However, despite its claims, this book is an excellent introduction to mathematical modelling, with a wealth of interesting case studies and lovely mathematics that will appeal to many of its target audience final year undergraduates, Masters and PhD students working in 'practical' mathematical modelling. The source of most of the case studies comes from the Study Groups with Industry and Mathematics that originated in 1968 at Oxford, organized by Alan Taylor and Leslie Fox, but is now a global activity. The book describes the type of problem, how they are approached and funded (typically a surprisingly cheap £10 000 to £15 000). The first chapter covers the mathematical preliminaries for the case studies which are all based on continuous media, and so all that is needed is diffusion and flow and deformation of solids and fluids. The next four chapters are based on elliptic partial differential equations and relate to simulation of a type of compressor, determination of the viscosity of a carbon paste used in smelting, simulation of an instrument for determining density, and modelling a form of nondestructive testing of pressure vessels. There follow six chapters devoted to a range of applications of the diffusion equation and various non-linear effects. These cover the cooking of a single cereal grain, waves of epidemics in animal populations, catalytic converters, problems with blast furnaces, the cooling of hot glass, and crystal growth. Chapter 11 looks at the load responses of filled viscoelastic materials. The last two chapters, based on hyperbolic equations, model the noise produced by a bird scare gun and the paper tension variations in a printing press.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/FB9EBD3320909B8F7F968615CD8463B2/S0025557200173425a.pdf/div-class-title-span-class-italic-statistical-inference-span-2nd-edn-by-paul-h-garthwaite-ian-t-jolliffe-and-byron-jones-pp-328-40-hbk-2002-isbn-0-19-857226-3-oxford-university-press-div.pdf

Statistical inference (2nd edn), by Paul H. Garthwaite, Ian T. Jolliffe and Byron Jones. Pp.328. £40 (hbk). 2002. ISBN 0 19 857226 3 (Oxford University Press).

Review: A survey on content-centric technologies for the current Internet: CDN and P2P solutions

Many important network design problems can be formulated as a combinatorial optimization problem. 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. Certain carefully designed Markov chains among this class yield distributed algorithms that solve the log-sum-exp approximated combinatorial network optimization problem. By three case studies, we illustrate that Markov approximation technique not only can provide fresh perspective to existing distributed solutions, but also can help us generate new distributed algorithms in various domains with provable performance. We believe the Markov approximation framework will find applications in many network optimization problems, and this paper serves as a call for participation.

/pdf/markov-approximation-for-combinatorial-network-optimization-jgr6xr8asv.pdf

Markov Approximation for Combinatorial Network Optimization

Internet-based cloud computing is a new computing paradigm aiming to provide agile and scalable resource access in a utility-like fashion. Other than being an ideal platform for computation-intensive tasks, clouds are believed to be also suitable to support large-scale applications with periods of flash crowds by providing elastic amounts of bandwidth and other resources on the fly. The fundamental question is how to configure the cloud utility to meet the highly dynamic demands of such applications at a modest cost. In this paper, we address this practical issue with solid theoretical analysis and efficient algorithm design using Video on Demand (VoD) as the example application. Having intensive bandwidth and storage demands in real time, VoD applications are purportedly ideal candidates to be supported on a cloud platform, where the on-demand resource supply of the cloud meets the dynamic demands of the VoD applications. We introduce a queueing network based model to characterize the viewing behaviors of users in a multichannel VoD application, and derive the server capacities needed to support smooth playback in the channels for two popular streaming models: client-server and P2P. We then propose a dynamic cloud resource provisioning algorithm which, using the derived capacities and instantaneous network statistics as inputs, can effectively support VoD streaming with low cloud utilization cost. Our analysis and algorithm design are verified and extensively evaluated using large-scale experiments under dynamic realistic settings on a home-built cloud platform.

CloudMedia: When Cloud on Demand Meets Video on Demand

In recent years there have been several large-scale deployments of P2P live video systems. Existing and future P2P live video systems will offer a large number of channels, with users switching frequently among the channels. In this paper, we develop infinite-server queueing network models to analytically study the performance of multi-channel P2P streaming systems. Our models capture essential aspects of multi-channel video systems, including peer channel switching, peer churn, peer bandwidth heterogeneity, and Zipf-like channel popularity. We apply the queueing network models to two P2P streaming designs: the isolated channel design (ISO) and the View-Upload Decoupling (VUD) design. For both of these designs, we develop efficient algorithms to calculate critical performance measures, develop an asymptotic theory to provide closed-form results when the number of peers approaches infinity, and derive near- optimal provisioning rules for assigning peers to groups in VUD. We use the analytical results to compare VUD with ISO. We show that VUD design generally performs significantly better, particularly for systems with heterogeneous channel popularities and streaming rates.

/pdf/queuing-network-models-for-multi-channel-p2p-live-streaming-4a3xo4hmiu.pdf

Queuing Network Models for Multi-Channel P2P Live Streaming Systems

Peer-assisted streaming is a promising way for service providers to offer high-quality IPTV to consumers at reasonable cost. In peer-assisted streaming, the peers exchange video chunks with one another, and receive additional data from the central server as needed. In this paper, we analyze how to provision resources for the streaming system, in terms of the server capacity, the video quality, and the depth of the distribution trees that deliver the content. We derive the performance bounds for minimum server load, maximum streaming rate, and minimum tree depth under different peer selection constraints. Furthermore, we show that our performance bounds are actually tight, by presenting algorithms for constructing trees that achieve our bounds.

/pdf/performance-bounds-for-peer-assisted-live-streaming-tdkn8hbjjl.pdf

Performance bounds for peer-assisted live streaming

Two of the fundamental problems in peer-to-peer (P2P) streaming are as follows: what is the maximum streaming rate that can be sustained for all receivers, and what peering algorithms can achieve close to this maximum? These problems of computing and approaching the P2P streaming capacity are often challenging because of the constraints imposed on overlay topology. In this paper, we focus on the limit of P2P streaming rate under node degree bound, i.e., the number of connections a node can maintain is upper bounded. We first show that the streaming capacity problem under node degree bound is NP Complete in general. Then, for the case of node out-degree bound, through the construction of a “Bubble algorithm”, we show that the streaming capacity is at least half of that of a much less restrictive and previously studied case, where we bound the node degree in each streaming tree but not the degree across all trees. Then, for the case of node total-degree bound, we develop a “Cluster-Tree algorithm” that provides probabilistic guarantee of achieving a rate close to the maximum rate achieved under no degree bound constraint, when the node degree bound is logarithmic in network size. The effectiveness of these algorithms in approaching the capacity limit is demonstrated in simulations using uplink bandwidth statistics of Internet hosts. Both analysis and numerical experiments show that peering in a locally dense and globally sparse manner achieves near-optimal streaming rate if the degree bound is at least logarithmic in network size.

/pdf/p2p-streaming-capacity-under-node-degree-bound-2xepg2jtty.pdf

P2P Streaming Capacity under Node Degree Bound

Peer-to-peer (P2P) systems provide a scalable way to stream content to multiple receivers over the Internet. The maximum rate achievable by all receivers is the capacity of a P2P streaming session. We provide a taxonomy of sixteen problem formulations, depending on whether there is a single P2P session or there are multiple concurrent sessions, whether the given topology is a full mesh graph or an arbitrary graph, whether the number of peers a node can have is bounded or not, and whether there are nonreceiver relay nodes or not. In each formulation, computing P2P streaming capacity requires the computation of an optimal set of multicast trees, with an exponential complexity, except in three simplest formulations that have been recently solved with polynomial time algorithms. These solutions, however, do not extend to the other more general formulations. In this paper, we develop a family of constructive, polynomial-time algorithms that can compute P2P streaming capacity and the associated multicast trees, arbitrarily accurately for seven formulations, to a factor of 4-approximation for two formulations, and to a factor of log of the number of receivers for two formulations. The optimization problem is reformulated in each case so as to convert the combinatorial problem into a linear program with an exponential number of variables. The linear program is then solved using a primal-dual approach. The algorithms combine an outer loop of primal-dual update with an inner loop of smallest price tree construction, driven by the update of dual variables in the outer loop. We show that when the construction of smallest price tree can be carried out arbitrarily accurately in polynomial time, so can the computation of P2P streaming capacity. We also develop several efficient algorithms for smallest price tree construction. Using the developed algorithms, we investigate the impact of several factors on P2P streaming capacity using topologies derived from statistics of uplink capacities of Internet hosts.

/pdf/peer-to-peer-streaming-capacity-2vin81fzsw.pdf

Peer-to-Peer Streaming Capacity

Peer-to-peer (P2P) systems provide a scalable way to stream content to multiple receivers over the Internet and has become a major type of application traffic. The maximum rate achievable by all receivers is the capacity of a P2P streaming session. We provide a taxonomy of the problem formulations. In each formulation, computing P2P streaming capacity requires the computation of an optimal set of multicast trees, generally with an exponential complexity. We survey the family of constructive, polynomial-time algorithms that can compute P2P streaming capacity and the associated multicast trees, arbitrarily accurately for some of the formulations, and to some approximation factors in other formulations. Performance evaluation using large-scale Internet trace is provided before open problems in this research area are discussed.

P2P streaming capacity: Survey and recent results

We address the following question in this study: Can a network application detect not only the occurrence, but also the location of congestion? Answering this question will not only help the diagnostic of network failure and monitor server's QoS, but also help developers to engineer transport protocols with more desirable congestion avoidance behavior. The paper answers this question through new analytic results on the two underlying technical difficulties: 1) synchronization effects of loss and delay in TCP, and 2) distributed hypothesis testing using only local loss and delay data. We present a practical Congestion Location Detection (CLD) algorithm that effectively allows an end host to distributively detect whether congestion happens in the local access link or in more remote links. We validate the effectiveness of CLD algorithm with extensive experiments.

/pdf/congestion-location-detection-methodology-algorithm-and-308gdta99u.pdf

Shao Liu

Papers

Performance bounds for peer-assisted live streaming

P2P Streaming Capacity under Node Degree Bound

Peer-to-Peer Streaming Capacity

P2P streaming capacity: Survey and recent results

Congestion location detection: Methodology, algorithm, and performance