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

[摘要] 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.

[学科分类] 统计和概率

[关键词] generalised Jackson networks;long term distribution;large deviation principle;idempotent probability