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Palm probabilities and stationary queues. (English) Zbl 0624.60107

Lecture Notes in Statistics, 41. Berlin etc.: Springer-Verlag. VII, 106 p.; DM 28.50 (1987).
This book contains two parts: 1) Stationary point processes and Palm probabilities, 2) Stationary queueing systems (of G/G/./.-type).
In the second part the existence of stationary states of queueing systems is investigated, queueing formulas (e.g. Little’s formula) are derived, and the theory of insensitivity and local balance theory for the “Bedienungssysteme” (generalized queueing systems in the sense of König, Matthes and Nawrotzki) is presented.
The methods and proofs depend on the general point process theory developed in part one, where a direct path to Palm probabilities is presented which then leads to stationary states.
Reviewer: H.Daduna

MSC:

60K25 Queueing theory (aspects of probability theory)
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B22 Queues and service in operations research