Difference Equations with Applications to Queues : Chapman & Hall/CRC Pure and Applied Mathematics - David L. Jagerman

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Difference Equations with Applications to Queues

Name: Difference Equations with Applications to Queues
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By: David L. Jagerman

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Hardcover | 22 August 2000 | Edition Number 1

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Hardcover
268 Pages

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23.4 x 15.6 x 1.78

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"Presents a theory of difference and functional equations with continuous argument based on a generalization of the Riemann integral introduced by N.E. Norlund, allowing differentation with respect to the independent variable and permitting greater flexibility in constructing solutions and approximations. Discusses linear transformations that state conditions for convergence of Newton series and Norlund sums!"

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." . .interesting. . .. . . .relevant." ---Zbl. Math ." . .a very useful survey. . ..intended for both beginners and specialists." ---Medical Reviews

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You Can Find This Book In

Non-Fiction Mathematics Probability & Statistics Applied Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Optimisation Game Theory

Preface	p. iii
Operators and Functions	p. 1
Operators	p. 1
Factorial function--Stirling numbers	p. 4
Beta function--factorial Series	p. 7
[psi] Function and primitives	p. 10
Laplace and Mellin transformations	p. 12
Some operational formulae	p. 17
Problems	p. 17
Generalities on Difference Equations	p. 21
Genesis of difference equations	p. 21
The M/M/C blocking model	p. 24
The M/M/1 delay model	p. 24
The time homogeneous first-order model	p. 25
The Euler equation	p. 25
Problems	p. 31
Norlund Sum: Part One	p. 32
Introduction	p. 32
Principal solution	p. 33
Some properties of the sum	p. 34
Summation of series	p. 37
Summation by parts	p. 38
Differentiation	p. 39
Extension of definition of sum	p. 39
Repeated summation	p. 40
Sum of Laplace transforms	p. 41
Homogeneous form and bounds	p. 44
Bernoulli's polynomials	p. 50
Computational formulae	p. 56
Problems	p. 68
Norlund Sum: Part Two
Introduction	p. 75
The Euler-Maclaurin expansion	p. 75
Existence of the principal sum	p. 77
Trigonometric expansions	p. 84
A class of linear transformations	p. 89
Applications to expansions and functional equations	p. 96
Application to the Norlund sum	p. 99
Bound, error estimate, and convolution form	p. 101
Consideration of some integral equations	p. 102
Bandlimited functions	p. 105
Problems	p. 105
The First-Order Difference Equation	p. 109
Introduction	p. 109
The linear homogeneous equation	p. 110
The inhomogeneous equation	p. 114
The differential-difference equation	p. 122
Derivative	p. 129
Functional equations	p. 132
U-operator solution of [characters not reproducible]Z = [theta](Z)	p. 138
Critical points	p. 143
A branching process approximation	p. 145
A perturbation solution of [characters not reproducible]Z = [theta](Z)	p. 147
Haldane's method for [characters not reproducible]Z = [theta](Z)	p. 149
Solution of G([phis](z)) - l(z)G(z) = m(z)	p. 151
Simultaneous first-order equations	p. 154
Problems	p. 162
The Linear Equation With Constant Coefficients	p. 172
Introduction	p. 172
The homogeneous equation	p. 173
The inhomogeneous equation	p. 179
Equations reducible to constant coefficients	p. 188
Partial difference equations	p. 189
Problems	p. 198
Linear Difference Equations with Polynomial Coefficients	p. 200
Introduction	p. 200
Depression of order	p. 201
The operators [pi] and [rho]	p. 203
General operational solution	p. 210
Exceptional cases	p. 217
The complete equation	p. 222
The LCFS M/M/C queue with reneging--introduction	p. 226
Formulation and solution	p. 228
An M/M/1 processor-sharing queue	p. 234
Problems	p. 236
References	p. 237
Index	p. 241
Table of Contents provided by Syndetics. All Rights Reserved.

Difference Equations with Applications to Queues

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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