Applied probability and queues /

Applied probability and queues /

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Bibliographic Details
Author / Creator:Asmussen, Soren.
Edition:2nd ed.
Imprint:New York : Springer, c2003.
Description:xii, 438 p. : ill. ; 25 cm.
Language:English
Series:Applications of mathematics ; 51
Subject:
Stochastic processes.
Queuing theory.
Markov processes.
Markov processes.
Queuing theory.
Stochastic processes.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4888846
Hidden Bibliographic Details
ISBN:0387002111 (alk. paper)
Notes:Includes bibliographical references (p. [416]-430) and index.
Table of Contents:
  • Preface
  • Notation and Conventions
  • Part A. Simple Markovian Models
  • I. Markov Chains
  • 1. Preliminaries
  • 2. Aspects of Renewal Theory in Discrete Time
  • 3. Stationarity
  • 4. Limit Theory
  • 5. Harmonic Functions, Martingales and Test Functions
  • 6. Nonnegative Matrices
  • 7. The Fundamental Matrix, Poisson's Equation and the CLT
  • 8. Foundations of the General Theory of Markov Processes
  • II. Markov Jump Processes
  • 1. Basic Structure
  • 2. The Minimal Construction
  • 3. The Intensity Matrix
  • 4. Stationarity and Limit Results
  • 5. Time Reversibility
  • III. Queueing Theory at the Markovian Level
  • 1. Generalities
  • 2. General Birth-Death Processes
  • 3. Birth-Death Processes as Queueing Models
  • 4. The Phase Method
  • 5. Renewal Theory for Phase-Type Distributions
  • 6. Lindley Processes
  • 7. A First Look at Reflected Lévy Processes
  • 8. Time-Dependent Properties of M/M/1
  • 9. Waiting Times and Queue Disciplines in M/M/1
  • IV. Queueing Networks and Insensitivity
  • 1. Poisson Departure Processes and Series of Queues
  • 2. Jackson Networks
  • 3. Insensitivity in Erlang's Loss System
  • 4. Quasi-Reversibility and Single-Node Symmetric Queues
  • 5. Quasi-Reversibility in Networks
  • 6. The Arrival Theorem
  • Part B. Some General Tools and Methods
  • V. Renewal Theory
  • 1. Renewal Processes
  • 2. Renewal Equations and the Renewal Measure
  • 3. Stationary Renewal Processes
  • 4. The Renewal Theorem in Its Equivalent Versions
  • 5. Proof of the Renewal Theorem
  • 6. Second-Moment Results
  • 7. Excessive and Defective Renewal Equations
  • VI. Regenerative Processes
  • 1. Basic Limit Theory
  • 2. First Examples and Applications
  • 3. Time-Average Properties
  • 4. Rare Events and Extreme Values
  • VII. Further Topics in Renewal Theory and Regenerative Processes
  • 1. Spread-Out Distributions
  • 2. The Coupling Method
  • 3. Markov Processes: Regeneration and Harris Recurrence
  • 4. Markov Renewal Theory
  • 5. Semi-Regenerative Processes
  • 6. Palm Theory, Rate Conservation and PASTA
  • VIII. Random Walks
  • 1. Basic Definitions
  • 2. Ladder Processes and Classification
  • 3. Wiener-Hopf Factorization
  • 4. The Spitzer-Baxter Identities
  • 5. Explicit Examples. M/G/1, GI/M/1, GI/PH/1
  • IX. Levy Processes, Reflection and Duality
  • 1. Lévy Processes
  • 2. Reflection and Loynes's Lemma
  • 3. Martingales and Transforms for Reflected Lévy Processes
  • 4. A More General Duality
  • Part C. Special Models and Methods
  • X. Steady-State Properties of GI/G/1
  • 1. Notation. The Actual Waiting Time
  • 2. The Moments of the Waiting Time
  • 3. The Workload
  • 4. Queue Length Processes
  • 5. M/G/1 and GI/M/1
  • 6. Continuity of the Waiting Time
  • 7. Heavy Traffic Limit Theorems
  • 8. Light Traffic
  • 9. Heavy-Tailed Asymptotics
  • XI. Markov Additive Models
  • 1. Some Basic Examples
  • 2. Markov Additive Processes
  • 3. The Matrix Paradigms GI/M/ 1 and M/G/1
  • 4. Solution Methods
  • 5. The Ross Conjecture and Other Ordering Results
  • XII. Many-Server Queues
  • 1. Comparisons with GI/G/1
  • 2. Regeneration and Existence of Limits
  • 3. The GI/M/s Queue
  • XIII. Exponential Change of Measure
  • 1. Exponential Families
  • 2. Large Deviations, Saddlepoints and the Relaxation Time
  • 3. Change of Measure: General Theory
  • 4. First Applications
  • 5. Cramér-Lundberg Theory
  • 6. Siegmund's Corrected Heavy Traffic Approximations
  • 7. Rare Events Simulation
  • 8. Markov Additive Processes
  • XIV. Dams, Inventories and Insurance Risk
  • 1. Compound Poisson Dams with General Release Rule
  • 2. Some Examples
  • 3. Finite Buffer Capacity Models
  • 4. Some Simple Inventory Models
  • 5. Dual Insurance Risk Models
  • 6. The Time to Ruin
  • Appendix
  • A1. Polish Spaces and Weak Convergence
  • A2. Right-Continuity and the Space D
  • A3. Point Processes
  • A4. Stochastical Ordering
  • A5. Heavy Tails
  • A6. Geometric Trials
  • A7. Semigroups of Positive Numbers
  • A8. Total Variation Convergence
  • A9. Transforms
  • A10. Stopping Times and Wald's Identity
  • A11. Discrete Skeletons
  • Bibliography
  • Index
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