Large deviations of the long term distribution of a non Markov process

2018/12/25 by Puhalskii, Anatolii A. · 2 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1812.10163

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 processes. The proof draws on developments in queueing network stability and idempotent probability.

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• On large queue lengths in generalised Jackson networks
• On tightness and exponential tightness in generalised Jackson networks

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