dynamic equilibrium solutions for general transportation networks.
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 field experiment in Yokohama (Japan) revealed that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. It was observed that when the highly scattered plots of flow vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped along a well defined curve. Despite these and other recent findings for the existence of well-defined MFDs for urban areas, these MFDs should not be universally expected. In this paper we investigate what are the properties that a network should satisfy, so that an MFD with low scatter exists. We show that the spatial distribution of vehicle density in the network is one of the key components that affect the scatter of an MFD and its shape. We also propose an analytical derivation of the spatial distribution of congestion that considers correlation between adjacent links. We investigate the scatter of an MFD in terms of errors in the probability density function of spatial link occupancy and errors of individual links' fundamental diagram (FD). Later, using real data from detectors for an urban arterial and a freeway network we validate the proposed derivations and we show that an MFD is not well defined in freeway networks as hysteresis effects are present. The datasets in this paper consist of flow and occupancy measures from 500 fixed sensors in the Yokohama downtown area in Japan and 600 loop detectors in the Twin Cities Metropolitan Area Freeway network in Minnesota, USA.
This paper uses the method of kinematic waves, developed in part I, but may be read independently. A functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing (§2). From this a theory of the propagation of changes in traffic distribution along these roads may be deduced (§§2, 3). The theory is applied (§4) to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road. It is suggested that it will move slightly slower than the mean vehicle speed, and that vehicles passing through it will have to reduce speed rather suddenly (at a ‘shock wave’) on entering it, but can increase speed again only very gradually as they leave it. The hump gradually spreads out along the road, and the time scale of this process is estimated. The behaviour of such a hump on entering a bottleneck, which is too narrow to admit the increased flow, is studied (§5), and methods are obtained for estimating the extent and duration of the resulting hold-up. The theory is applicable principally to traffic behaviour over a long stretch of road, but the paper concludes (§6) with a discussion of its relevance to problems of flow near junctions, including a discussion of the starting flow at a controlled junction. In the introductory sections 1 and 2, we have included some elementary material on the quantitative study of traffic flow for the benefit of scientific readers unfamiliar with the subject.
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.
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.
Incluye bibliografía e índice
A field experiment in Yokohama (Japan) reveals that a macroscopic fundamental diagram (MFD) linking space-mean flow, density and speed exists on a large urban area. The experiment used a combination of fixed detectors and floating vehicle probes as sensors. It was observed that when the somewhat chaotic scatter-plots of speed vs. density from individual fixed detectors were aggregated the scatter nearly disappeared and points grouped neatly along a smoothly declining curve. This evidence suggests, but does not prove, that an MFD exists for the complete network because the fixed detectors only measure conditions in their proximity, which may not represent the whole network. Therefore, the analysis was enriched with data from GPS-equipped taxis, which covered the entire network. The new data were filtered to ensure that only full-taxi trips (i.e., representative of automobile trips) were retained in the sample. The space-mean speeds and densities at different times-of-day were then estimated for the whole study area using relevant parts of the detector and taxi data sets. These estimates were still found to lie close to a smoothly declining curve with deviations smaller than those of individual links - and entirely explained by experimental error. The analysis also revealed a fixed relation between the space-mean flows on the whole network, which are easy to estimate given the existence of an MFD, and the trip completion rates, which dynamically measure accessibility.
An enhanced 0-1 mixed-integer linear programming formulation based on the cell-transmission model is proposed for the traffic signal optimization problem. This formulation has several features that are currently unavailable in other existing models developed with a similar approach, including the components for handling the number of stops, fixed or dynamic cycle length and splits, and lost time. The problem of unintended vehicle holding, which is common in analytical models, is explicitly treated. The formulation can be utilized in developing strategies for adaptive traffic-control systems. It can also be used as a benchmark for examining the convergence behavior of heuristic algorithms based on the genetic algorithm, fuzzy logic, neural networks, or other approaches that are commonly used in this field. The discussion of extending the proposed model to capture traffic signal preemption in the presence of emergency vehicles is given. In terms of computational efficiency, the proposed formulation has the least number of binary integers as compared with other existing formulations that were developed with the same approach.
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Effectiveness of traffic restraint for a congested urban network: A simulation study
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