Equilibrium in vacation queueing system with complementary services

Abstract

This paper studies a queue with server vacations where customers need complementary services. The main service provider or the queue server may become absent for a random period of time called a vacation. More specifically, the server adopts a multiple vacation policy which means that the server keeps taking vacations until at least a customer waiting at the vacation completion instant. The secondary service provider offers an instantaneous service (no delay or no queue). The two services are complementary and a customer must receive both services if he or she joins the system. We investigate the equilibriums of such a system in a time-based fee model under competition and monopoly cases, respectively. Furthermore, a fixed or flat fee model is also analysed.

Keywords:

• Multiple vacations
• queueing system
• game theory
• complementary services
• nash equilibrium

Acknowledgements

Yan M. would like to thank China Scholarship Council for supporting her visit to Simon Fraser University.

Notes

No potential conflict of interest was reported by the authors.

Present address: School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China.

Additional information

Funding

This work was supported by the National Science Foundation of China [grant number 11271373], Hunan Provincial Innovation Foundation For Postgraduate [grant number CX2013B042], Startup Research Fund of Zhengzhou University [grant number 129-51090091].