Abstract
In this paper, the quasi-compactness and irreducibility of two queueing systems are investigated by abstract functional analytical methods. More precisely, the systems fit into Greiner’s framework and Greiner’s idea of boundary perturbation of the generator is utilized. Quasi-compactness or irreducibility of the semigroup generated by the system operator is obtained through special properties of the boundary perturbation operators. Moreover, the exponential stability of the queueing models is analyzed based on the quasi-compactness and irreducibility.
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Acknowledgments
This work was supported by the National Natural Science Foundation of China (11201037, 11371070). The authors would like to thank the reviewers for their helpful comments and suggestions.
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Communicated by Markus Hasse.
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Zheng, F., Guo, BZ. Quasi-compactness and irreducibility of queueing models. Semigroup Forum 91, 560–572 (2015). https://doi.org/10.1007/s00233-014-9663-3
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DOI: https://doi.org/10.1007/s00233-014-9663-3