Optimal strategy analysis of a Markovian queue with variable vacation and vacation interruptions under unobservable cases

ABSTRACT

This paper makes a game-theoretic analysis of an M/M/1 queue with variable vacation and vacation interruptions. The Nash equilibrium mixed strategy and social utility maximization are derived based on a non-cooperative game theory and an optimization theory under different information precision levels, namely almost unobservable and fully unobservable cases. The explicit solutions of the entrance probabilities and the steady-state probability distribution of the system are investigated using the probability generating function and nonhomogeneous linear difference equations. Furthermore, the effects of the information levels and diverse system parameters on the equilibrium strategies, the arrival rates, and the expected benefits are explicitly illustrated by numerical comparisons. The research results can provide a theoretical basis and performance analysis tool for the optimal design in the wireless transmission and network communication system.

KEYWORDS:

• variable vacation
• vacation interruptions
• unobservable
• equilibrium strategy

Acknowledgements

The authors would like to thank the support of the National Natural Science Foundation (Nos. 62171143), China.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported by the National Natural Science Foundation of China [62171143]

Notes on contributors

Yitong Zhang

Yitong Zhang received a B.S. degree in mathematics and applied mathematics from the Hebei Normal University, Shijiazhuang, China, in 2018, and is currently working toward a Ph.D. in management science and engineering with Yanshan University, Qinhuangdao, China. Her current research interests include queueing economics and operations management.

Xiuli Xu

Xiuli Xu is a professor of statistics in the School of Science, Yanshan University, Qinhuangdao, China. Her main research interests include queueing theory, fluid model, and equilibrium analysis. She has published many papers on these topics in international journals, conferences as well as book chapters.

Mingxin Liu

Mingxin Liu is a professor of communication engineering in the School of Electronics and Information Engineering, Guangdong Ocean University, Zhanjiang, China. His main research interests include performance analysis of wireless sensor networks and underwater acoustic communication networks. He has published many papers on these topics in international journals and conferences.