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6385 results in Communications and signal processing

Page 159 of 320

  • 4 - Scheduling in packet switches

  • from I - Network architecture and algorithms
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 86-109

  • Summary

    In Chapter 2, we learned about routing algorithms that determine the sequence of links a packet should traverse to get to its destination. But we did not explain how a router actually moves a packet from one link to another. To understand this process, let us first look at the architecture of a router. Generally speaking, a router has four major components: the input and the output ports, which are interfaces connecting the router to input and output links, respectively, a switch fabric, and a routing processor, as shown in Figure 4.1. The routing processor maintains the routing table and makes routing decisions. The switch fabric is the component that moves packets from one link to another link. In this chapter, we will assume that all packets are of equal size. In reality, packets in the Internet have widely variable sizes. In the switch fabric, packets are divided into equal-sized cells and reassembled at the output, hence our assumption holds.

    Earlier, we implicitly assumed that this switch fabric operates infinitely fast, so packets are moved from input ports to output ports immediately. This allowed us to focus on the buffers at output ports. So, all our discussions so far on buffer overflow probabilities are for output queues since an output buffer is the place where packets “enter” a link. For example, WFQ, introduced in Chapter 3, may be implemented at output port buffers to provide isolation among flows. However, in reality, the switch fabric does not really operate at infinite speed.

  • Preface

  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp xi-xii

  • Summary

    Why we wrote this book

    Traditionally, analytical techniques for communication networks discussed in textbooks fall into two categories: (i) analysis of network protocols, primarily using queueing theoretic tools, and (ii) algorithms for network provisioning which use tools from optimization theory. Since the mid 1990s, a new viewpoint of the architecture of a communication network has emerged. Network architecture and algorithms are now viewed as slow-time-scale, distributed solutions to a large-scale optimization problem. This approach illustrates that the layered architecture of a communication network is a natural by-product of the desire to design a fair and stable system. On the other hand, queueing theory, stochastic processes, and combinatorics play an important role in designing low-complexity and distributed algorithms that are viewed as operating at fast time scales.

    Our goal in writing this book is to present this modern point of view of network protocol design and analysis to a wide audience. The book provides readers with a comprehensive view of the design of communication networks using a combination of tools from optimization theory, control theory, and stochastic networks, and introduces mathematical tools needed to analyze the performance of communication network protocols.

    Organization of the book

    The book has been organized into two major parts. In the first part of the book, with a few exceptions, we present mathematical techniques only as tools to design algorithms implemented at various layers of a communication network. We start with the transport layer, and then consider algorithms at the link layer and the medium access layer, and finally present a unified view of all these layers along with the network layer.

  • 1 - Introduction

  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 1-4

  • Summary

    A communication network is an interconnection of devices designed to carry information from various sources to their respective destinations. To execute this task of carrying information, a number of protocols (algorithms) have to be developed to convert the information to bits and transport these bits reliably over the network. The first part of this book deals with the development of mathematical models which will be used to design the protocols used by communication networks. To understand the scope of the book, it is useful first to understand the architecture of a communication network.

    The sources (also called end hosts) that generate information (also called data) first convert the data into bits (0s and 1s) which are then collected into groups called packets. We will not discuss the process of converting data into packets in this book, but simply assume that the data are generated in the form of packets. Let us consider the problem of sending a stream of packets from a source S to destination D, and assume for the moment that there are no other entities (such as other sources or destinations or intermediate nodes) in the network. The source and destination must be connected by some communication medium, such as a coaxial cable, telephone wire, or optical fiber, or they have to communicate in a wireless fashion. In either case, we can imagine that S and D are connected by a communication link, although the link is virtual in the case of wireless communication.

  • 3 - Links: statistical multiplexing and queues

  • from I - Network architecture and algorithms
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 49-85

  • Summary

    In Chapter 2, we assumed that the transmission rates xr are positive, and we derived fair and stable resource allocation algorithms. In reality, since data are transmitted in the form of packets, the rates xr are converted to discrete window sizes, which results in bursty (non-smooth) arrival rates at the links in the network. In addition, many flows in the Internet are very short (consisting of only a few packets), for which the convergence analysis in the previous chapter does not apply. Further, there may also be flows which are not congestion controlled. Because of these deviations, the number of incoming packets at a link varies over time and may exceed the link capacity occasionally even if the mean arrival rate is less than the link capacity. So buffers are needed to absorb bursty arrivals and to reduce packet losses. To understand the effect of bursty arrivals and the role of buffering in communication networks, in this chapter we model packet arrivals at links as random processes and study the packet level performance at a link using discrete-time queueing theory. This chapter is devoted to answering the following questions.

  • • How large should the buffer size be to store bursty packet arrivals temporarily before transmission over a link?

  • • What is the relationship between buffer overflow probabilities, delays, and the burstiness of the arrival processes?

  • • How do we provide isolation among flows so that each flow is guaranteed a minimum rate at a link, independent of the burstiness of the other flows sharing the link?

Communication Networks
  • An Optimization, Control, and Stochastic Networks Perspective
  • R. Srikant, Lei Ying
  • Published online:
    30 January 2019
    Print publication:
    14 November 2013
  • Provides a modern mathematical approach to the design of communication networks for graduate students, blending control, optimization, and stochastic network theories. A broad range of performance analysis tools are discussed, including important advanced topics that have been made accessible to students for the first time. Taking a top-down approach to network protocol design, the authors begin with the deterministic model and progress to more sophisticated models. Network algorithms and protocols are tied closely to the theory, illustrating the practical engineering applications of each topic. The background behind the mathematical analyses is given before the formal proofs and is supported by worked examples, enabling students to understand the big picture before going into the detailed theory. End-of-chapter problems cover a range of difficulties, with complex problems broken into several parts, and hints to many problems are provided to guide students. Full solutions are available online for instructors.

  • 5 - Scheduling in wireless networks

  • from I - Network architecture and algorithms
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 110-141

  • Summary

    So far we have looked at resource allocation algorithms in networks with wireline links. In this chapter, we consider networks with wireless components. The major difference between wireless and wireline networks is that in wireless networks links contend for a common resource, namely the wireless spectrum. As a result, we have to design Medium Access Control (MAC) algorithms to decide which links access the wireless medium at each time instant. As we will see, wireless MAC algorithms have features similar to scheduling algorithms for high-speed switches, which were studied in Chapter 4. However, there are some differences: wireless networks are subject to time-varying link quality due to channel fluctuations, also known as channel fading; and transmissions in wireless networks may interfere with each other, so transmissions have to be scheduled to avoid interference. In addition, some wireless networks do not have a central coordinator to perform scheduling, so scheduling decisions have to be taken independently by each link. In this chapter, we will address the following issues specific to wireless networks.

  • • Does channel-state information play a critical role in scheduling in wireless networks?

  • • What is the capacity region of a cellular network, and what scheduling algorithm can be used to achieve the full capacity region?

  • • What is the capacity region of an ad hoc wireless network, what scheduling algorithm can be used to support the capacity region, and can the algorithm be implemented in a distributed fashion?

  • 9 - Queueing theory in continuous time

  • from II - Performance analysis
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 229-289

  • Summary

    We have learned about Discrete-Time Markov Chains (DTMCs) and discrete-time queueing systems in Chapter 3. In this chapter, we will look at continuous-time queueing systems, which were first developed to analyze telephone networks but has broader applications in communication networks, manufacturing, and transportation. The focus of this chapter is on the basics of continuous-time queueing theory and its application to communication networks. As in the case of discrete-time queueing systems, continuous-time queueing systems will be analyzed by relating them to Markov chains. For this purpose, we will first introduce Continuous-Time Markov Chains (CTMCs) and related concepts, such as the global balance equation, the local balance equation, and the Foster–Lyapunov theorem for CTMCs. Then, we will introduce and study simple queueing models including the M/M/1 queue, the M/GI/1 queue, the GI/GI/1 queue, and the Jackson network, as well as important concepts such as reversibility and insensitivity to service time distributions. Finally, we will relate CTMCs and queueing theory to the study of connection-level stability in the Internet, distributed admission control, telephone networks, and P2P file-sharing protocols. The following questions will be answered in this chapter.

  • • Under what conditions does a CTMC have a stationary distribution, and how should it be computed if it exists?

  • • What are the mean delays and queue lengths of simple queueing models?

  • • What is the reverse chain ofa CTMC, and how does the concept of reversibility help the calculation of the stationary distributions of queueing networks?

  • • How should CTMCs and queueing theory be used to model and analyze communication networks, including the Internet, telephone networks, and P2P networks?

  • 7 - Network protocols

  • from I - Network architecture and algorithms
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 165-194

  • Summary

    In this chapter, we explore the relationship between the algorithms discussed in the previous chapters and the protocols used in the Internet and wireless networks today. We will first discuss protocols used in the wired Internet, and then discuss protocols used in wireless networks.

    It is important to note that Internet congestion control protocols were not designed using the optimization formulation of the resource allocation problem discussed earlier. The predominant concern while designing these protocols was to minimize the risk of congestion collapse, i.e., large-scale buffer overflows, and hence they tended to be rather conservative in their behaviors. Even though the current Internet protocols were not designed with clearly defined fairness and stability ideas in mind, they bear a strong resemblance to the ideas of fair resource allocation that we have discussed so far. In fact, the utility maximization methods presented earlier provide a solid framework that could be for understanding the operation of these congestion control algorithms. Further, going forward, the utility maximization approach seems like a natural candidate framework that could be used to modify existing protocols to adapt to the evolution of the Internet as it continues to grow faster.

    In our earlier discussion on network utility maximization for the Internet, we assumed that routes are Axed. In this chapter, we discuss how the Internet chooses a route for each source-destination pair. Further, we also discuss the addressing protocol used in the Internet which allows one to implement routing protocols.

  • 8 - Peer-to-peer networks

  • from I - Network architecture and algorithms
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 195-226

  • Summary

    As we have seen so far, the Internet is a collection of physical links and routers that communicate with each other using a common set of protocols. Many applications run on top of this physical network. Some of these applications involve a collection of computers (called peers), which form a logical overlay network on top of the physical Internet. When communication takes place between the peers, the underlying physical network is transparent to them, and so the communication appears as though it takes place between the peers without the participation of any intermediate nodes. Hence, these types of networks are called Peer-to-Peer (P2P) networks.

    Typically, P2P networks are used for high bandwidth data transfer due to its scalability. In a traditional client-server system, the capacity of the system is limited by the bandwidth of the server. In a P2P network, peers upload data to other peers while receiving the data, so the network capacity increases with the number of peers. In this chapter, we will introduce three P2P applications: Distributed Hash Tables (DHTs), file-sharing applications, and streaming systems. A DHT protocol is a distributed database which stores (key, value) pairs at participating peers and facilitates the retrieval of content location. In filesharing applications, peers who are interested in the same content (such as a movie or a music file) exchange content pieces among themselves.

  • 11 - Geometric random graph models of wireless networks

  • from II - Performance analysis
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 323-339

  • Summary

    In earlier chapters, we considered distributed resource allocation algorithms for ad hoc wireless networks. We showed that there exist algorithms, called throughput-optimal algorithms, that maximize the network throughput. However, we do not yet have a simple expression for the total amount of information that can be transferred in an ad hoc wireless network. The problem of computing such an expression is challenging due to interference caused by simultaneous wireless transmissions. This chapter focuses on understanding the limitations on network throughput imposed by wireless interference. We will introduce geometric random graph models of wireless networks, in which n wireless nodes are distributed over a geographical area. Two nodes can communicate if the distance between them is smaller than a threshold and if no nodes near the receiver are transmitting at the same time. The capacity region of such a network is difficult to characterize exactly. Therefore, we will study the network capacity when the number of wireless nodes becomes large. We will show that, in such an asymptotic regime, one can obtain expressions for the network capacity that are asymptotically correct in a sense that will be made precise. A key insight of this chapter is that the throughput per source diminishes as the number of wireless nodes (in a fixed geographical area) increases because of wireless interference. The following questions will be addressed in this chapter.

  • What is the maximum achievable throughput in a network of n wireless nodes distributed over a geographical area, and how does the maximum throughput scale with the number of wireless nodes?

  • What algorithms should be used to achieve the maximum throughput?

  • 2 - Mathematics of Internet architecture

  • from I - Network architecture and algorithms
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 7-48

  • Summary

    In this chapter, we will develop a mathematical formulation of the problem of resource allocation in the Internet. A large communication network such as the Internet can be viewed as a collection of communication links shared by many sources. Congestion control algorithms are protocols that allocate the available network resources in a fair, distributed, and stable manner among the sources. In this chapter, we will introduce the network utility maximization formulation for resource allocation in the Internet, where each source is associated with a utility function Ur(xr), and xr is the transmission rate allocated to source r. The goal of fair resource allocation is to maximize the net utility Σr Ur (xr) subject to resource constraints. We will derive distributed, congestion control algorithms that solve the network utility maximization problem. In a later chapter, we will discuss the relationship between the mathematical models developed in this chapter to transport layer protocols used in the Internet. Optimality and stability of the congestion control algorithms will be established using convex optimization and control theory. We will also introduce a game-theoretical view of network utility maximization and study the impact of strategic users on the efficiency of network utility maximization. Finally, routing and IP addressing will be discussed. The following key questions will be answered in this chapter.

  • • What is fair resource allocation?

  • • How do we use convex optimization and duality to design distributed resource allocation algorithms to achieve a fair and stable resource allocation?

  • • What are the game-theoretic implications offair resource allocation?

  • 6 - Back to network utility maximization

  • from I - Network architecture and algorithms
  • R. Srikant, University of Illinois, Urbana-Champaign, Lei Ying, Arizona State University
  • Book:
    Communication Networks
    Published online:
    30 January 2019
    Print publication:
    14 November 2013, pp 142-164

  • Summary

    In Chapter 5, we looked at scheduling in wireless networks, where the focus was to design a scheduling algorithm that can support any traffic strictly within the capacity region. Implicitly, we assumed that data flows were regulated by congestion control so the incoming traffic was always within the capacity region. However, in practice, the behavior of congestion control algorithms themselves may be affected by scheduling algorithms. For example, a dual congestion control algorithm which reacts to delays, so the source rates would be regulated based on queueing delays, which could be quite different under different scheduling algorithms. Therefore, to achieve fair resource allocation in wireless networks, we need to revisit the network utility maximization formulation introduced in Chapter 2. In Chapter 2, we assumed that routes from sources to their destinations are given. In this chapter, we will study a more general model in which routes are not given and are part of the resource allocation decision process. We will consider the network utility maximization problem for wireless networks, and answer the following questions.

  • • How should the Lagrangian duality to derive joint congestion control, routing, and scheduling algorithms that maximize the sum network utility be used?

  • • How should the performance of the joint algorithms using discrete-time Markov chains be analyzed?

  • • What is the difference between the network utility maximization formulation for the Internet and that for wireless networks, and what is the rationale behind the difference?

  • • What is the relationship between proposed models/algorithms and practical MAC/physical layer protocols?

  • Preface

  • Pete Symons
  • Book:
    Digital Waveform Generation
    Published online:
    05 November 2013
    Print publication:
    17 October 2013, pp xi-xv

  • Summary

    Most electronic design engineers, irrespective of being the ‘analogue’ or ‘digital’ variety, are occasionally faced with the task of designing an oscillatory signal generator with particular implementation constraints, control and performance requirements. These requirements might include extremely low distortion, unusual ‘application specific’ waveshape, wide frequency tuning range, low temperature drift, and so on. Historically, such a task will have been tackled with a wholly analogue design, possibly augmented by digital control, where extremely high levels of performance are evident in some cases. If we take high-end audio test instrumentation as an example, the now legendary Hewlett Packard HP8903B and Audio Precision AP1 audio test sets both use digitally controlled analogue state variable oscillators to generate extremely low distortion sine waves. The state variable analogue oscillator is effectively an analogue computer model designed to compute solutions of a second-order differential equation. A specific class of solution (under certain parametric conditions) is a continuous sinusoidal oscillation. These generators are outstanding examples of what can be achieved with innovative analogue design. However, the world is becoming increasingly digital and very high levels of digital processing power can be implemented at relatively low cost. Various ‘all digital’ waveform generation techniques are therefore now practicable; and when all of their advantages are weighed up against the disadvantages (yes, digital processing is not necessarily a panacea to guarantee ideal performance), they nearly always represent the best solution. This approach is reinforced, if not driven, by the ever-improving performance of commercial digital to analogue conversion (DAC) devices as measured by their spurious-free dynamic range (i.e. distortion) and bandwidth. It is not unreasonable to state that the integrated DAC is the foremost enabling technology for nearly all applications of digital waveform generation. Exceptions to this observation apply to purely digital signals, which exist as a discrete-time sequence of binary numbers representing the signal waveform samples.

Page 159 of 320