Abstract
This paper investigates a fluid model driven by an M/M/1 queue with working vacations and RCE (Removal of customer in the end) policy of negative customer. In the external environment, the negative customer is not served by the server and only removes the positive customer in the end one-to-one. We establish a fluid flow model based on this stochastic process, and obtain the mean buffer content and the probability of empty buffer for this fluid queue using the LT (Laplace transform) method. Moreover, several special cases of the model here are obtained. Finally, some numerical examples are presented to demonstrate the effects of parameters on the performance indices of the fluid model.
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Acknowledgements
The authors would like to thank the anonymous referees for their constructive comments that help us to improve the present paper.
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Supported by the National Natural Science Foundation of China (No. 11201408) and Natural Science Foundation of Hebei Province (No. A2013203148).
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Xu, Xl., Wang, Xy., Song, Xf. et al. Fluid Model Modulated by an M/M/1 Working Vacation Queue with Negative Customer. Acta Math. Appl. Sin. Engl. Ser. 34, 404–415 (2018). https://doi.org/10.1007/s10255-018-0751-0
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DOI: https://doi.org/10.1007/s10255-018-0751-0
Keywords
- fluid model
- negative customer
- RCE (Removal of customer in the end) policy
- buffer content
- LT (Laplace transform)