Coverart for item
The Resource Difference and differential equations with applications in queueing theory, Aliakbar Montazer Haghighi, Department of Mathematics, Prairie View A & M University, Prairie View, TX, Dimitar P. Mishev, Department of Mathematics, Prairie View A & M University, Prairie View, TX

Difference and differential equations with applications in queueing theory, Aliakbar Montazer Haghighi, Department of Mathematics, Prairie View A & M University, Prairie View, TX, Dimitar P. Mishev, Department of Mathematics, Prairie View A & M University, Prairie View, TX

Label
Difference and differential equations with applications in queueing theory
Title
Difference and differential equations with applications in queueing theory
Statement of responsibility
Aliakbar Montazer Haghighi, Department of Mathematics, Prairie View A & M University, Prairie View, TX, Dimitar P. Mishev, Department of Mathematics, Prairie View A & M University, Prairie View, TX
Creator
Contributor
Provider
Subject
Language
eng
Summary
"This book features a collection of topics that are used in stochastic processes and, particularly, in queueing theory. Differential equations, difference equations, and Markovian queues (as they relate to systems of linear differential difference equations) are presented, and the relationship between the methods and applications are thoroughly addressed"--Provided by publisher
Cataloging source
NhCcYBP
http://library.link/vocab/creatorName
Haghighi, Aliakbar Montazer
Index
index present
LC call number
QA274.8
LC item number
.H338 2013
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
http://library.link/vocab/relatedWorkOrContributorName
  • Mishev, D. P.
  • Wiley Online Library
http://library.link/vocab/subjectName
  • Queuing theory
  • Difference equations
  • Differential equations
Label
Difference and differential equations with applications in queueing theory, Aliakbar Montazer Haghighi, Department of Mathematics, Prairie View A & M University, Prairie View, TX, Dimitar P. Mishev, Department of Mathematics, Prairie View A & M University, Prairie View, TX
Instantiates
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Machine generated contents note: 1.Probability and Statistics -- 1.1.Basic Definitions and Concepts of Probability -- 1.2.Discrete Random Variables and Probability Distribution Functions -- 1.3.Moments of a Discrete Random Variable -- 1.4.Continuous Random Variables -- 1.5.Moments of a Continuous Random Variable -- 1.6.Continuous Probability Distribution Functions -- 1.7.Random Vector -- 1.8.Continuous Random Vector -- 1.9.Functions of a Random Variable -- 1.10.Basic Elements of Statistics -- 1.10.1.Measures of Central Tendency -- 1.10.2.Measure of Dispersion -- 1.10.3.Properties of Sample Statistics -- 1.11.Inferential Statistics -- 1.11.1.Point Estimation -- 1.11.2.Interval Estimation -- 1.12.Hypothesis Testing -- 1.13.Reliability -- Exercises -- 2.Transforms -- 2.1.Fourier Transform -- 2.2.Laplace Transform -- 2.3.Z-Transform -- 2.4.Probability Generating Function -- 2.4.1.Some Properties of a Probability Generating Function -- Exercises -- 3.Differential Equations -- 3.1.Basic Concepts and Definitions -- 3.2.Existence and Uniqueness -- 3.3.Separable Equations -- 3.3.1.Method of Solving Separable Differential Equations -- 3.4.Linear Differential Equations -- 3.4.1.Method of Solving a Linear First-Order Differential Equation -- 3.5.Exact Differential Equations -- 3.6.Solution of the First ODE by Substitution Method -- 3.6.1.Substitution Method -- 3.6.2.Reduction to Separation of Variables -- 3.7.Applications of the First-Order ODEs -- 3.8.Second-Order Homogeneous ODE -- 3.8.1.Solving a Linear Homogeneous Second-Order Differential Equation -- 3.9.The Second-Order Nonhomogeneous Linear ODE with Constant Coefficients -- 3.9.1.Method of Undetermined Coefficients -- 3.9.2.Variation of Parameters Method -- 3.10.Miscellaneous Methods for Solving ODE -- 3.10.1.Cauchy-Euler Equation -- 3.10.2.Elimination Method to Solve Differential Equations -- 3.10.3.Application of Laplace Transform to Solve ODE -- 3.10.4.Solution of Linear ODE Using Power Series -- 3.11.Applications of the Second-Order ODE -- 3.11.1.Spring-Mass System: Free Undamped Motion -- 3.11.2.Damped-Free Vibration -- 3.12.Introduction to PDE: Basic Concepts -- 3.12.1.First-Order Partial Differential Equations -- 3.12.2.Second-Order Partial Differential Equations -- Exercises -- 4.Difference Equations -- 4.1.Basic Terms -- 4.2.Linear Homogeneous Difference Equations with Constant Coefficients -- 4.3.Linear Nonhomogeneous Difference Equations with Constant Coefficients -- 4.3.1.Characteristic Equation Method -- 4.3.2.Recursive Method -- 4.4.System of Linear Difference Equations -- 4.4.1.Generating Functions Method -- 4.5.Difference Equations -- 4.6.Nonlinear Difference Equations -- Exercises -- 5.Queueing Theory -- 5.1.Introduction -- 5.2.Markov Chain and Markov Process -- 5.3.Birth and Death (B-D) Process -- 5.4.Introduction to Queueing Theory -- 5.5.Single-Server Markovian Queue, M/M/1 -- 5.5.1.Transient Queue Length Distribution for M/M/1 -- 5.5.2.Stationary Queue Length Distribution for M/M/1 -- 5.5.3.Stationary Waiting Time of a Task in M/M/1 Queue -- 5.5.4.Distribution of a Busy Period for M/M/1 Queue -- 5.6.Finite Buffer Single-Server Markovian Queue: M/M/1/N -- 5.7.M/M/1 Queue with Feedback -- 5.8.Single-Server Markovian Queue with State-Dependent Balking -- 5.9.Multiserver Parallel Queue -- 5.9.1.Transient Queue Length Distribution for M/M/m -- 5.9.2.Stationary Queue Length Distribution for M/M/m -- 5.9.3.Stationary Waiting Time of a Task in M/M/m Queue -- 5.10.Many-Server Parallel Queues with Feedback -- 5.10.1.Introduction -- 5.10.2.Stationary Distribution of the Queue Length -- 5.10.3.Stationary Waiting Time of a Task in Many-Server Queue with Feedback -- 5.11.Many-Server Queues with Balking and Reneging -- 5.11.1.Priority M/M/2 with Constant Balking and Exponential Reneging -- 5.11.2.M/M/m with Constant Balking and Exponential Reneging -- 5.11.3.Distribution of the Queue Length for M/M/m System with Constant Balking and Exponential Reneging -- 5.12.Single-Server Markovian Queueing System with Splitting and Delayed Feedback -- 5.12.1.Description of the Model -- 5.12.2.Analysis -- 5.12.3.Computation of Expected Values of the Queue Length and Waiting Time at each Station, Algorithmically -- 5.12.4.Numerical Example -- 5.12.5.Discussion and Conclusion -- Exercises -- Appendix -- The Poisson Probability Distribution -- The Chi-Square Distribution -- The Chi-Square Distribution (continued) -- The Standard Normal Probability Distribution -- The Standard Normal Probability Distribution (continued) -- The (Student's) t Probability Distribution
Extent
1 online resource ( xiii, 404 pages.)
Form of item
online
Isbn
9781118400678
Isbn Type
(electronic bk.)
Lccn
2013011634
Media category
computer
Media MARC source
rdamedia
Media type code
c
Reproduction note
Electronic reproduction.
Specific material designation
remote
Stock number
10004639
System control number
(DLC)10004639
Label
Difference and differential equations with applications in queueing theory, Aliakbar Montazer Haghighi, Department of Mathematics, Prairie View A & M University, Prairie View, TX, Dimitar P. Mishev, Department of Mathematics, Prairie View A & M University, Prairie View, TX
Publication
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Machine generated contents note: 1.Probability and Statistics -- 1.1.Basic Definitions and Concepts of Probability -- 1.2.Discrete Random Variables and Probability Distribution Functions -- 1.3.Moments of a Discrete Random Variable -- 1.4.Continuous Random Variables -- 1.5.Moments of a Continuous Random Variable -- 1.6.Continuous Probability Distribution Functions -- 1.7.Random Vector -- 1.8.Continuous Random Vector -- 1.9.Functions of a Random Variable -- 1.10.Basic Elements of Statistics -- 1.10.1.Measures of Central Tendency -- 1.10.2.Measure of Dispersion -- 1.10.3.Properties of Sample Statistics -- 1.11.Inferential Statistics -- 1.11.1.Point Estimation -- 1.11.2.Interval Estimation -- 1.12.Hypothesis Testing -- 1.13.Reliability -- Exercises -- 2.Transforms -- 2.1.Fourier Transform -- 2.2.Laplace Transform -- 2.3.Z-Transform -- 2.4.Probability Generating Function -- 2.4.1.Some Properties of a Probability Generating Function -- Exercises -- 3.Differential Equations -- 3.1.Basic Concepts and Definitions -- 3.2.Existence and Uniqueness -- 3.3.Separable Equations -- 3.3.1.Method of Solving Separable Differential Equations -- 3.4.Linear Differential Equations -- 3.4.1.Method of Solving a Linear First-Order Differential Equation -- 3.5.Exact Differential Equations -- 3.6.Solution of the First ODE by Substitution Method -- 3.6.1.Substitution Method -- 3.6.2.Reduction to Separation of Variables -- 3.7.Applications of the First-Order ODEs -- 3.8.Second-Order Homogeneous ODE -- 3.8.1.Solving a Linear Homogeneous Second-Order Differential Equation -- 3.9.The Second-Order Nonhomogeneous Linear ODE with Constant Coefficients -- 3.9.1.Method of Undetermined Coefficients -- 3.9.2.Variation of Parameters Method -- 3.10.Miscellaneous Methods for Solving ODE -- 3.10.1.Cauchy-Euler Equation -- 3.10.2.Elimination Method to Solve Differential Equations -- 3.10.3.Application of Laplace Transform to Solve ODE -- 3.10.4.Solution of Linear ODE Using Power Series -- 3.11.Applications of the Second-Order ODE -- 3.11.1.Spring-Mass System: Free Undamped Motion -- 3.11.2.Damped-Free Vibration -- 3.12.Introduction to PDE: Basic Concepts -- 3.12.1.First-Order Partial Differential Equations -- 3.12.2.Second-Order Partial Differential Equations -- Exercises -- 4.Difference Equations -- 4.1.Basic Terms -- 4.2.Linear Homogeneous Difference Equations with Constant Coefficients -- 4.3.Linear Nonhomogeneous Difference Equations with Constant Coefficients -- 4.3.1.Characteristic Equation Method -- 4.3.2.Recursive Method -- 4.4.System of Linear Difference Equations -- 4.4.1.Generating Functions Method -- 4.5.Difference Equations -- 4.6.Nonlinear Difference Equations -- Exercises -- 5.Queueing Theory -- 5.1.Introduction -- 5.2.Markov Chain and Markov Process -- 5.3.Birth and Death (B-D) Process -- 5.4.Introduction to Queueing Theory -- 5.5.Single-Server Markovian Queue, M/M/1 -- 5.5.1.Transient Queue Length Distribution for M/M/1 -- 5.5.2.Stationary Queue Length Distribution for M/M/1 -- 5.5.3.Stationary Waiting Time of a Task in M/M/1 Queue -- 5.5.4.Distribution of a Busy Period for M/M/1 Queue -- 5.6.Finite Buffer Single-Server Markovian Queue: M/M/1/N -- 5.7.M/M/1 Queue with Feedback -- 5.8.Single-Server Markovian Queue with State-Dependent Balking -- 5.9.Multiserver Parallel Queue -- 5.9.1.Transient Queue Length Distribution for M/M/m -- 5.9.2.Stationary Queue Length Distribution for M/M/m -- 5.9.3.Stationary Waiting Time of a Task in M/M/m Queue -- 5.10.Many-Server Parallel Queues with Feedback -- 5.10.1.Introduction -- 5.10.2.Stationary Distribution of the Queue Length -- 5.10.3.Stationary Waiting Time of a Task in Many-Server Queue with Feedback -- 5.11.Many-Server Queues with Balking and Reneging -- 5.11.1.Priority M/M/2 with Constant Balking and Exponential Reneging -- 5.11.2.M/M/m with Constant Balking and Exponential Reneging -- 5.11.3.Distribution of the Queue Length for M/M/m System with Constant Balking and Exponential Reneging -- 5.12.Single-Server Markovian Queueing System with Splitting and Delayed Feedback -- 5.12.1.Description of the Model -- 5.12.2.Analysis -- 5.12.3.Computation of Expected Values of the Queue Length and Waiting Time at each Station, Algorithmically -- 5.12.4.Numerical Example -- 5.12.5.Discussion and Conclusion -- Exercises -- Appendix -- The Poisson Probability Distribution -- The Chi-Square Distribution -- The Chi-Square Distribution (continued) -- The Standard Normal Probability Distribution -- The Standard Normal Probability Distribution (continued) -- The (Student's) t Probability Distribution
Extent
1 online resource ( xiii, 404 pages.)
Form of item
online
Isbn
9781118400678
Isbn Type
(electronic bk.)
Lccn
2013011634
Media category
computer
Media MARC source
rdamedia
Media type code
c
Reproduction note
Electronic reproduction.
Specific material designation
remote
Stock number
10004639
System control number
(DLC)10004639

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