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

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.