This book examines how messages move through network switches and queues when service times are fixed and inputs follow simple probabilistic rules. It treats the infinite-capacity case as a random walk on the nonnegative integers, then extends the idea to the output process and the first-return behavior. The discussion blends exact difference equations with generating functions to reveal steady-state distributions and waiting-time properties. It also contrasts two finite-capacity queue models, showing how boundary conditions alter performance in practical settings.

Readers will see how to translate queue behavior into solvable mathematical forms, understand the role of i.i.d. inputs, and compare single- and multi-stage systems. The text emphasizes the relationships between queue length, waiting time, and output clusters, providing a toolkit for analyzing similar stochastic systems.

How a queue can be modeled as a random walk on a half-line and solved with generating functions
Methods for deriving steady-state distributions and moments of waiting time
Characterization of the output process and the distribution of output clusters
Two finite-capacity models and their different boundary conditions

Ideal for readers of stochastic processes, operations research, and applied probability who want concrete techniques for queue analysis.

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