Today's data centers need efficient traffic management to improve resource utilization in their networks. In this work, we study a joint tenant (e.g., server or virtual machine) placement and routing problem to minimize traffic costs. These two complementary degrees of freedom-placement and routing-are mutually-dependent, however, are often optimized separately in today's data centers. Leveraging and expanding the technique of Markov approximation, we propose an efficient online algorithm in a dynamic environment under changing traffic loads. The algorithm requires a very small number of virtual machine migrations and is easy to implement in practice. Performance evaluation that employs the real data center traffic traces under a spectrum of elephant and mice flows, demonstrates a consistent and significant improvement over the benchmark achieved by common heuristics.

We develop DeepOPF as a Deep Neural Network (DNN) approach for solving security-constrained direct current optimal power flow (SC-DCOPF) problems, which are critical for reliable and cost-effective power system operation. DeepOPF is inspired by the observation that solving SC-DCOPF problems for a given power network is equivalent to depicting a high-dimensional mapping from the load inputs to the generation and phase angle outputs. We first train a DNN to learn the mapping and predict the generations from the load inputs. We then directly reconstruct the phase angles from the generations and loads by using the power flow equations. Such a predict-and-reconstruct approach reduces the dimension of the mapping to learn, subsequently cutting down the size of the DNN and the amount of training data needed. We further derive a condition for tuning the size of the DNN according to the desired approximation accuracy of the load-generation mapping. We develop a post-processing procedure based on $\ell_1$ -projection to ensure the feasibility of the obtained solution, which can be of independent interest. Simulation results for IEEE test cases show that DeepOPF generates feasible solutions with less than 0.2% optimality loss, while speeding up the computation time by up to two orders of magnitude as compared to a state-of-the-art solver.

To flexibly explore the trade-offs between storage space and access efficiency in reliable data storage systems, we describe two classes of erasure resilient coding schemes: basic and generalized pyramid codes. The basic pyramid codes can be simply derived from any existing codes, and thus all known efficient encoding/decoding techniques directly apply. The generalized pyramid codes are radically advanced new codes, which can further improve access efficiency and/or reliability upon the basic pyramid codes. We also establish a necessary condition for any failure pattern to be ever recoverable, and show that the generalized pyramid codes are optimal in failure recovery (i.e., the necessary condition is also sufficient, and any failure pattern that is ever recoverable can indeed be recovered).

To cope with increasing uncertainty from renewable generation and flexible load, grid operators need to solve alternative current optimal power flow (AC-OPF) problems more frequently for efficient and reliable operation. In this article, we develop a deep neural network (DNN) approach, called DeepOPF, for solving AC-OPF problems in a fraction of the time used by conventional iterative solvers. A key difficulty for applying machine learning techniques for solving AC-OPF problems lies in ensuring that the obtained solutions respect the equality and inequality physical and operational constraints. Generalized a prediction-and-reconstruction procedure in our previous studies, DeepOPF first trains a DNN model to predict a set of independent operating variables and then directly compute the remaining ones by solving the power flow equations. Such an approach not only preserves the power-flow balance equality constraints but also reduces the number of variables to be predicted by the DNN, cutting down the number of neurons and training data needed. DeepOPF then employs a penalty approach with a zero-order gradient estimation technique in the training process toward guaranteeing the inequality constraints. We also drive a condition for tuning the DNN size according to the desired approximation accuracy, which measures its generalization capability. It provides theoretical justification for using DNN to solve AC-OPF problems. Simulation results for IEEE 30/118/300-bus and a synthetic 2000-bus test cases demonstrate the effectiveness of the penalty approach. They also show that DeepOPF speeds up the computing time by up to two orders of magnitude as compared to a state-of-the-art iterative solver, at the expense of $< $ 0.2% cost difference.

Many important network design problems are fundamentally combinatorial optimization problems. A large number of such problems, however, cannot readily be tackled by distributed algorithms. The Markov approximation framework studied in this paper is a general technique for synthesizing distributed algorithms. We show that when using the log-sum-exp function to approximate the optimal value of any combinatorial problem, we end up with a solution that can be interpreted as the stationary probability distribution of a class of time-reversible Markov chains. Selected Markov chains among this class yield distributed algorithms that solve the log-sum-exp approximated combinatorial network optimization problem. By examining three applications, we illustrate that the Markov approximation technique not only provides fresh perspectives to existing distributed solutions, but also provides clues leading to the construction of new distributed algorithms in various domains with provable performance. We believe the Markov approximation techniques will find applications in many other network optimization problems.

Today's Internet has witnessed an increase in the popularity of mobile video streaming, which is expected to exceed 3/4 of the global mobile data traffic by 2019. To satisfy the considerable amount of mobile video requests, video service providers have been pushing their content delivery infrastructure to edge networks-from regional content delivery network (CDN) servers to peer CDN servers (e.g., smartrouters in users' homes)-to cache content and serve users with storage and network resources nearby. Among the edge network content caching paradigms, Wi-Fi access point caching and cellular base station caching have become two mainstream solutions. Thus, understanding the effectiveness and performance of these solutions for large-scale mobile video delivery is important. However, the characteristics and request patterns of mobile video streaming are unclear in practical wireless network. In this paper, we use real-world data sets containing 50 million trace items of nearly 2 million users viewing more than 0.3 million unique videos using mobile devices in a metropolis in China over two weeks, not only to understand the request patterns and user behaviors in mobile video streaming, but also to evaluate the effectiveness of Wi-Fi and cellular-based edge content caching solutions. To understand the performance of edge content caching for mobile video streaming, we first present temporal and spatial video request patterns, and we analyze their impacts on caching performance using frequency-domain and entropy analysis approaches. We then study the behaviors of mobile video users, including their mobility and geographical migration behaviors, which determine the request patterns. Using trace-driven experiments, we compare strategies for edge content caching, including least recently used (LRU) and least frequently used (LFU), in terms of supporting mobile video requests. We reveal that content, location, and mobility factors all affect edge content caching performance. Moreover, we design an efficient caching strategy based on the measurement insights and experimentally evaluate its performance. The results show that our design significantly improves the cache hit rate by up to 30% compared with LRU/LFU.