Abstract
In queueing theory the question of invariance is well known: under what conditions the stationary probabilities of states of the queueing system are independent on the form of distribution functions of the elements (for example, of the service time) if there are given finite values of mathematical expectation? For the Erlang loss system with independent service times Sevastjanov [1] gave a complete answer; in the case of depending service times in the sense of stochastic point process see [2], [5], [6]. For other systems Kovalenko [3] proved a condition of invariance. A theory of invariance including algebraic criteria of invariance and connection with the so called set up of product of Sevastjanov [1] for a formalized class of queueing and reliability models is found in [4], [5], [6].
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References
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© 1977 ACADEMIA, Publishing House of the Czechoslovak Academy of Science, Prague
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König, D., Jansen, U. (1977). Stochastic Processes and Properties of Invariance for Queueing Systems with Speeds and Temporary Interruptions. In: Kožešnik, J. (eds) Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians. Transactions of the Seventh Prague Conference on Information Theory, Statistical Decision Functions, Random Processes and of the 1974 European Meeting of Statisticians, vol 7A. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9910-3_34
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DOI: https://doi.org/10.1007/978-94-010-9910-3_34
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