Applications of Queueing Theory

1. Front Matter

   Pages i-xvi

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2. Introduction

   • G. F. Newell

   Pages 1-23

3. Deterministic fluid approximation — single server

   • G. F. Newell

   Pages 25-52

4. Simple queueing systems

   • G. F. Newell

   Pages 53-104

5. Stochastic models

   • G. F. Newell

   Pages 105-142

6. Equilibrium distributions

   • G. F. Newell

   Pages 143-176

7. Independent or weakly interacting customers

   • G. F. Newell

   Pages 177-213

8. Diffusion equations

   • G. F. Newell

   Pages 215-236

9. Diffusion approximation for equilibrium and transient queue behavior

   • G. F. Newell

   Pages 237-261

10. Time-dependent queues

    • G. F. Newell

    Pages 263-291

11. Back Matter

    Pages 293-303

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The literature on queueing theory is already very large. It contains more than a dozen books and about a thousand papers devoted exclusively to the subject; plus many other books on probability theory or operations research in which queueing theory is discussed. Despite this tremendous activity, queueing theory, as a tool for analysis of practical problems, remains in a primitive state; perhaps mostly because the theory has been motivated only superficially by its potential applications. People have devoted great efforts to solving the 'wrong problems. ' Queueing theory originated as a very practical subject. Much ofthe early work was motivated by problems concerning telephone traffic. Erlang, in particular, made many important contributions to the subject in the early part of this century. Telephone traffic remained one of the principle applications until about 1950. After World War II, activity in the fields of operations research and probability theory grew rapidly. Queueing theory became very popular, particularly in the late 1950s, but its popularity did not center so much around its applications as around its mathematical aspects. With the refine­ ment of some clever mathematical tricks, it became clear that exact solutions could be found for a large number of mathematical problems associated with models of queueing phenomena. The literature grew from 'solutions looking for a problem' rather than from 'problems looking for a solution.

• Erlang
• Fusion
• M/M/1 queue
• Poisson distribution
• approximation
• behavior
• distribution
• modeling
• operations research
• probability
• queueing theory
• server
• storage
• system
• types

• University of California, Berkeley, USA

  G. F. Newell

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