/pdf/convex-analysisnoer-san-nojin-zhan-nituite-5dl2rbmoyr.pdf

Convex Analysisの二,三の進展について

Probability and Measure

WITH the ever-widening scope of modern mathematical analysis and its many ramifications, it is quite impossible to include, in a single volume of reasonable size, an adequate and exhaustive discussion of the calculus in its more advanced stages. It therefore becomes necessary, in planning a thoroughly sound course in the subject, to consider several important aspects of the vast field confronting a modern writer. The limitation of space renders the selection of subject-matter fundamentally dependent upon the aim of the course, which may or may not be related to the content of specific examination syllabuses. Logical development, too, may lead to the inclusion of many topics which, at present, may only be of academic interest, while others, of greater practical value, may have to be omitted. The experience and training of the writer may also have, more or less, a bearing on both these considerations.Advanced CalculusBy Dr. C. A. Stewart. Pp. xviii + 523. (London: Methuen and Co., Ltd., 1940.) 25s.

Advanced Calculus I

国際会議開催報告:2013 IEEE International Symposium on Information Theory

Diagnosing problems in networks is a time-consuming and error-prone process. Existing tools to assist operators primarily focus on analyzing control plane configuration. Configuration analysis is limited in that it cannot find bugs in router software, and is harder to generalize across protocols since it must model complex configuration languages and dynamic protocol behavior.This paper studies an alternate approach: diagnosing problems through static analysis of the data plane. This approach can catch bugs that are invisible at the level of configuration files, and simplifies unified analysis of a network across many protocols and implementations. We present Anteater, a tool for checking invariants in the data plane. Anteater translates high-level network invariants into boolean satisfiability problems (SAT), checks them against network state using a SAT solver, and reports counterexamples if violations have been found. Applied to a large university network, Anteater revealed 23 bugs, including forwarding loops and stale ACL rules, with only five false positives. Nine of these faults are being fixed by campus network operators.

/pdf/debugging-the-data-plane-with-anteater-iis2j6n8oe.pdf

Debugging the data plane with anteater

The increasing demand of various services from the Internet has led to an exponential growth of Internet traffic in the last decade, and that growth is likely to continue. With this demand comes the increasing importance of network operations management, planning, provisioning and traffic engineering. A key input into these processes is the traffic matrix, and this is the focus of this chapter. The traffic matrix represents the volumes of traffic from sources to destinations in a network. Here, we first explore the various issues involved in measuring and characterising these matrices. The insights obtained are used to develop models of the traffic, depending on the properties of traffic to be captured: temporal, spatial or spatio-temporal properties. The models are then used in various applications, such as the recovery of traffic matrices, network optimisation and engineering activities, anomaly detection and the synthesis of artificial traffic matrices for testing routing protocols. We conclude the chapter by summarising open questions in Internet traffic matrix research and providing a list resources useful for the researcher and practitioner.

/pdf/internet-traffic-matrices-a-primer-3unf7agjhz.pdf

Internet Traffic Matrices: A Primer

The flow size distribution is a useful metric for traffic modeling and management. It is well known however that its estimation based on sampled data is problematic. Previous work has shown that flow sampling (FS) offers enormous statistical benefits over packet sampling, however it suffers from high resource requirements and is not currently used in routers. In this paper we present Dual Sampling, which can to a large extent provide flow-sampling-like statistical performance for packet-sampling-like computational cost. Our work is grounded in a Fisher information based approach recently used to evaluate a number of sampling schemes, excluding however FS, for TCP flows. We show how to revise and extend the approach to include FS as well as DS and others, and how to make rigorous and fair comparisons. We show how DS significantly outperforms other packet based methods, but also prove that DS is inferior to flow sampling. However, since DS is a two-parameter family of methods which includes FS as a special case, DS can be used to approach flow sampling continuously. We then describe a packet sampling based implementation of DS and analyze its key computational costs to show that router implementation is feasible. Our approach offers insights into many issues, including how the notions of 'flow quality' and 'packet gain' can be used to understand the relative performance of methods, and how the problem of optimal sampling can be formulated. Our work is theoretical with some simulation support and a case study on Internet data.

Towards optimal sampling for flow size estimation

Traffic matrices describe the volume of traffic between a set of sources and destinations within a network. These matrices are used in a variety of tasks in network planning and traffic engineering, such as the design of network topologies. Traffic matrices naturally possess complex spatiotemporal characteristics, but their proprietary nature means that little data about them is available publicly, and this situation is unlikely to change. Our goal is to develop techniques to synthesize traffic matrices for researchers who wish to test new network applications or protocols. The paucity of available data, and the desire to build a general framework for synthesis that could work in various settings requires a new look at this problem. We show how the principle of maximum entropy can be used to generate a wide variety of traffic matrices constrained by the needs of a particular task, and the available information, but otherwise avoiding hidden assumptions about the data. We demonstrate how the framework encompasses existing models and measurements, and we apply it in a simple case study to illustrate the value.

/pdf/spatiotemporal-traffic-matrix-synthesis-2xa1m7pphh.pdf

Spatiotemporal Traffic Matrix Synthesis

We propose a novel access technique for cellular downlink resource sharing. In particular, a distributed self-selection procedure is combined with the technique of compressed sensing to identify a set of users who are getting simultaneous access to the downlink broadcast channel. The performance of the proposed method is analyzed, and its suitability as an alternate access mechanism is argued.

Downlink scheduling using compressed sensing

The flow size distribution is a useful metric for traffic modeling and management. Its estimation based on sampled data, however, is problematic. Previous work has shown that flow sampling (FS) offers enormous statistical benefits over packet sampling but high resource requirements precludes its use in routers. We present dual sampling (DS), a two-parameter family, which, to a large extent, provide FS-like statistical performance by approaching FS continuously, with just packet-sampling-like computational cost. Our work utilizes a Fisher information based approach recently used to evaluate a number of sampling schemes, excluding FS, for TCP flows. We revise and extend the approach to make rigorous and fair comparisons between FS, DS, and others. We show how DS significantly outperforms other packet based methods, including Sample and Hold, the closest packet sampling-based competitor to FS. We describe a packet sampling-based implementation of DS and analyze its key computational costs to show that router implementation is feasible. Our approach offers insights into numerous issues, including the notion of “flow quality” for understanding the relative performance of methods, and how and when employing sequence numbers is beneficial. Our work is theoretical with some simulation support and case studies on Internet data.

Paul Tune

Papers

Internet Traffic Matrices: A Primer

Towards optimal sampling for flow size estimation

Spatiotemporal Traffic Matrix Synthesis

Downlink scheduling using compressed sensing

Fisher Information in Flow Size Distribution Estimation