Elements of Queueing Theory: Palm Martingale Calculus and Stochastic Recurrences

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This book gives the mathematical foundations of the theory of stationary queuing systems. In particular, it contains a thorough treatment of the Palm theory and of the Loynes theory of stationary systems, the two pillars of the modern approach to queuing. This approach helps to clarify the picture, in that it separates the task of obtaining the key system formulas from that of proving convergence to a stationary state and computing its law. The theory is constantly illustrated by classical results and models: Pollaczek-Khintchin and Tacacs formulas, Jackson and Gordon-Newell networks, multiserver queues, blocking queues, loss systems etc., but it also contains recent and significant examples, where the tools developed turn out to be indispensable. Several other mathematical tools which are useful within this approach are also presented such as the martingale calculus for point processes, or stochastic ordering for stationary recurrences. This thoroughly revised second edition contains a substantial number of additions with the aim of rendering this now classic reference suitable for use as a textbook. In particular, exercises and their solutions have been added.