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Large deviations of the long term distribution of a non Markov process. (English) Zbl 1441.60025
The author continues investigations in the field of large deviation theory by means of idempotent measure theory. The paper considers the long-term distribution of the non-Markov process of queue length in an ergodic generalized Jackson networks and establishes a large deviation principle. The deviation function is given by the quasipotential related to the stationary idempotent distribution of the limit idempotent process. The latter distribution is also a unique long-term idempotent distribution. The geometric ergodicity of the queue length process implies that the long-term idempotent distribution is the large deviation limit of the long-term queue length distributions.
60F10 Large deviations
60K25 Queueing theory (aspects of probability theory)
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