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V-uniform ergodicity for fluid queues

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Abstract

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.

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Authors and Affiliations

  1. School of Mathematics and Statistics, New Campus, Central South University, Changsha, 410083, China

    Yuan-yuan Liu & Yang Li

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  1. Yuan-yuan Liu
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  2. Yang Li
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Correspondence to Yuan-yuan Liu.

Additional information

Supported by the National Natural Science Foundation of China (11571372, 11771452) and the Innovation Program of Central South University (10900-50601010).

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Liu, Yy., Li, Y. V-uniform ergodicity for fluid queues. Appl. Math. J. Chin. Univ. 34, 82–91 (2019). https://doi.org/10.1007/s11766-019-3543-2

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  • DOI: https://doi.org/10.1007/s11766-019-3543-2

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