Probability and Queuing Theory

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Published by Vijay Nicole Imprints Private Limited

Publication Date: Thu Dec 01 00:00:00 UTC 2011 Available in all formats

ISBN: 9789394681453

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Description

Table of contents

Biographical note

User Reviews

This book Probability and Queuing Theory is designed to meet the revised and latest requirements of Anna University. The emphasis is on clear concepts, comprehensive coverage, solved problems and easy understanding.

Cover
Title Page
Copyright Page
Contents
Preface
Acknowledgement
CHAPTER 1 RANDOM VARIABLES
- Introduction
  - Random Experiment
  - Sample Space
  - Trial and Event
  - Probability
  - Axioms of Theory of Probability
  - Theorems
  - Conditional Probability
- Baye’s Theorem
- Random Variables
- Discrete Random Variable
- Continuous Random Variable
- Probability Mass Function
- Probability Density Function
- Cumulative Distribution Function (CDF)
  - Mathematical Expectation or Mean of Random Variable
  - Variance of the Random Variable
- Moments of the Random Variable
- Moments Generating Function (MGF)
  - Properties
- Standard Distributions
- Discrete Distributions
- Binomial Distribution
  - Assumptions for Binomial Distribution
  - Mean and Variance of a Binomial Distribution
  - Moment Generating Function (MGF) of a Binomial Distribution
  - Additive Property of Binomial Distribution
- Poisson Distribution
  - Mean and Variance of Poisson Distribution
  - MGF of Poisson Distribution
  - Additive Property of Poisson Distribution
- Geometric Distribution
  - Mean and Variance of Geometric Distribution
  - MGF Functions of Geometric Distribution
  - Memoryless (forgetfulness) Property of Geometric Distribution
- Negative Binomial Distribution
  - MGF of Negative Binomial Distribution
  - Mean and Variance of NBD
- Continuous Distributions
- Uniform Distribution
  - Mean and Variance Uniform Distribution
  - MGF of Uniform Distribution
- Exponential Distribution
  - Mean and Variance of Exponential Distribution
  - Moment Generating Function (MGF) of Exponential Distribution
  - Memoryless Property of Exponential Distribution [Forgetfulness Property]
- Gamma Distribution (Erlang Distribution)
  - Mean and Variance of Gamma Distribution
  - Moment Generating Function (MGF) of Gamma Distribution
  - Additive Property
- Weibull Distribution
  - Mean and Variance of Weibull Distribution
  - Moment Generating Function (MGF)
- Exercise
- Solved Two Mark Questions
CHAPTER 2 Two Dimensional Random Variables
- Joint distributions—Marginal and conditional distributions
  - Two Dimensional Random Variable
  - Two Dimensional Discrete Random Variable
  - Two Dimensional Continuous Random Variable
  - Joint Probability Function
  - Joint Probability Density Function
  - Marginal Distribution Function
  - Marginal Density Function
  - Joint (Cumulative) Distribution Function
  - Conditional Distribution of a Random Variable
- Independent Random Variables
- Covariance
  - Properties
- Correlation
  - Type of Correlation
  - Karl Pearson’s Co-efficient of Correlation
  - Rank Correlation
  - Repeated Rank Correlation
- Regression
  - Regression Co-efficient
- Transformation of Random Variables
- Central Limit Theorem (CLT)
  - Applications of CLT
- Exercise
- Solved Two marks Questions
CHAPTER 3 Classification of Random Process
- Classification of Random Process
  - Deterministic (or) Predictable Random Process
  - Non-Deterministic Random Process
  - Correlation
  - Mean of a Random Process
  - Auto Correlation of Random Process
  - Auto Covariance or Covariance Function of Random Process
  - Relation Between Mean, Auto Correlation and Auto Covariance
  - Cross Correlation
  - Cross Covariance
  - Relation Between Cross Correlation and Cross Covariance
- Stationary Process
  - Strict Sense Stationary (SSS) Process
  - Jointly Stationary Process
  - Wide Sense Stationary (WSS) Process
  - Non-stationary (or) Evolutionary Process
  - Time Average and Ensemble Average
  - Markov Process
  - Classification of Markov Process
  - One Step Transition Probability
  - Homogeneous Markov Chain
  - Stochastic Matrix
- Transition Probability Matrix (TPM)
  - Regular Matrix
  - N-Step Transition Probability
  - Chapman-Kolmogorov Theorem
  - Probability Distribution of the Process
  - Steady State (or) Stationary Distribution
- Poisson Process
  - Probability function of Poisson process{X(t)}
  - Probability Law for Poisson Process
  - MGF of Poisson Process
  - Autocorrelation of the Poisson Process
  - Auto Covariance of Poisson Process
  - Correlation coefficient of poisson process
  - Properties of Poisson Process
- Binomial Process
- Normal(Gaussian) Process
- Sine Wave Process
- Random Telegraph Process
  - Mean and Autocorrelation of Telegraph Process
- Exercise
- Solved Two Mark Questions
CHAPTER 4 Queueing Theory
- Introduction to Queueing Models
  - Characteristics of a Queueing System
- Customer Behavior
- Kendal’s Notation for Representing Queue Mode
- Model 1: Single Server Poisson Queue Model (M/M/1) : (∞/FIFO)
- Model 2: Multi Server Poisson Queue Model
- Model 3: Finite Capacity, Single Server Queue(M/M/1) : (N/FCFS)
- Model 4: Finite Capacity Multi Server Queue Model(M/M/C) : (N/FCFS).
- Model 5: [Self Service Model]
- Exercise
- Solved Two Mark Questions
CHAPTER 5 Non Markovian Queues and Queue Networks
- Birth and death Process
  - Probability Distribution of X(t)
  - Pure - Birth and Pure - Death Process
  - Probability Pn (t) of Pure - Birth Process
  - Probability Function of Pure - Death Process
- Pollaczek - Khintchine (P-K) Formula
- M/G/1 Queue
  - Various Formula for (M/ G / 1) : (∞ / GD)
- Networks of Queues
- Series Queues
  - Series Queues with Blocking
  - Jackson Network
  - Closed Jackson Networks
  - The Arrival Theorem
  - Mean Value Analysis
- Exercise
- Solved Two Marks Questions
Question Paper

Dr. R Pugalarsu is currently Associate Professor, Department of Mathematics, RMK Group of Institution, Chennai.

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Description

Table of contents

Cover
Title Page
Copyright Page
Contents
Preface
Acknowledgement
CHAPTER 1 RANDOM VARIABLES
- Introduction
  - Random Experiment
  - Sample Space
  - Trial and Event
  - Probability
  - Axioms of Theory of Probability
  - Theorems
  - Conditional Probability
- Baye’s Theorem
- Random Variables
- Discrete Random Variable
- Continuous Random Variable
- Probability Mass Function
- Probability Density Function
- Cumulative Distribution Function (CDF)
  - Mathematical Expectation or Mean of Random Variable
  - Variance of the Random Variable
- Moments of the Random Variable
- Moments Generating Function (MGF)
  - Properties
- Standard Distributions
- Discrete Distributions
- Binomial Distribution
  - Assumptions for Binomial Distribution
  - Mean and Variance of a Binomial Distribution
  - Moment Generating Function (MGF) of a Binomial Distribution
  - Additive Property of Binomial Distribution
- Poisson Distribution
  - Mean and Variance of Poisson Distribution
  - MGF of Poisson Distribution
  - Additive Property of Poisson Distribution
- Geometric Distribution
  - Mean and Variance of Geometric Distribution
  - MGF Functions of Geometric Distribution
  - Memoryless (forgetfulness) Property of Geometric Distribution
- Negative Binomial Distribution
  - MGF of Negative Binomial Distribution
  - Mean and Variance of NBD
- Continuous Distributions
- Uniform Distribution
  - Mean and Variance Uniform Distribution
  - MGF of Uniform Distribution
- Exponential Distribution
  - Mean and Variance of Exponential Distribution
  - Moment Generating Function (MGF) of Exponential Distribution
  - Memoryless Property of Exponential Distribution [Forgetfulness Property]
- Gamma Distribution (Erlang Distribution)
  - Mean and Variance of Gamma Distribution
  - Moment Generating Function (MGF) of Gamma Distribution
  - Additive Property
- Weibull Distribution
  - Mean and Variance of Weibull Distribution
  - Moment Generating Function (MGF)
- Exercise
- Solved Two Mark Questions
CHAPTER 2 Two Dimensional Random Variables
- Joint distributions—Marginal and conditional distributions
  - Two Dimensional Random Variable
  - Two Dimensional Discrete Random Variable
  - Two Dimensional Continuous Random Variable
  - Joint Probability Function
  - Joint Probability Density Function
  - Marginal Distribution Function
  - Marginal Density Function
  - Joint (Cumulative) Distribution Function
  - Conditional Distribution of a Random Variable
- Independent Random Variables
- Covariance
  - Properties
- Correlation
  - Type of Correlation
  - Karl Pearson’s Co-efficient of Correlation
  - Rank Correlation
  - Repeated Rank Correlation
- Regression
  - Regression Co-efficient
- Transformation of Random Variables
- Central Limit Theorem (CLT)
  - Applications of CLT
- Exercise
- Solved Two marks Questions
CHAPTER 3 Classification of Random Process
- Classification of Random Process
  - Deterministic (or) Predictable Random Process
  - Non-Deterministic Random Process
  - Correlation
  - Mean of a Random Process
  - Auto Correlation of Random Process
  - Auto Covariance or Covariance Function of Random Process
  - Relation Between Mean, Auto Correlation and Auto Covariance
  - Cross Correlation
  - Cross Covariance
  - Relation Between Cross Correlation and Cross Covariance
- Stationary Process
  - Strict Sense Stationary (SSS) Process
  - Jointly Stationary Process
  - Wide Sense Stationary (WSS) Process
  - Non-stationary (or) Evolutionary Process
  - Time Average and Ensemble Average
  - Markov Process
  - Classification of Markov Process
  - One Step Transition Probability
  - Homogeneous Markov Chain
  - Stochastic Matrix
- Transition Probability Matrix (TPM)
  - Regular Matrix
  - N-Step Transition Probability
  - Chapman-Kolmogorov Theorem
  - Probability Distribution of the Process
  - Steady State (or) Stationary Distribution
- Poisson Process
  - Probability function of Poisson process{X(t)}
  - Probability Law for Poisson Process
  - MGF of Poisson Process
  - Autocorrelation of the Poisson Process
  - Auto Covariance of Poisson Process
  - Correlation coefficient of poisson process
  - Properties of Poisson Process
- Binomial Process
- Normal(Gaussian) Process
- Sine Wave Process
- Random Telegraph Process
  - Mean and Autocorrelation of Telegraph Process
- Exercise
- Solved Two Mark Questions
CHAPTER 4 Queueing Theory
- Introduction to Queueing Models
  - Characteristics of a Queueing System
- Customer Behavior
- Kendal’s Notation for Representing Queue Mode
- Model 1: Single Server Poisson Queue Model (M/M/1) : (∞/FIFO)
- Model 2: Multi Server Poisson Queue Model
- Model 3: Finite Capacity, Single Server Queue(M/M/1) : (N/FCFS)
- Model 4: Finite Capacity Multi Server Queue Model(M/M/C) : (N/FCFS).
- Model 5: [Self Service Model]
- Exercise
- Solved Two Mark Questions
CHAPTER 5 Non Markovian Queues and Queue Networks
- Birth and death Process
  - Probability Distribution of X(t)
  - Pure - Birth and Pure - Death Process
  - Probability Pn (t) of Pure - Birth Process
  - Probability Function of Pure - Death Process
- Pollaczek - Khintchine (P-K) Formula
- M/G/1 Queue
  - Various Formula for (M/ G / 1) : (∞ / GD)
- Networks of Queues
- Series Queues
  - Series Queues with Blocking
  - Jackson Network
  - Closed Jackson Networks
  - The Arrival Theorem
  - Mean Value Analysis
- Exercise
- Solved Two Marks Questions
Question Paper

Biographical note

Dr. R Pugalarsu is currently Associate Professor, Department of Mathematics, RMK Group of Institution, Chennai.

User Reviews

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