Boundary Value Problems in Queueing System Analysis
Published on 14. May 2014
418 pages
978-0-08-087190-5 (ISBN)
Description
Boundary Value Problems in Queueing System Analysis
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Language
English
Place of publication
Amsterdam
Netherlands
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Windows
ISBN-13
978-0-08-087190-5 (9780080871905)
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Additional editions
J.W. Cohen | O.J. Boxma
Boundary Value Problems in Queueing System Analysis: Volume 79
Book
04/2000
North-Holland
€185.70
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Content
- Front Cover
- Boundary Value Problems in Queueing System Analysis
- Copyright Page
- Contents
- Preface
- Note on Notations and Referencing
- GENERAL INTRODUCTION
- PART I: INTRODUCTION TO BOUNDARY VALUE PROBLEMS
- CHAPTER I.1. SINGULAR INTEGRALS
- I.1.1. Introduction
- I.1.2. Smooth arcs and contours
- I.1.3. The Hölder condition
- I.1.4. The Cauchy integral
- I.1.5. The singular Cauchy integral
- I.1.6. Limiting values of the Cauchy integral
- I.1.7. The basic boundary value problem
- I.1.8. The basic singular integral equation
- I.1.9. Conditions for analytic continuation of a function given on the boundary
- I.1.10. Derivatives of singular integrals
- CHAPTER I.2. THE RIEMANN BOUNDARY VALUE PROBLEM
- I.2.1. Formulation of the problem
- I.2.2. The index of G(t), t ? L
- I.2.3. The homogeneous problem
- I.2.4. The nonhomogeneous problem
- I.2.5. A variant of the boundary value problem (1.2)
- CHAPTER I.3. THE RIEMANN-HILBERT BOUNDARY VALUE PROBLEM
- I.3.1. Formulation of the problem
- I.3.2. The Dirichlet problem
- I.3.3. Boundary value problem with a pole
- I.3.4. Regularizing factor
- I.3.5. Solution of the Riemann-Hilbert problem
- CHAPTER I.4. CONFORMAL MAPPING
- I.4.1. Introduction
- I.4.2. The Riemann mapping theorem
- I.4.3. Reduction of boundary value problem for L+ to that for a circular region
- I.4.4. Theodorsen's procedure
- PART II: ANALYSIS OF TWO-DIMENSIONAL RANDOM WALK
- CHAPTER II.1. THE RANDOM WALK
- II.1.1. Definitions
- II.1.2. The component random walk {x_n, n = 0,1,2 ,... }
- CHAPTER II.2. THE SYMMETRIC RANDOM WALK
- II.2.1. Introduction
- II.2.2. The kernel
- II.2.3. S1(r) and S2(r) for ?(0,0) & 0, 0 & r & 1
- II.2.4. ?(r,z) and L(r)
- II.2.5. The functional equation
- II.2.6. The solution of the boundary value problem
- II.2.7. The determination of Fxy(r,p1,p2)
- II.2.8. Analytic continuation
- II.2.9. The expression for Fxy(r,p1,p2) with ?(0,0)&0, 0& r & 1
- II.2.10. On Fxy(r,p1,p2,q1,q2)
- II.2.11. The random walk {(µn,vn), n=0,1,2 ,... }
- II.2.12. The return time
- II.2.13. The kernel with r =1, E{x} = E{y} & 1
- II.2.14. The case E{x} = E{y} & 1
- II.2.15. The stationary distribution with ?(0,0) & 0
- II.2.16. Direct derivation of the stationary distribution with ?(0,0) & 0
- CHAPTER II.3. THE GENERAL RANDOM WALK
- II.3.1. Introduction
- II.3.2. The kernel with ?(0,0)&0
- II.3.3. A conformal mapping of S+1 (r) and of S+2 (r)
- II.3.4. Boundary value problem with a shift
- II.3.5. Proof of theorem 3.1
- II.3.6. The integral equations
- II.3.7. Analytic continuation
- II.3.8. The functional equation with ?(0,0)&0, 0&r& 1
- II.3.9. The stationary distribution with ?(0,0)&0, {E x} & {1, E Y} & 1
- II.3.10. The case ?(0,0)=a00 = 0
- II.3.11. The case a00 = 0, a01 ?a10, 0 & r & 1
- II.3.12. The case a00 = 0, a01 = a10?0, 0 & r & 1
- CHAPTER II.4. RANDOM WALK WITH POISSON KERNEL
- II.4.1. Introduction
- II.4.2. The Poisson kernel
- II.4.3. The functional equation
- II.4.4. The functional equation for the stationary case
- II.4.5. The stationary distribution
- PART III: ANALYSIS OF VARIOUS QUEUEING MODELS
- CHAPTER III.1. TWO QUEUES IN PARALLEL
- III.1.1. The model
- III.1.2. Analysis of the functional equation
- II.1.3. The case a1 = a2 = a, p1 = p2 = 1/2
- III.1.4. Analysis of integral expressions
- III.1.5. Some comments concerning another approach
- CHAPTER III.2. THE ALTERNATING SERVICE DISCIPLINE
- III.2.1. The model
- III.2.2. The functional equation
- III.2.3. The solution of the functional equation
- III.2.4. The symmetric case
- CHAPTER III.3. A COUPLED PROCESSOR MODEL
- III.3.1. The model
- III.3.2. The functional equation
- III.3.3. The kernel
- III.3.4. The functional equation, continuation
- III.3.5. The case 1/?1 + 1/?2 = 1
- III.3.6. The case 1/?1 + 1/?2 ? 1
- III.3.7. The ergodicity conditions
- CHAPTER III.4. THE M/G/2 QUEUEING MODEL
- III.4.1. Introduction
- III.4.2. The functional equation
- III.4.3. The solution of the functional equation
- III.4.4. The waiting time distribution
- III.4.5. The matrix M(2s)
- PART IV: ASPECTS OF NUMERICAL ANALYSIS
- CHAPTER IV.1. THE ALTERNATING SERVICE DISCIPLINE
- IV.1.1. Introduction
- IV.1.2. Expressions for the mean queue lengths
- IV.1.3. The numerical approach of Theodorsen's integral equation
- IV.1.4. The nearly circular approximation
- IV.1.5. Conditions for 2r2 ? F+
- IV.1.6. Numerical results
- IV.1.7. Asymptotic results
- CHAPTER IV.2. THE ALTERNATING SERVICE DISCIPLINE - A RANDOM WALK APPROACH
- IV.2.1. Introduction
- IV.2.2. Preparatory results
- IV.2.3. The numerical approach
- IV.2.4. Numerical results
- REFERENCES
- SUBJECT INDEX
