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Equilibrium Strategies in a Fluid Queue with Working Vacations

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Abstract

We consider a fluid queue with working vacations. Once the buffer becomes empty during the normal working period, the buffer will enter a working vacation period during which the outflow rate of fluids will be switched to a lower rate than that in normal working period. After this working vacation period, if the buffer is non-empty, the outflow rate of fluids will be switched to normal rate immediately; otherwise, the buffer will enter another working vacation until the buffer is non-empty after one working vacation. For such a fluid queue, based on the utility function, we analyze the strategic behavior of the fluids, regarding the joining/balking dilemma, under the fully observable case, almost observable case and fully unobservable case. Furthermore, the expected equilibrium social benefits under different cases are discussed. At last, the optimal social benefit strategy is analyzed and the inefficiency of the equilibrium strategies is quantified via the Price of Anarchy (PoA) measure.

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Acknowledgements

The authors are grateful to the anonymous referees for their constructive comments that help us to improve the present paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing, 210044, Jiangsu, China

    Si-Jia Cai, Qing-Qing Ye & Yu-Fei Liu

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  1. Si-Jia Cai
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Contributions

S.-J. Cai contributed to the analysis and manuscript preparation; Q.-Q. Ye contributed to the conception of the study and helped perform the analysis with constructive discussions; Y.-F. Liu performed the experiment.

Corresponding author

Correspondence to Qing-Qing Ye.

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The authors declare that they have no competing interests

Additional information

The research was supported by the National Natural Science Foundation of China (Nos. 11901307 and 42275160).

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Cai, SJ., Ye, QQ. & Liu, YF. Equilibrium Strategies in a Fluid Queue with Working Vacations. J. Oper. Res. Soc. China (2023). https://doi.org/10.1007/s40305-023-00517-w

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