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Convex Analysisの二,三の進展について

Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

The design and optimization of multicarrier communications systems often involve a maximization of the total throughput subject to system resource constraints. The optimization problem is numerically difficult to solve when the problem does not have a convexity structure. This paper makes progress toward solving optimization problems of this type by showing that under a certain condition called the time-sharing condition, the duality gap of the optimization problem is always zero, regardless of the convexity of the objective function. Further, we show that the time-sharing condition is satisfied for practical multiuser spectrum optimization problems in multicarrier systems in the limit as the number of carriers goes to infinity. This result leads to efficient numerical algorithms that solve the nonconvex problem in the dual domain. We show that the recently proposed optimal spectrum balancing algorithm for digital subscriber lines can be interpreted as a dual algorithm. This new interpretation gives rise to more efficient dual update methods. It also suggests ways in which the dual objective may be evaluated approximately, further improving the numerical efficiency of the algorithm. We propose a low-complexity iterative spectrum balancing algorithm based on these ideas, and show that the new algorithm achieves near-optimal performance in many practical situations

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Dual methods for nonconvex spectrum optimization of multicarrier systems

The state-of-the-art models for medical image segmentation are variants of U-Net and fully convolutional networks (FCN). Despite their success, these models have two limitations: (1) their optimal depth is apriori unknown, requiring extensive architecture search or inefficient ensemble of models of varying depths; and (2) their skip connections impose an unnecessarily restrictive fusion scheme, forcing aggregation only at the same-scale feature maps of the encoder and decoder sub-networks. To overcome these two limitations, we propose UNet++, a new neural architecture for semantic and instance segmentation, by (1) alleviating the unknown network depth with an efficient ensemble of U-Nets of varying depths, which partially share an encoder and co-learn simultaneously using deep supervision; (2) redesigning skip connections to aggregate features of varying semantic scales at the decoder sub-networks, leading to a highly flexible feature fusion scheme; and (3) devising a pruning scheme to accelerate the inference speed of UNet++. We have evaluated UNet++ using six different medical image segmentation datasets, covering multiple imaging modalities such as computed tomography (CT), magnetic resonance imaging (MRI), and electron microscopy (EM), and demonstrating that (1) UNet++ consistently outperforms the baseline models for the task of semantic segmentation across different datasets and backbone architectures; (2) UNet++ enhances segmentation quality of varying-size objects—an improvement over the fixed-depth U-Net; (3) Mask RCNN++ (Mask R-CNN with UNet++ design) outperforms the original Mask R-CNN for the task of instance segmentation; and (4) pruned UNet++ models achieve significant speedup while showing only modest performance degradation. Our implementation and pre-trained models are available at https://github.com/MrGiovanni/UNetPlusPlus .

UNet++: Redesigning Skip Connections to Exploit Multiscale Features in Image Segmentation

This document provides updates to IEEE Std 802.16's MIB for the MAC, PHY and asso- ciated management procedures in order to accommodate recent extensions to the standard.

IEEE Standard for Local and Metropolitan Area Networks Part 16: Air Interface for Fixed Broadband Wireless Access Systems Draft Amendment: Management Information Base Extensions

In this paper, we provide a theoretical framework for cross-layer optimization for orthogonal frequency division multiplexing (OFDM) wireless networks. The utility is used in our study to build a bridge between the physical layer and the media access control (MAC) layer and to balance the efficiency and fairness of wireless resource allocation. We formulate the cross-layer optimization problem as one that maximizes the average utility of all active users subject to certain conditions, which are determined by adaptive resource allocation schemes. We present necessary and sufficient conditions for utility-based optimal subcarrier assignment and power allocation and discuss the convergence properties of optimization. Numerical results demonstrate a significant performance gain for the cross-layer optimization and the gain increases with the number of active users in the networks.

Cross-layer optimization for OFDM wireless networks-part I: theoretical framework

We have established a theoretical framework for cross-layer optimization in orthogonal frequency division multiplexing (OFDM) wireless networks. In this paper, we focus on effective and practical algorithms for efficient and fair resource allocation in OFDM wireless networks. We have taken various conditions into account and developed a variety of efficient algorithms, including sorting-search dynamic subcarrier assignment, greedy bit loading, and power allocation, as well as objective aggregation algorithms. We have also modified those algorithms for a certain type of nonconcave utility functions. To further improve performance by exploiting time diversity, a low-pass time filter can be easily incorporated into all of the algorithms. Simulation results have confirmed that the utility-based cross-layer optimization can significantly enhance the system performance and guarantee fairness. The gains come from multiuser diversity, frequency diversity, as well as time diversity. The fairness is automatically achieved by the behavior of marginal utility functions.

Cross-layer optimization for OFDM wireless networks-part II: algorithm development

This article discusses downlink resource allocation and scheduling for OFDM-based broadband wireless networks. We present a cross-layer resource management framework leveraged by utility optimization. It includes utility-based resource management and QoS architecture, resource allocation algorithms, rate-based and delay-based multichannel scheduling that exploits wireless channel and queue information, and theoretical exploration of the fundamental mechanisms in wireless resource management, such as capacity, fairness, and stability. We also provide a solution that can efficiently allocate resources for heterogeneous traffic with diverse QoS requirements.

Utility-based resource allocation and scheduling in OFDM-based wireless broadband networks

This paper investigates multiuser downlink data scheduling with quality-of-service (QoS) provisioning over multiple shared fading channels, which, for a network point of view, provides line flexibility and granularity for resource allocation. A user-centric metric-a utility function with respect to mean waiting time-which is able to maintain fairness among users while providing delay QoS to individual users is used. This paper proposes scheduling algorithms that are aware of both channel and queue state information to achieve the maximum aggregate utility in the network. Simulation results confirm the significant performance and stability improvement provided by the utility-based scheduling scheme balancing multiuser diversity and queueing delay.

Joint channel-aware and queue-aware data scheduling in multiple shared wireless channels

In this paper, we provide an asymptotic performance analysis of channel-aware packet scheduling based on the extreme value theory. We first address the average throughput of systems with a homogeneous average signal-to-noise ratio (SNR), and obtain its asymptotic expression. Compared with the exact throughput expression, the asymptotic one, which is applicable to a broader range of fading channels, is more concise and easier from which to get insights. Furthermore, we confirm the accuracy of the asymptotic results by theoretical analysis and numerical simulation. For a system with heterogeneous SNRs, normalized-SNR-based scheduling needs to be used for fairness. We also investigate the asymptotic average throughput of the normalized-SNR-based scheduling, and prove that the average throughput in this case is less than that in the homogeneous case with a power constraint

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Guocong Song

Papers

Cross-layer optimization for OFDM wireless networks-part I: theoretical framework

Cross-layer optimization for OFDM wireless networks-part II: algorithm development

Utility-based resource allocation and scheduling in OFDM-based wireless broadband networks

Joint channel-aware and queue-aware data scheduling in multiple shared wireless channels

Asymptotic Throughput Analysis for Channel-Aware Scheduling