Waiting line systems are any systems that provide service of some kind to customers who arrive at them. Calls on a telephone network or airplanes heading to an airport are examples of such customers, while the provided service is the conversation and landing, respectively. The randomness inherent in arrival and service times results in the evolution of the system over time [e.g., the number of customers present as a function of time or the waiting times of successive customers] being a stochastic process or evolution. Queueing theory is based on studies by A.K. Erlang in the early 20th century, and due to the significant practical and theoretical interest in these models, this theory continues to develop at a steady pace to this day.

The subject of this book is precisely queueing theory and networks of queues, starting from the simplest models and progressing to more complex general models. Because understanding this – beyond Probability Theory – also requires a good knowledge of Stochastic Processes Theory, the first chapter is dedicated to an overview of the most useful concepts and results of this theory.

The book contains approximately 130 exercises with solutions, additional unsolved problems, and includes English terminology useful for further study of international literature.