Control Theoretic Approaches to Congestion Pricing for High-occupancy Toll Lanes

The purpose of this study is to propose control theoretic approaches for high-occupancy toll (HOT) lanes operation. This dissertation considers different operation objectives, and provides pricing schemes for HOT lanes accordingly.To improve the system performance, the study first proposes a simultaneous estimation and control method for the same system as that in (Yin and Lou, 2009). An integral controller is applied to estimate the average value of time (VOT) of SOVs, and the dynamic prices are calculated based on the logit model. The closed-loop system is proved to be stable and guaranteed to converge to the optimal state both analytically and numerically. Two convergence patterns, Gaussian or exponential, are revealed. The effect of the scale parameter in the logit model is also examined.Then, a new lane choice model, i.e., the vehicle-based user equilibrium principle, is proposed to capture the lane choice of SOVs. A general lane choice model is derived based on the characteristics of the logit and the vehicle-based UE model. An insight regarding the dynamic price is obtained by analytically solving the optimal dynamic prices with constant demands of HOVs and SOVs, and then a feedback controller is designed to determine the dynamic prices without knowing SOVs’ lane choice models, but to satisfy the two control objectives: maximizing the flow-rate but not forming a queue on the HOT lanes. If the type of the lane choice model is given, the distribution of VOTs of the SOVs can be estimated.Next, an optimal control problem is proposed to examine the statement that revenue maximization should generally coincide with the optimization of freeway performances, such as maximizing overall travel-time savings or throughput. Results show that operators need to make different strategies based on the traffic demand. In order to maximize the revenue, operators should set a higher price to make the HOT lanes underutilized if the demand of HOVs is low. However, if the demand of HOVs is high, operators need to set a lower price to attract more SOVs to create congestion on the HOT lanes.It has long been known that drivers’ departure time choice behavior is one fundamental cause of congestion. In the last part of this dissertation, pricing schemes are proposed to consider both lane choice and departure time choice. In the study period, the demands for the HOT and GP lanes are higher than their capacities, which means the whole freeway is congested. However, the congestion period on the HOT lanes is short than that on the GP lanes. So, the HOT lanes are “underutilized”. It turns out that flat (instead of dynamic) pricing schemes are able to meet the following two constraints: (1) the total travel time and scheduling cost is minimized; and (2) the costs for each non-switching and switching SOV are the same. We show that different revenue and tolling constrains for certain type of vehicles lead to different pricing schemes

Systems-compatible Incentives

Originally, the Internet was a technological playground, a collaborative endeavor among researchers who shared the common goal of achieving communication. Self-interest used not to be a concern, but the motivations of the Internet's participants have broadened. Today, the Internet consists of millions of commercial entities and nearly 2 billion users, who often have conflicting goals. For example, while Facebook gives users the illusion of access control, users do not have the ability to control how the personal data they upload is shared or sold by Facebook. Even in BitTorrent, where all users seemingly have the same motivation of downloading a file as quickly as possible, users can subvert the protocol to download more quickly without giving their fair share. These examples demonstrate that protocols that are merely technologically proficient are not enough. Successful networked systems must account for potentially competing interests. In this dissertation, I demonstrate how to build systems that give users incentives to follow the systems' protocols. To achieve incentive-compatible systems, I apply mechanisms from game theory and auction theory to protocol design. This approach has been considered in prior literature, but unfortunately has resulted in few real, deployed systems with incentives to cooperate. I identify the primary challenge in applying mechanism design and game theory to large-scale systems: the goals and assumptions of economic mechanisms often do not match those of networked systems. For example, while auction theory may assume a centralized clearing house, there is no analog in a decentralized system seeking to avoid single points of failure or centralized policies. Similarly, game theory often assumes that each player is able to observe everyone else's actions, or at the very least know how many other players there are, but maintaining perfect system-wide information is impossible in most systems. In other words, not all incentive mechanisms are systems-compatible. The main contribution of this dissertation is the design, implementation, and evaluation of various systems-compatible incentive mechanisms and their application to a wide range of deployable systems. These systems include BitTorrent, which is used to distribute a large file to a large number of downloaders, PeerWise, which leverages user cooperation to achieve lower latencies in Internet routing, and Hoodnets, a new system I present that allows users to share their cellular data access to obtain greater bandwidth on their mobile devices. Each of these systems represents a different point in the design space of systems-compatible incentives. Taken together, along with their implementations and evaluations, these systems demonstrate that systems-compatibility is crucial in achieving practical incentives in real systems. I present design principles outlining how to achieve systems-compatible incentives, which may serve an even broader range of systems than considered herein. I conclude this dissertation with what I consider to be the most important open problems in aligning the competing interests of the Internet's participants

Modeling and optimizing network infrastructure for autonomous vehicles

Autonomous vehicle (AV) technology has matured sufficiently to be in testing on public roads. However, traffic models of AVs are still in development. Most previous work has studied AV technologies in micro-simulation. The purpose of this dissertation is to model and optimize AV technologies for large city networks to predict how AVs might affect city traffic patterns and travel behaviors. To accomplish these goals, we construct a dynamic network loading model for AVs, consisting of link and node models of AV technologies, which is used to calculate time-dependent travel times in dynamic traffic assignment. We then study several applications of the dynamic network loading to predict how AVs might affect travel demand and traffic congestion. AVs admit reduced perception-reaction times through technologies such as (cooperative) adaptive cruise control, which can reduce following headways and increase capacity. Previous work has studied these in micro-simulation, but we construct a mesoscopic simulation model for analyses on large networks. To study scenarios with both autonomous and conventional vehicles, we modify the kinematic wave theory to include multiple classes of flow. The flow-density relationship also changes in space and time with the class proportions. We present multiclass cell transmission model and prove that it is a Godunov approximation to the multiclass kinematic wave theory. We also develop a car-following model to predict the fundamental diagram at arbitrary proportions of AVs. Complete market penetration scenarios admit dynamic lane reversal -- changing lane direction at high frequencies to more optimally allocate road capacity. We develop a kinematic wave theory in which the number of lanes changes in space and time, and approximately solve it with a cell transmission model. We study two methods of determining lane direction. First, we present a mixed integer linear program for system optimal dynamic traffic assignment. Since this program is computationally difficult to solve, we also study dynamic lane reversal on a single link with deterministic and stochastic demands. The resulting policy is shown to significantly reduce travel times on a city network. AVs also admit reservation-based intersection control, which can make greater use of intersection capacity than traffic signals. AVs communicate with the intersection manager to reserve space-time paths through the intersection. We create a mesoscopic node model by starting with the conflict point variant of reservations and aggregating conflict points into capacity-constrained conflict regions. This model yields an integer program that can be adapted to arbitrary objective functions. To motivate optimization, we present several examples on theoretical and realistic networks demonstrating that naïve reservation policies can perform worse than traffic signals. These occur due to asymmetric intersections affecting optimal capacity allocation and/or user equilibrium route choice behavior. To improve reservations, we adapt the decentralized backpressure wireless packet routing and P0 traffic signal policies for reservations. Results show significant reductions in travel times on a city network. Having developed link and node models, we explore how AVs might affect travel demand and congestion. First, we study how capacity increases and reservations might affect freeway, arterial, and city networks. Capacity increases consistently reduced congestion on all networks, but reservations were not always beneficial. Then, we use dynamic traffic assignment within a four-step planning model, adding the mode choice of empty repositioning trips to avoid parking costs. Results show that allowing empty repositioning to encourage adoption of AVs could reduce congestion. Also, once all vehicles are AVs, congestion will still be significantly reduced. Finally, we present a framework to use the dynamic network loading model to study shared AVs. Results show that shared AVs could reduce congestion if used in certain ways, such as with dynamic ride-sharing. However, shared AVs also cause significant congestion. To summarize, this dissertation presents a complete mesoscopic simulation model of AVs that could be used for a variety of studies of AVs by planners and practitioners. This mesoscopic model includes new node and link technologies that significantly improve travel times over existing infrastructure. In addition, we motivate and present more optimal policies for these AV technologies. Finally, we study several travel behavior scenarios to provide insights about how AV technologies might affect future traffic congestion. The models in this dissertation will provide a basis for future network analyses of AV technologies.Civil, Architectural, and Environmental Engineerin

Participation of distributed loads in power markets that co-optimize energy and reserves

Thesis (Ph.D.)--Boston UniversityAs the integration of Renewable Generation into today's Power Systems is progressing rapidly, capacity reserve requirements needed to compensate for the intermittency of renewable generation is increasing equally rapidly. A major objective of this thesis is to promote the affordability of incremental reserves by enabling loads to provide them through demand response. Regulation Service (RS) reserves, a critical type of bi-directional Capacity Reserves, are provided today by expensive and environmentally unfriendly centralized fossil fuel generators. In contrast, we investigate the provision of low-cost RS reserves by the demand-side. This is a challenging undertaking since loads must first promise reserves in the Hour Ahead Markets, and then be capable of responding to the dynamic ISO signals by adjusting their consumption effectively and efficiently. To this end, we use Stochastic Control, Optimization Theory, and Approximate Dynamic Programming to develop a decision support framework that assists Smart Neighborhood Operators or Smart Building Operators (SNOs/SBOs) to become demand-side-providers of RS reserve. We first address the SNO/SBO short time scale operational task of responding to the Independent System Operator's (ISO) dynamic RS requests. We start by developing a model-based Markovian decision problem that trades off ISO RS tracking against demand response related utility loss. Starting with a model based approach we obtain near optimal operational policies through a novel approximate policy iteration technique and an actor critic approach which is robust to partial knowledge of the underlying system dynamics. We then abandon the model based terrain and solve the dynamic operational problem through reinforcement learning that is capable of modeling a population of duty cycle appliances with realistic thermodynamics. We finally propose a smart thermostat design and develop an adaptive control policy that can drive the smart thermostat effectively. The latter approach is particularly suited for systems whose dynamics and dynamically changing consumer preferences are not known or observed beyond the total power consumption. We then address the SNO/SBO task of bidding RS reserves to the hour ahead market. This task determines the maximal RS reserves that the SNO/SBO can promise based on information available at the beginning of an hour, so as to maximize the associated hour-ahead revenues minus the expected average operating cost that will be incurred during the operational task to follow. To accomplish this task, we (i) develop probabilistic constraints that model the feasible maximum reserves which can be offered to the market without exceeding the SNO/SBO's ability to later track the unanticipated dynamic ISO RS signal, and (ii) calibrate a describing function that approximates the average operational cost as a function of the maximal reserves that can be feasibly offered in the day ahead market. The above is made possible by statistical analysis of the controlled system's stochastic dynamics and properties of the optimal dynamic policies that we derive. The contribution of the thesis is twofold: The solution of a difficult stochastic control problem that is crucial for effective demand-response-based provision of regulation service, and, the characterization of key properties of the stochastic control problem solution, which allow its integration into the hour-ahead market bidding problem

INCORPORATING TRAVEL TIME RELIABILITY INTO TRANSPORTATION NETWORK MODELING

Travel time reliability is deemed as one of the most important factors affecting travelers’ route choice decisions. However, existing practices mostly consider average travel time only. This dissertation establishes a methodology framework to overcome such limitation. Semi-standard deviation is first proposed as the measure of reliability to quantify the risk under uncertain conditions on the network. This measure only accounts for travel times that exceed certain pre-specified benchmark, which offers a better behavioral interpretation and theoretical foundation than some currently used measures such as standard deviation and the probability of on-time arrival. Two path finding models are then developed by integrating both average travel time and semi-standard deviation. The single objective model tries to minimize the weighted sum of average travel time and semi-standard deviation, while the multi-objective model treats them as separate objectives and seeks to minimize them simultaneously. The multi-objective formulation is preferred to the single objective model, because it eliminates the need for prior knowledge of reliability ratios. It offers an additional benefit of providing multiple attractive paths for traveler’s further decision making. The sampling based approach using archived travel time data is applied to derive the path semi-standard deviation. The approach provides a nice workaround to the problem that there is no exact solution to analytically derive the measure. Through this process, the correlation structure can be implicitly accounted for while simultaneously avoiding the complicated link travel time distribution fitting and convolution process. Furthermore, the metaheuristic algorithm and stochastic dominance based approach are adapted to solve the proposed models. Both approaches address the issue where classical shortest path algorithms are not applicable due to non-additive semi-standard deviation. However, the stochastic dominance based approach is preferred because it is more computationally efficient and can always find the true optimal paths. In addition to semi-standard deviation, on-time arrival probability and scheduling delay measures are also investigated. Although these three measures share similar mathematical structures, they exhibit different behaviors in response to large deviations from the pre-specified travel time benchmark. Theoretical connections between these measures and the first three stochastic dominance rules are also established. This enables us to incorporate on-time arrival probability and scheduling delay measures into the methodology framework as well

Modeling and Analysis of Power Processing Systems (MAPPS), initial phase 2

The overall objective of the program is to provide the engineering tools to reduce the analysis, design, and development effort, and thus the cost, in achieving the required performances for switching regulators and dc-dc converter systems. The program was both tutorial and application oriented. Various analytical methods were described in detail and supplemented with examples, and those with standardization appeals were reduced into computer-based subprograms. Major program efforts included those concerning small and large signal control-dependent performance analysis and simulation, control circuit design, power circuit design and optimization, system configuration study, and system performance simulation. Techniques including discrete time domain, conventional frequency domain, Lagrange multiplier, nonlinear programming, and control design synthesis were employed in these efforts. To enhance interactive conversation between the modeling and analysis subprograms and the user, a working prototype of the Data Management Program was also developed to facilitate expansion as future subprogram capabilities increase