Applications of Queueing Theory

ISBN-13: 9789400959729 / Angielski / Miękka / 2013 / 303 str.

C. Newell

Opis

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.

Spis treści

1 Introduction.- 1.1 Nature of the subject.- 1.2 Mathematical and graphical representation of events.- 1.3 Modelling.- 1.4 Averages.- 1.5 Applications of L = ?W.- 1.6 Other graphical representations.- Problems.- 2 Deterministic fluid approximation — single server.- 2.1 Introduction.- 2.2 A rush hour.- 2.3 A slight overload.- 2.4 Delays over many years.- 2.5 Queueing to meet a schedule.- 2.6 Pulsed service.- 2.7 Applications.- Problems.- 3 Simple queueing systems.- 3.1 Introduction.- 3.2 Series or tandem queues.- 3.3 Sorting of mail.- 3.4 A continuum of service points in series.- 3.5 Tandem queues with finite storage.- 3.6 The effect of finite storage on the capacity of synchronized traffic signals.- 3.7 Parallel or multiple-channel servers.- 3.8 Several customer types.- 3.9 Work conserving queues.- 3.10 Queueing at freeway ramps.- 3.11 Nonlinear cost of delay.- 3.12 A baggage claim.- Problems.- 4 Stochastic models.- 4.1 Probability postulates.- 4.2 Service and arrival distributions.- 4.3 A Poisson process.- 4.4 Robustness of the Poisson distribution.- 4.5 Deviations from a Poisson process.- 4.6 The normal approximation.- 4.7 The departure process.- 4.8 Queue lengths and waiting times.- 4.9 Work conserving systems.- Problems.- 5. Equilibrium distributions.- 5.1 Stationary processes.- 5.2 Dimensional estimates.- 5.3 Random walk.- 5.4 The M/M/1 queue.- 5.5 The M/M/m queue.- 5.6 The M/M/m/c system.- 5.7 The M/G/1 system.- 5.8 The GI/G/1 system.- Problems.- 6 Independent or weakly interacting customers.- 6.1 Introduction.- 6.2 Independent arrivals: the M/G/? system.- 6.3 Multiple events.- 6.4 Dependent arrivals.- 6.5 Loss systems with Poisson arrivals, exponential service time.- 6.6 Loss systems, general service times.- 6.7 Bounds for the m-channel server.- 6.8 Successive approximations for small queues.- 6.9 The M/G/m system for light traffic.- Problems.- 7 Diffusion equations.- 7.1 Introduction.- 7.2 The diffusion equation.- 7.3 Special solutions with no boundaries.- 7.4 Marginal distributions and boundary conditions.- 8 Diffusion approximation for equilibrium and transient queue behavior.- 8.1 Equilibrium distributions.- 8.2 Transient behavior, ?= ?.- 8.3 Transient behavior, ? ? ?.- Problems.- 9 Time-dependent queues.- 9.1 Introduction.- 9.2 Small deviations from the equilibrium distribution.- 9.3 Transition through saturation.- 9.4 A mild rush hour.- 9.5 Pulsed service, queue clears.- 9.6 Pulsed service with overflow.- Books on queueing theory in English.- Deterministic queueing models.- Author index.