Analysis of customer behavior under uncertainty on distribution of service time parameter in M/M/1 queueing system

In this paper, we first study the customer behaviors in an rechargeable single-server queueing system in which both optimistic and pessimistic customers who adopt different uncertainty decision criteria exist in the market. All the potential customers can't observe the queue length and are informed that the serve time is exponentially distributed with unknown parameter, which belongs to μ1, μ2. We study and compare the equilibrium percentages of queueing up among optimistic and pessimistic customers. We find that the former one is no less than the latter one. Besides, we do the necessary sensitive analysis and find that the price is not always has negative influence on the enthusiasm of queueing of the customers.