Applications of Queueing Theory

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.