Performance Analysis of Queuing and Computer Networks

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Features

  • Includes simple, analytically tractable models, such as optimization of saturated CSMA/CD and CSMA/CA LANs
  • Presents models for complex systems as analyzable modifications and/or interconnections of simple models
  • Discusses in detail timing and synchronization in the analysis of discrete time (slotted) networks
  • Contains a wide variety of queuing models, including bursty, MMPP, approximate self-similar traffic, and fluid flow
  • Introduces queuing theory from the fundamental principles of Poisson and exponential distributions
  • Provides a brief yet rigorous, self-contained review of elementary probability theory in the appendix
  • Summary

    Performance Analysis of Queuing and Computer Networks develops simple models and analytical methods from first principles to evaluate performance metrics of various configurations of computer systems and networks. It presents many concepts and results of probability theory and stochastic processes.

    After an introduction to queues in computer networks, this self-contained book covers important random variables, such as Pareto and Poisson, that constitute models for arrival and service disciplines. It then deals with the equilibrium M/M/1/∞queue, which is the simplest queue that is amenable for analysis. Subsequent chapters explore applications of continuous time, state-dependent single Markovian queues, the M/G/1 system, and discrete time queues in computer networks. The author then proceeds to study networks of queues with exponential servers and Poisson external arrivals as well as the G/M/1 queue and Pareto interarrival times in a G/M/1 queue. The last two chapters analyze bursty, self-similar traffic, and fluid flow models and their effects on queues.

    Table of Contents

    Introduction
    Background
    Queues in Computers and Computer Networks
    Queuing Models
    Conclusion
    Characterization of Data Traffic
    The Pareto Random Variable
    The Poisson Random Variable
    Simulation
    Elements of Parameter Estimation
    Sequences of Random Variables
    Elements of Digital Communication and Data Link Performance
    The M/M/1/Queue
    Derivation of Equilibrium State Probabilities
    Simple Performance Figures
    Response Time and Its Distribution
    More Performance Figures for M/M/1/∞ System
    Waiting Time Distribution
    Departures from Equilibrium M/M/1/∞ System
    Analysis of ON-OFF Model of Packet Departures
    Round Robin Operating System
    Examples
    Analysis of Busy Times
    Forward Data Link Performance and Optimization
    State-Dependent Markovian Queues
    Stochastic Processes
    Continuous Parameter Markov Chains
    Markov Chains for State-Dependent Queues
    Intuitive Approach for Time Averages
    Statistical Analysis of Markov Chains’ Sample Functions
    Little’s Result
    Application Systems
    Medium Access in Local Area Networks
    The M/G/1 Queue
    Imbedded Processes
    Equilibrium and Long-Term Operation of M/G/1/∞Queue
    Derivation of the Pollaczek–Khinchin Mean Value Formula
    Application Examples
    Special Cases
    Discrete Time Queues
    Timing and Synchronization
    State Transitions and Their Probabilities
    Discrete Parameter Markov Chains
    Classification of States
    Analysis of Equilibrium Markov Chains
    Performance Evaluation of Discrete Time Queues
    Applications
    Conclusion
    Continuous Time Queuing Networks
    Model and Notation for Open Networks
    Global Balance Equations
    Traffic Equations
    The Product Form Solution
    Validity of Product Form Solution
    Development of Product Form Solution for Closed Networks
    Convolution Algorithm
    Performance Figures from the g(n,m) Matrix
    Mean Value Analysis
    Conclusion
    The G/M/1 Queue
    The Imbedded Markov Chain for G/M/1/∞Queue
    Analysis of the Parameter α
    Performance Figures in G/M/1/∞Queue
    Finite Buffer G/M/1/k Queue
    Pareto Arrivals in a G/M/1/∞Queue
    Queues with Bursty, MMPP, and Self-Similar Traffic
    Distinction between Smooth and Bursty Traffic
    Self-Similar Processes
    Hyperexponential Approximation to Shifted Pareto Interarrival Times
    Characterization of Merged Packet Sources
    Product Form Solution for the Traffic Source Markov Chain
    Joint Markov Chain for the Traffic Source and Queue Length
    Evaluation of Equilibrium State Probabilities
    Queues with MMPP Traffic and Their Performance
    Performance Figures
    Conclusion
    Analysis of Fluid Flow Models
    Leaky Bucket with Two State ON-OFF Input
    Little’s Result for Fluid Flow Systems
    Output Process of Buffer Fed by Two State ON-OFF Chain
    General Fluid Flow Model and Its Analysis
    Leaky Bucket Fed by M/M/1/∞ Queue Output
    Appendix: Review of Probability Theory
    Index
    An Introduction and Exercises appear in each chapter.

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