Approximate Behavior of Tandem Queues

Approximate Behavior of Tandem Queues by G.F. Newell.

The following monograph deals with the approximate stochastic behavior of a system consisting of a sequence of servers in series with finite storage between consecutive servers. The methods employ deterministic queueing and diffusion approximations which are valid under conditions in which the stora...

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Bibliographic Details
Main Author: Newell, G.F (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1979.
Edition:1st ed. 1979.
Series:Lecture Notes in Economics and Mathematical Systems, 171
Springer eBook Collection.
Subjects:
Operations research.
Decision making.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • I. General Theory
  • 1. Introduction
  • 2. Graphical Representations and Deterministic Approximation
  • 3. Motion of Holes
  • 4. Diffusion Equation
  • 5. Queue Length Distribution
  • 6. Soft Boundaries
  • 7. Moments
  • References
  • II. A Single Server
  • 1. Diffusion Equation
  • 2. Queue Distribution
  • 3. Service Rates
  • 4. Longtime Behavior of the Joint Distributions
  • 5. Service Variances
  • 6. Image Solution c1 = ?
  • 7. Longtime Behavior c1 = ?
  • 8. Discussion
  • III. Equilibrium Queue Distributions Two Servers, ?0 = ?1 = ?2, Theory
  • 1. Introduction
  • 2. Formulation
  • 3. Conformal Mappings
  • 4. Marginal Distributions
  • 5. Symmetry
  • 6. Saddle Points and Singularities
  • 7. One Large Storage
  • 8. Expansions of the Marginal Distributions
  • References
  • IV. Equilibrium Queue Distributions, Two Servers ?0 = ?1 = ?2, Numerical Results
  • 1. Introduction
  • 2. Marginal Distributions for c2 = ?
  • 3. Relation between c*1, c*2 and w1, w3
  • 4. Marginal Distributions c*1 c*2 < ?
  • 5. The Service Rate
  • 6. Joint Distributions
  • V. Time-dependent Solutions ?0 = ?1 = ?2
  • 1. Introduction
  • 2. Image Solution
  • 3. Time-dependent Queue Distribution
  • VI. Laplace Transform Methods, Equilibrium Queue Distributions for n = 2, ?0 < ?1 ? ?2
  • 1. Analysis of Transforms
  • 2. Equilibrium Distributions c1 = c2 = ?, ?0 = ?2 = 0
  • 3. Numerical Evaluations
  • 4. Equilibrium Distributions c1 = c2 = ?
  • 5. Other Special Cases
  • 6. Interpretation
  • VII. Equilibrium Queue Distributions; n=2; ?1 < ?0, ?2; c1 c2 ??
  • 1. Introduction
  • 2. Joint Distribution for ?0 = ?2 = 0
  • 3. Joint Distribution for ?0, ?2 > 0
  • 4. Service Rate for Large But Finite c1, c2
  • VIII. Epilogue
  • 1. What Was the Question?
  • 2. Graphical Representations
  • 3. Diffusion Approximations
  • 4. A Single Server
  • 5. Joint Probability Density for Q1 Q2
  • Notation.

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