We study the problem of job assignment in a large-scale realistically dimensioned server farm comprising multiple processor-sharing servers with different service rates, energy consumption rates, and buffer sizes. Our aim is to optimize the energy efficiency of such a server farm by effectively controlling carried load on networked servers. To this end, we propose a job assignment policy, called Most energy-efficient available server first Accounting for Idle Power (MAIP), which is both scalable and near optimal. MAIP focuses on reducing the productive power used to support the processing service rate. Using the framework of semi-Markov decision process, we show that, with exponentially distributed job sizes, MAIP is equivalent to the well-known Whittle's index policy. This equivalence and the methodology of Weber and Weiss enable us to prove that, in server farms where a loss of jobs happens if and only if all buffers are full, MAIP is asymptotically optimal, as the number of servers tends to infinity under certain conditions associated with the large number of servers, as we have in a real server farm. Through extensive numerical simulations, we demonstrate the effectiveness of MAIP and its robustness to different job-size distributions, and observe that significant improvement in energy efficiency can be achieved by utilizing the knowledge of energy consumption rate of idle servers.

We study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. It is modeled as a set of heterogeneous restless multiarmed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle’s relaxation idea and Weber and Weiss’ asymptotic optimality proof, we propose a simple policy and prove it to be asymptotically optimal in a regime where both arrival rates and capacities increase. We provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. The effectiveness of these results is demonstrated by numerical experiments. To the best of our knowledge, this is the first work providing asymptotic optimality results for such a resource allocation problem and such a combination of multiple RMABPs.

We study a job-assignment problem in a large-scale server farm system with geographically deployed servers as abstracted computer components (e.g., storage, network links, and processors) that are potentially diverse. We aim to maximize the energy efficiency of the entire system by effectively controlling carried load on networked servers. A scalable, near-optimal job-assignment policy is proposed. The optimality is gauged as, roughly speaking, energy cost per job. Our key result is an upper bound on the deviation between the proposed policy and the asymptotically optimal energy efficiency, when job sizes are exponentially distributed and blocking probabilities are positive. Relying on Whittle relaxation and the asymptotic optimality theorem of Weber and Weiss, this bound is shown to decrease exponentially as the number of servers and the arrival rates of jobs increase arbitrarily and in proportion. In consequence, the proposed policy is asymptotically optimal and, more importantly, approaches asymptotic optimality quickly (exponentially). This suggests that the proposed policy is close to optimal even for relatively small systems (and indeed any larger systems), and this is consistent with the results of our simulations. Simulations indicate that the policy is effective, and robust to variations in job-size distributions.

This article addresses state estimation problems with unknown process and measurement noise covariances in both linear and nonlinear systems. By formulating the joint estimation of system state and noise parameters into an optimization problem, a novel adaptive Kalman filter method based on conjugate-computation variational inference, referred to as CVIAKF, is proposed to approximate the joint posterior probability density function of the latent variables. Unlike existing adaptive Kalman filter methods utilizing variational inference in natural parameter space, CVIAKF performs optimization in expectation parameter space, resulting in a faster and simpler solution, particularly for nonlinear state estimation. Meanwhile, CVIAKF divides optimization objectives into conjugate and non-conjugate parts of nonlinear dynamical models, whereas conjugate computations and stochastic mirror-descent are applied, respectively. Notably, the reparameterization trick is employed to minimize the variance of stochastic gradients for the non-conjugate parts. The effectiveness of CVIAKF is validated through synthetic and real-world datasets of maneuvering target tracking.

The Internet of Robotic Things (IoRT) merges the capabilities of robotics with the connectivity and computing power of Internet of Things (IoT) technologies, enabling seamless data collection, processing, and exchange. This integration enhances robotic systems with greater intelligence, mobility, and autonomy, unlocking significant potential across various applications, including sustainable agriculture. However, deploying IoRT systems in unpredictable environments poses challenges, such as network instability and hardware failures, which have not been thoroughly explored in the literature. To address these issues, this article introduces Mobility-as-a-Resilience Service (MaaRS), a model that leverages the mobility of active uncrewed aerial vehicles (UAVs), strategically relocating them to critical points of interest in response to potential data collection failures, optimizing resource allocation and enhancing system resilience, particularly in smart farm scenarios. Additionally, a robust multiagent deep deterministic policy gradient (RMADDPG) method is devised to enable efficient task allocation and system recovery in the presence of model uncertainty, observation noise, and reward uncertainty. Extensive simulations demonstrate that the proposed method achieved a significant boost in performance, efficiency, and stability over the state-of-the-art.

The Erlang loss formula, also known as the Erlang B formula, has been known for over a century and has been used in a wide range of applications, from telephony to hospital intensive care unit management. It provides the blocking probability of arriving customers to a loss system involving a finite number of servers without a waiting room. Because of the need to introduce priorities in many services, an extension of the Erlang B formula to the case of a loss system with preemptive priority is valuable and essential. This paper analytically establishes the consistency between the global balance (steady state) equations for a loss system with preemptive priorities and a known result obtained using traffic loss arguments for the same problem. This paper, for the first time, derives this known result directly from the global balance equations based on the relevant multidimensional Markov chain. The paper also addresses the question of whether or not the well-known insensitivity property of the Erlang loss system is also applicable to the case of a loss system with preemptive priorities, provides explanations, and demonstrates through simulations that, except for the blocking probability of the highest priority customers, the blocking probabilities of the other customers are sensitive to the service time distributions and that a larger service time variance leads to a lower blocking probability of the lower priority traffic.