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A computationally efficient model predictive controller for congestion control in freeway networks is presented in this paper. The controller utilizes a modified Link-Node Cell Transmission Model (LN-CTM) to simulate traffic state trajectories under the effect of ramp metering, variable speed limit control and compute performance objectives. The modified LN-CTM simulates freeway traffic dynamics in the presence of capacity drop and ramp weaving effects. The objective of the controller can be chosen to represent commonly used congestion performance measures like total congestion delay measured in units of vehicle hours. The optimal control formulation based on this modified model is non-convex making it inefficient for direct use within a model predictive framework. Heuristic restrictions and relaxations are presented which allow the computation of the solution using optimal solutions of a sequence of derived linear programs. Mainly, the freeway is cleverly divided into regions, and limited restrictions are placed on solution trajectories to allow us to derive computationally efficient control actions. In the absence of capacity drop, this solution strategy provides optimal solutions to the original optimal control problem by solving a single linear program. The properties of the solution are discussed along with the role of variable speed limits when capacity drop is present/absent. Examples are provided to showcase the computational efficiency of the solution strategy, and scenarios simulated using the modified LN-CTM are analyzed to investigate the role of variable speed limits as a congestion control strategy. [ABSTRACT FROM AUTHOR]

The need for monitoring the state of a traffic network versus the costly installation and maintenance of roadside sensors constitutes the tough sensor placement problem in designing transportation networks. Placement problems naturally lie in the category of subset selection problems, which are known to be inherently combinatorial, and therefore, finding their exact solution is intractable for large problems. Due to this intractability, numerous heuristics have been proposed in the literature for approximately solving placement problems for traffic networks. Among these approaches, it has been observed that greedy algorithms normally outperform other heuristics. In this paper, we show the mathematics of why greedy algorithms are appropriate proxies for solving these subset selection problems; similar to placement problems for linear systems, placement problems for traffic networks also normally have a submodular structure. In this work, we analyze the problem of road sensor placement for transportation networks under different information structures available: when no vehicle routing information is available, when vehicles' routings are known, and when it is necessary to maximize the number of origin–destination (O/D) traffic flows that are monitored with a set of sensors. We show that in all these cases, the placement problem has a submodular monotone structure. It is well known that the submodularity and monotonicity of discrete optimization problems can be leveraged to derive greedy algorithms that approximate the optimal solution. Consequently, our result is of great practical importance since by exploiting the submodularity and monotonicity of a problem, we show that it is possible to use polynomial-time greedy algorithms to approximate the combinatorial optimization problem with guaranteed optimality bounds for large problems, which are intractable to solve otherwise. Our results shed light upon the success of heuristic greedy algorithms that have been developed in some of the literature for solving placement problems at scale. To demonstrate the applicability of submodular optimization for solving placement problems, we first compare the performance of our polynomial-time approximation algorithm with the true optimum in an example traffic network which is small enough for finding the exact optimal solution with enumerating all possible subsets. Then, we investigate and validate our submodular approach in a case study involving a large-scale traffic network in Berkeley, California, where finding the exact optimal solution is intractable. Submodularity of the placement problem in these scenarios provides a powerful computational tool which can be further extended to other placement problem formulations that can become a reference for solving similar problems in the transportation literature. • Sensor placement problems on large scale networks are intractable. • Three different sensor placement problems are shown to share the submodular feature. • Submodular optimization problems have efficient solutions. • The submodular optimization algorithm is validated on both small and large networks. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the problem of finding a controller for a discrete time linear periodically time-varying system with structured parametric uncertainty which achieves robust semi-norm performance (the equivalent of robust norm performance for time-varying systems). This problem is shown to be a generalization of a guaranteed cost control problem when the structure of the uncertainty is neglected. To reduce the conservatism when the uncertainty structure is considered, static uncertainty scalings such as those used in the D-K iteration heuristic for -synthesis are introduced. Although the problem of simultaneously optimizing the controller and uncertainty scalings in non-convex, it is shown that it lends itself to a solution methodology conceptually similar to D-K iteration in which each step is a convex optimization. To demonstrate the effectiveness of the developed methodology, the control of a set of hard disk drives with multirate sampling characteristics and uncertain parameters is considered and a controller is designed which minimizes the worst-case semi-norm performance of the system. It is then shown that the resulting robust controller achieves worst-case semi-norm performance which is comparable to the best achievable semi-norm performance for the nominal system. [Copyright &y& Elsevier]

Abstract: 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 prevails in all sections, and a unique most congested equilibrium n con. In every other equilibrium n e one or more sections are congested, and n u ⩽ n e ⩽ 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. [Copyright &y& Elsevier]

Abstract: This paper discusses two mechatronic innovations in magnetic hard disk drive servo systems, which may have to be deployed in the near future, in order to sustain the continuing 60% annual increase in storage density of these devices. The first is the use of high bandwidth dual-stage actuator servo systems to improve the precision and track-following capability of the read/write head positioning control system. The second is the instrumentation of disk drive suspensions with vibration sensing strain gages, in order to enhance airflow-induced suspension vibration suppression in hard disk drives. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]

Abstract: Traffic flow propagation stability is concerned about whether a traffic flow perturbation will propagate and form a traffic shockwave. In this paper, we discuss a general approach to the macroscopic traffic flow propagation stability for adaptive cruise controlled (ACC) vehicles. We present a macroscopic model with velocity saturation for traffic flow in which each individual vehicle is controlled by an adaptive cruise control spacing policy. A nonlinear traffic flow stability criterion is investigated using a wavefront expansion technique. Quantitative relationships between traffic flow stability and model parameters (such as traffic flow and speed, etc.) are derived for a generalized ACC traffic flow model. The newly derived stability results are in agreement with previously derived results that were obtained using both microscopic and macroscopic models with a constant time headway (CTH) policy. Moreover, the stability results derived in this paper provide sufficient and necessary conditions for ACC traffic flow stability and can be used to design other ACC spacing policies. [Copyright &y& Elsevier]

Traffic flow control in automated highway systems (AHS) is addressed. A link layer controller for a hierarchical AHS architecture is presented. The controller proposed in this paper stabilizes the vehicular density and flow around predetermined profiles in a stretch of highway using speed and lane changes as control signals. Multiple lane highways in which vehicles have different destinations and types are considered. The control laws are derived from a model based on a principle of vehicle conservation and Lyapunov stability techniques. The implementation requires only local information. Simulation results are presented. [Copyright &y& Elsevier]

Provides information on the development of controls for the link layer in the Automated Highway System hierarchy proposed in the Partners for Advanced Transit and Highways. Description of the link layer; Way in which other desired traffic conditions are perceived; Conceptualization of laws for highway control.

• We have modified the introduction and rewritten parts of it to highlight the importance of our work and discuss how it is different from the previous work. • We have included a detailed description of our simulation study so that the reader can go over the setting of the simulation. • We have changed some of the plots of the mixed-autonomy section as there was a mistake in our previous results. • We have also changed the notation. Vehicle bypassing is known to increase delays at traffic diverges. However, due to the complexities of this phenomenon, accurate and yet simple models of such lane change maneuvers are hard to develop. In this work, we present a macroscopic model for predicting the number of vehicles that perform a bypass at a traffic diverge when taking an exit link. We interpret the bypassing maneuver of vehicles at a traffic diverge as drivers acting selfishly; every vehicle selects lanes such that its own cost of travel is minimized. We discuss how we model the costs that are incurred by the vehicles. Then, taking into account the selfish behavior of vehicles, we model the lane choice of vehicles at a traffic diverge as a Wardrop equilibrium. We state and prove the properties of the equilibrium in our model. We show that there always exists an equilibrium for our model. Moreover, although our model is an instance of nonlinear asymmetrical routing games which in general have multiple equilibria, we prove that the equilibrium of our model is unique under certain assumptions that we observed to hold in all our case studies. We discuss how our model can be calibrated by running a simple optimization problem. Then, using our calibrated model, we validate it through simulation studies and demonstrate that our model successfully predicts the aggregate lane change maneuvers that are performed by vehicles at a traffic diverge. Having shown the predictive power of our model, we discuss how our model can be employed to obtain the optimal lane choice behavior of vehicles, where the social or the overall cost of all vehicles is minimized. Finally, we demonstrate how our model can be utilized in scenarios where a central authority can dictate the lane choice and trajectory of certain vehicles, for example autonomous vehicles directed by a central authority, so as to increase the overall vehicle mobility at a traffic diverge. Examples of such scenarios include the case when both human driven and autonomous vehicles coexist in the network. [ABSTRACT FROM AUTHOR]

Macroscopic traffic models are necessary for simulation and study of traffic’s complex macro-scale dynamics, and are often used by practitioners for road network planning, integrated corridor management, and other applications. These models have two parts: a link model, which describes traffic flow behavior on individual roads, and a node model, which describes behavior at road junctions. As the road networks under study become larger and more complex — nowadays often including arterial networks — the node model becomes more important. Despite their great importance to macroscopic models, however, only recently have node models had similar levels of attention as link models in the literature. This paper focuses on the first order node model and has two main contributions. First, we formalize the multi-commodity flow distribution at a junction as an optimization problem with all the necessary constraints. Most interesting here is the formalization of input flow priorities. Then, we discuss a very common “conservation of turning fractions” or “first-in-first-out” (FIFO) constraint, and how it often produces unrealistic spillback. This spillback occurs when, at a diverge, a queue develops for a movement that only a few lanes service, but FIFO requires that all lanes experience spillback from this queue. As we show, avoiding this unrealistic spillback while retaining FIFO in the node model requires complicated network topologies. Our second contribution is a “partial FIFO” mechanism that avoids this unrealistic spillback, and a (first-order) node model and solution algorithm that incorporates this mechanism. The partial FIFO mechanism is parameterized through intervals that describe how individual movements influence each other, can be intuitively described from physical lane geometry and turning movement rules, and allows tuning to describe a link as having anything between full FIFO and no FIFO. Excepting the FIFO constraint, the present node model also fits within the well-established “general class of first-order node models” for multi-commodity flows. Several illustrative examples are presented. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an algorithm and analysis of distributed learning and cooperative control for a multi-agent system so that a global goal of the overall system can be achieved by locally acting agents. We consider a resource-constrained multi-agent system, in which each agent has limited capabilities in terms of sensing, computation, and communication. The proposed algorithm is executed by each agent independently to estimate an unknown field of interest from noisy measurements and to coordinate multiple agents in a distributed manner to discover peaks of the unknown field. Each mobile agent maintains its own local estimate of the field and updates the estimate using collective measurements from itself and nearby agents. Each agent then moves towards peaks of the field using the gradient of its estimated field while avoiding collision and maintaining communication connectivity. The proposed algorithm is based on a recursive spatial estimation of an unknown field. We show that the closed-loop dynamics of the proposed multi-agent system can be transformed into a form of a stochastic approximation algorithm and prove its convergence using Ljung’s ordinary differential equation (ODE) approach. We also present extensive simulation results supporting our theoretical results. [Copyright &y& Elsevier]

In this paper, second-order macroscopic vehicle traffic flow models are discussed from the perspective of their capability to reproduce stable and unstable traffic flow behaviors observed in real traffic. To achieve this goal, a nonlinear traffic flow stability criterion is derived using a wavefront expansion technique. Qualitative relationships between traffic flow stability and model parameters are derived for an entire class of second-order macroscopic traffic flow models. The stability criterion is illustrated by numerical results using the CLAWPACK package for the well-known Payne–Whitham (PW) model. The newly derived stability results are consistent with previously reported results obtained using both microscopic models and approximate linearization methods. Moreover, the stability criteria derived in this paper can provide more refined information regarding the propagation of traffic flow perturbations and shock waves in second-order models than previously established methodologies. [Copyright &y& Elsevier]