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2019 Large deviations of the long term distribution of a non Markov process
Anatolii Puhalskii
Electron. Commun. Probab. 24(none): 1-11 (2019). DOI: 10.1214/19-ECP243

Abstract

We prove that the long term distribution of the queue length process in an ergodic generalised Jackson network obeys the Large Deviation Principle with a deviation function given by the quasipotential. The latter is related to the unique long term idempotent distribution, which is also a stationary idempotent distribution, of the large deviation limit of the queue length process. The proof draws on developments in queueing network stability and idempotent probability.

Citation

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Anatolii Puhalskii. "Large deviations of the long term distribution of a non Markov process." Electron. Commun. Probab. 24 1 - 11, 2019. https://doi.org/10.1214/19-ECP243

Information

Received: 26 December 2018; Accepted: 16 May 2019; Published: 2019
First available in Project Euclid: 22 June 2019

zbMATH: 07088976
MathSciNet: MR3978684
Digital Object Identifier: 10.1214/19-ECP243

Subjects:
Primary: 60F10, 60K25

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