TAILIEUCHUNG - Queueing Theory

In general we do not like to wait. But reduction of the waiting time usually requires extra investments. To decide whether or not to invest, it is important to know the e ect of the investment on the waiting time. So we need models and techniques to analyse such this course we treat a number of elementary queueing models. Attention is paid to methods for the analysis of these models, and also to applications of queueing models. Important application areas of queueing models are production systems, transportation and stocking systems, communication systems and information processing systems. Queueing models are particularly useful for the design of. | Queueing Theory Ivo Adan and Jacques Resing Department of Mathematics and Computing Science Eindhoven University of Technology . Box 513 5600 MB Eindhoven The Netherlands February 28 2002 Contents 1 Introduction 7 Examples . 7 2 Basic concepts from probability theory 11 Random variable. 11 Generating function. 11 Laplace-Stieltjes transform. 12 Useful probability distributions . 12 Geometric distribution. 12 Poisson distribution. 13 Exponential distribution. 13 Erlang distribution. 14 Hyperexponential distribution. 15 Phase-type distribution. 16 Fitting distributions . 17 Poisson process. 18 Exercises. 20 3 Queueing models and some fundamental relations 23 Queueing models and Kendall s notation. 23 Occupation rate. 25 Performance measures . 25 Little s law . 26 PASTA property . 27 Exercises. 28 4 M M 1 queue 29 Time-dependent behaviour. 29 Limiting behavior . 30 Direct approach. 31 Recursion . 31 Generating function approach . 32 Global balance principle . 32

• Toán học
• probability theory
• Random variable
• Generating function
• Geometric distribution
• Poisson distribution
• Exponential distribution
• Erlang distribution
• Lecture Probability Theory
• Lý thuyết xác suất
• Extinction Probability for Queues
• Extinction Probability for Martingales
• Axioms of Probability
• Conditional probability
• Properties of conditional probability
• Binomial Random Variable Applications
• Conditional Probability Density Function
• Stirling’s Formula
• Two Random Variables
• Joint probability density function
• Multiple Random Variables
• Hai biến ngẫu nhiên
• Bernoulli Trials
• Bernoulli Numbers
• Day trading strategy
• Random Variables
• Distribution Function
• Continuous type random variables
• Discrete type random variables
• Function of a Random Variable
• Functions of a discrete type r v
• Expected Value
• Characteristic Function
• One Function of Two Random Variables
• Poisson random
• Two Functions of Two Random Variables
• Joint Moments
• Joint Characteristic Functions
• Conditional Density Functions
• Conditional Expected Values
• Principles of Parameter Estimation
• Parameter Estimation
• Maximum Likelihood
• The Weak Law of Large numbers
• The Strong Law of Large numbers
• Stochastic Processes
• Stationary Stochastic Processes
• Systems with Stochastic Inputs
• Poisson Processes
• Distribution of number of arrivals
• Distribution of interarrival times
• Mean square Estimation
• Minimization of the Mean Square Error
• Long Term Trends
• Hurst Phenomena
• Power Spectrum
• Power Spectra
• Linear Systems
• Series Representation of Stochastic processes
• Discrete mathematics
• Modeling computation
• Number theory
• Advanced counting techniques
• Discrete probability
• Bayes’ theorem
• probability
• theory
• measure
• lectures
• Fundamental
• Event algebra
• Statistics biologists
• Independent events
• Frequently applied probability distributions
• Networking theory
• Queueing Theory
• Lecture Networking theory
• Packet networks
• The poisson process
• Little’s Theorem
• Probability models
• Definitions of probability
• Axiom systems
• Elements of asymptotic theory
• Criteria for point estimation