V-uniform ergodicity for fluid queues
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In this paper, we show that a positive recurrent fluid queue is automatically V-uniformly ergodic for some function V ≥ 1 but never uniformly ergodic. This reveals a similarity of ergodicity between a fluid queue and a quasi-birth-and-death process. As a byproduct of V-uniform ergodicity, we derive computable bounds on the exponential moments of the busy period.
Keywordsfluid queues QBD processes ergodicity the extended generator
MR Subject Classification60J25 37A25
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