<p>Queueing systems are everywhere: in transportation networks, service centers, communication systems, clinics, manufacturing systems, etc. In this dissertation, we contribute to the theory of queueing in two aspects. In the first part, we dilate the interplay between retrials and strategic arrival behavior in single-class queueing networks. Specifically, we study a variation of the ‘Network Concert Queueing Game,’ wherein a fixed but large number of strategic users arrive at a network of queues where they can be routed to other queues in the network following a fixed routing matrix, or potentially fedback to the end of the queue they arrive at. Working in a non-atomic setting, we prove the existence of Nash equilibrium arrival and routing profiles in three simple, but non-trivial, network topologies/architectures. In two of them, we also prove the uniqueness of the equilibrium. Our results prove that Nash equilibrium decisions on when to arrive and which queue to join in a network are substantially impacted by routing, inducing ‘herding’ behavior under certain conditions on the network architecture. Our theory raises important design implications for capacity-sharing in systems with strategic users, such as ride-sharing and crowdsourcing platforms.</p> <p><br></p> <p>In the second part, we develop a new method of data-driven model calibration or estimation for queueing models. Statistical and theoretical analyses of traffic traces show that the doubly stochastic Poisson processes are appropriate models of high intensity traffic arriving at an array of service systems. On the other hand, the statistical estimation of the underlying latent stochastic intensity process driving the traffic model involves a rather complicated nonlinear filtering problem. In this thesis we use deep neural networks to ‘parameterize’ the path measures induced by the stochastic intensity process, and solve this nonlinear filtering problem by maximizing a tight surrogate objective called the evidence lower bound (ELBO). This framework is flexible in the sense that we can also estimate other stochastic processes (e.g., the queue length process) and their related parameters (e.g., the service time distribution). We demonstrate the effectiveness of our results through extensive simulations. We also provide approximation guarantees for the estimation/calibration problem. Working with the Markov chain induced by the Euler-Maruyama discretization of the latent diffusion, we show that (1) there exists a sequence of approximate data generating distributions that converges to the “ground truth” distribution in total variation distance; (2) the variational gap is strictly positive for the optimal solution to the ELBO. Extending to the non-Markov setting, we identify the variational gap minimizing approximate posterior for an arbitrary (known) posterior and further, prove a lower bound on the optimal ELBO. Recent theoretical results on optimizing the ELBO for related (but ultimately different) models show that when the data generating distribution equals the ground truth distribution and the variational gap is zero, the probability measures that achieve these conditions also maximize the ELBO. Our results show that this may not be true in all problem settings.</p>

With the interactivity and immersion of players into video games, rising development costs, and heightened expectations from AAA developers video games need to make sure they hit their target market more than ever. This is something that is less extreme in the educational game development space; but ultimately true with limited grant funding, limited development time within a student developer’s schedule, and how rapidly a recently leased student content creator will need to learn the space and needs of the client. When a student is brought on late into a development cycle, it can become troublesome when they are required to meet new developing features on a changing project. This paper looks over how one team approached this issue, with a focus on meeting the needs of a group of American high school teachers. Within this paper, the focus is how they tackled the issue, and how the teachers reacted to the end prototype, with some insight into the older prototypes of the project. Throughout it they had reinforced the ideas that communication, data validity, and set contract goals are important identifiers for project success. Teachers looking at video games care more about the data being valid and clearly communicated more than if a game is fun or laden with features and mini-games.

<div> <div> <div> <p>Real-time pricing (RTP) of electricity for consumers has long been argued to be crucial for realizing the many envisioned benefits of demand flexibility in a smart grid. However, many details of how to actually implement a RTP scheme are still under debate. Since most of the organized wholesale electricity markets in the US implement a two-settlement mechanism, with day-ahead electricity price forecasts guiding financial and physical transactions in the next day and real-time ex post prices settling any real-time imbalances, it is a natural idea to let consumers respond to the day-ahead prices in real-time. However, if such an idea is not controlled properly, the inherent closed-loop operation may lead consumers to all respond in the same fashion, causing large swings of real-time demand and prices, which may jeopardize system stability and increase consumers’ financial risks. </p><p><br></p> <p>To overcome the potential uncertainties and undesired demand peak caused by “selfish” behaviors by individual consumers under RTP, in this research, we develop a fully decentralized price-driven demand response (DR) approach under game- theoretical frameworks. In game theory, agents usually make decisions based on their belief about competitors’ states, which needs to maintain a large amount of knowledge and thus can be intractable and implausible for a large population. Instead, we propose using regret-based learning in games by focusing on each agent’s own history and utility received. We study two learning mechanisms: bandit learning with incomplete information feedback, and low regret learning with full information feedback. With the learning in games, we establish performance guarantees for each individual agent (i.e., regret minimization) and the overall system (i.e., bounds on price of anarchy).</p><p><br></p></div></div></div><div><div><div> <p>In addition to the game-theoretical framework for price-driven demand response, we also apply such a framework for peer-to-peer energy trading auctions. The market- based approach can better incentivize the development of distributed energy resources (DERs) on demand side. However, the complexity of double-sided auctions in an energy market and agents’ bounded rationality may invalidate many well-established theories in auction design, and consequently, hinder market development. To address these issues, we propose an automated bidding framework based on multi-armed bandit learning through repeated auctions, and is aimed to minimize each bidder’s cumulative regret. We also use such a framework to compare market outcomes of three different auction designs. </p> </div> </div> </div>

<div>In this thesis, we explore different methods to enhance the safety and robustness for autonomous systems. We achieve this goal using concepts and tools from reachability analysis and control barrier functions. We first take on a multi-player reach-avoid game that involves two teams of players with competing objectives, namely the attackers and the defenders. We analyze the problem and solve the game from the attackers' perspectives via a moving horizon approach. The resulting solution provides a safety guarantee that allows attackers to reach their goals while avoiding all defenders. </div><div><br></div><div>Next, we approach the problem of target re-association after long-term occlusion using concepts from reachability as well as Bayesian inference. Here, we set out to find the probability identity matrix that associates the identities of targets before and after an occlusion. The solution of this problem can be used in conjunction with existing state-of-the-art trackers to enhance their robustness.</div><div><br></div><div>Finally, we turn our attention to a different method for providing safety guarantees, namely control barrier functions. Since the existence of a control barrier function implies the safety of a control system, we propose a framework to learn such function from a given user-specified safety requirement. The learned CBF can be applied on top of an existing nominal controller to provide safety guarantees for systems.</div>

<p>Facing increasingly sophisticated attacks from external adversaries, interdependent systems owners have to judiciously allocate their (often limited) security budget in order to reduce their cyber risks. However, when modeling human decision-making, behavioral economics has shown that humans consistently deviate from classical models of decision-making. Most notably, prospect theory, for which Kahneman won the 2002 Nobel memorial prize in economics, argues that humans perceive gains, losses and probabilities in a skewed manner. While there is a rich literature on prospect theory in economics and psychology, most of the existing work studying the security of interdependent systems does not take into account the aforementioned biases.</p> <p><br></p> <p>In this thesis, we propose novel mathematical behavioral security game models for the study of human decision-making in interdependent systems modeled by directed attack graphs. We show that behavioral biases lead to suboptimal resource allocation patterns. We also analyze the outcomes of protecting multiple isolated assets with heterogeneous valuations via decision- and game-theoretic frameworks, including simultaneous and sequential games. We show that behavioral defenders over-invest in higher-valued assets compared to rational defenders. We then propose different learning-based techniques and adapt two different tax-based mechanisms for guiding behavioral decision-makers towards optimal security investment decisions. In particular, we show the outcomes of such learning and mechanisms on four realistic interdependent systems. In total, our research establishes rigorous frameworks to analyze the security of both large-scale interdependent systems and heterogeneous isolated assets managed by human decision makers, and provides new and important insights into security vulnerabilities that arise in such settings.  </p>