We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

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

To be agile and cost effective, data centers should allow dynamic resource allocation across large server pools. In particular, the data center network should enable any server to be assigned to any service. To meet these goals, we present VL2, a practical network architecture that scales to support huge data centers with uniform high capacity between servers, performance isolation between services, and Ethernet layer-2 semantics. VL2 uses (1) flat addressing to allow service instances to be placed anywhere in the network, (2) Valiant Load Balancing to spread traffic uniformly across network paths, and (3) end-system based address resolution to scale to large server pools, without introducing complexity to the network control plane. VL2's design is driven by detailed measurements of traffic and fault data from a large operational cloud service provider. VL2's implementation leverages proven network technologies, already available at low cost in high-speed hardware implementations, to build a scalable and reliable network architecture. As a result, VL2 networks can be deployed today, and we have built a working prototype. We evaluate the merits of the VL2 design using measurement, analysis, and experiments. Our VL2 prototype shuffles 2.7 TB of data among 75 servers in 395 seconds - sustaining a rate that is 94% of the maximum possible.

/pdf/vl2-a-scalable-and-flexible-data-center-network-dkbtxdift1.pdf

VL2: a scalable and flexible data center network

We analyze 20 large sets of actual variable-bit-rate (VBR) video data, generated by a variety of different codecs and representing a wide range of different scenes. Performing extensive statistical and graphical tests, our main conclusion is that long-range dependence is an inherent feature of VBR video traffic, i.e., a feature that is independent of scene (e.g., video phone, video conference, motion picture video) and codec. In particular, we show that the long-range dependence property allows us to clearly distinguish between our measured data and traffic generated by VBR source models currently used in the literature. These findings give rise to novel and challenging problems in traffic engineering for high-speed networks and open up new areas of research in queueing and performance analysis involving long-range dependent traffic models. A small number of analytic queueing results already exist, and we discuss their implications for network design and network control strategies in the presence of long-range dependent traffic. >

Long-range dependence in variable-bit-rate video traffic

To be agile and cost effective, data centers must allow dynamic resource allocation across large server pools. In particular, the data center network should provide a simple flat abstraction: it should be able to take any set of servers anywhere in the data center and give them the illusion that they are plugged into a physically separate, noninterfering Ethernet switch with as many ports as the service needs. To meet this goal, we present VL2, a practical network architecture that scales to support huge data centers with uniform high capacity between servers, performance isolation between services, and Ethernet layer-2 semantics. VL2 uses (1) flat addressing to allow service instances to be placed anywhere in the network, (2) Valiant Load Balancing to spread traffic uniformly across network paths, and (3) end system--based address resolution to scale to large server pools without introducing complexity to the network control plane. VL2's design is driven by detailed measurements of traffic and fault data from a large operational cloud service provider. VL2's implementation leverages proven network technologies, already available at low cost in high-speed hardware implementations, to build a scalable and reliable network architecture. As a result, VL2 networks can be deployed today, and we have built a working prototype. We evaluate the merits of the VL2 design using measurement, analysis, and experiments. Our VL2 prototype shuffles 2.7 TB of data among 75 servers in 395 s---sustaining a rate that is 94% of the maximum possible.

Queueing theory is generally known as the study of the performance of queues. In this paper, we are interested in another aspect of queueing theory, the constructions of queues via switched delay lines (SDLs). We consider three types of discrete-time queues: linear compressors, nonovertaking delay lines, and flexible delay lines. These three types of queues correspond to certain conditional nonblocking switches and (in a strict sense) nonblocking switches in switching theory. Analogous to their counterparts in switching theory, there exist multistage constructions for these three types of queues. Specifically, we develop a two-stage construction of a linear compressor. For nonovertaking delay lines and flexible delay lines, however, we develop a three-stage construction. Moreover, a flexible delay line can also be constructed by a layered Cantor network. As applications of these constructions, we show two optical switch architectures that achieve exact emulation of output-buffered switches.

Constructions of linear compressors, nonovertaking delay lines, and flexible delay lines for optical packet switching

In this letter, we consider the discrete-time setting and propose a construction of an optical flexible delay line by parallel variable optical delay lines (VODLs) under a very simple packet routing scheme. We show that to exactly emulate an optical flexible delay line with maximum delay d (time slots), where d is a positive integer, it is necessary and sufficient to have at least [(2d+1)/3] VODLs with maximum delay d (time slots) in our proposed architecture. We also show that under a uniform traffic model, the average number of busy VODLs is approximately d+1-(2d+1)(d/(d+1))d, which is quite close to our simulation result. Through simulations, we further show that if we can tolerate a loss probability of, say 10-3, then we only need at most 1.7 times of the average number of busy VODLs, which is much smaller than the worst-case bound [(2d+1)/3].

/pdf/emulation-of-an-optical-flexible-delay-line-by-parallel-20jr7udrcg.pdf

Emulation of an Optical Flexible Delay Line by Parallel Variable Optical Delay Lines

TCP congestion control has been widely discussed on various networks under wireline or wireless environment. Many research studies have been raised to help TCP be more sensitive to the network congestion by adding explicit notifications in TCP connection or letting the intermediate nodes in the network to join TCP congestion control. In GPRS/EGPRS systems and other 3G cellular networks, the radio network controller chooses among several channel coders according to the signal to interference ratio. Hence, the channel data rate that an individual user experiences is time-dependent and variable. We propose a TCP window control mechanism that adapts to the variable channel data rates. Our simulations show that the window adaptive TCP decreases the buffer occupancy and packet transmission delay, and achieves better throughput utilization when compared with the standard TCP Tahoe version and the Reno version.

Window Adaptive TCP for EGPRS Networks.

Recently there has been a tremendous growth in the popularity of wireless packet switched networks. In addition to the traditional voice services, wireless service providers and equipment manufacturers are working hard on offering higher speed data access over cellular wireless networks. One of the key challenges of the next generation wireless networks (such as EGPRS) is the ability to provide different grade of QoS (quality of service) services to the users. In the wireline networks, the QoS mechanisms have been extensively studied and researchers have agreed that weighted fair queueing (WFQ) is a popular scheduling algorithm to guarantee bounded delay, bounded throughput and fairness. However, adapting the WFQ scheduler to wireless networks is not trivial due to the location and weather dependent data rates. In this paper we propose optimal schemes that are based on combining WFQ with compensation techniques which swap channel access among traffic flows that experience variable data rates, so that the variable data rates are transparent to the users.

Weighted fair queueing and compensation techniques for wireless packet switched networks

The constructions of optical buffers is one of the most critically sought after optical technologies in all-optical packet-switched networks, and constructing optical buffers directly via optical switches and fiber delay lines (SDL) has received a lot of attention recently in the literature. A practical and challenging issue of the constructions of optical buffers that has not been addressed before is on the fault tolerant capability of such constructions. In this paper, we focus on the constructions of fault tolerant linear compressors and linear decompressors. The basic network element for our constructions is scaled optical memory cell, which is constructed by a 2 x 2 optical crossbar switch and a fiber delay line. We give a multistage construction of a self-routing linear compressor by a concatenation of scaled optical memory cells. We also show that if the delays, say d1,d2,... ,dm , of the fibers in the scaled optical memory cells satisfy a certain condition (specifically, the condition in (A 2) given in Section I), then our multistage construction can be operated as a self-routing linear compressor with maximum delay Sigma M-F i=1 d i even after up to F of the M scaled optical memory cells fail to function properly, where 0 les F les M - 1. Furthermore, we prove that our multistage construction with the fiber delays d1, d2, ... , d M given by the generalized Fibonacci sequence of order F is the best among all constructions of a linear compressor that can tolerate up to F faulty scaled optical memory cells by using M scaled optical memory cells. Similar results are also obtained for the constructions of fault tolerant linear decompressors.

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Duan-Shin Lee

Papers

Constructions of linear compressors, nonovertaking delay lines, and flexible delay lines for optical packet switching

Emulation of an Optical Flexible Delay Line by Parallel Variable Optical Delay Lines

Window Adaptive TCP for EGPRS Networks.

Weighted fair queueing and compensation techniques for wireless packet switched networks

Constructions of Fault Tolerant Linear Compressors and Linear Decompressors