Strategic joining in an M/M/1 queue with risk-sensitive customers

Abstract

To analyze a stochastic service system with customers choosing to join or balk upon arrival, we model the system as a single server Markovian queue with a quadratic utility function for customers. In contrast to classical models with risk-neutral customers, we focus on the queueing model with risk-sensitive ones and study customer strategies under individual interest equilibrium, server’s profit optimization, and social welfare optimization. The quadratic utility function allows us to take the risk and return tradeoff into account in analyzing customer joining strategies. We show that while some of the well-known results for the risk-neutral customer situation apply, others may fail to hold in some realistic risk-sensitive customer situations. Furthermore, we examine the queue length information effect on different performance measures from server’s profit and social welfare perspectives. A practical implication of this study is that managers of service systems should be very cautious about relying on classical stationary queueing analysis when customers are risk-sensitive.

Keywords:

• Absolute risk aversion coefficient
• equilibrium strategy
• quadratic utility function
• Markovian queue
• social welfare optimization
• profit maximization

Acknowledgements

The authors would like to thank the Editor and the anonymous referees for their valuable comments and suggestions which improved the presentation and the quality of this paper.

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The first author acknowledges the financial support to this project by National Natural Science Foundation of China [grant number 71571014], [grant number 71390334]; the second author acknowledges the financial support by Natural Sciences and Engineering Research Council of Canada [grant number RGPIN197319].