Equilibrium analysis of the fluid model with two types of parallel customers and incomplete fault

Abstract

This article considers the individual equilibrium behavior and socially optimal strategy in a fluid queue with two types of parallel customers and incomplete fault. Assume that the working state and the incomplete fault state appear alternately in the buffer. Different from the linear revenue and expenditure structure, an exponential utility function can be constructed to obtain the equilibrium balking thresholds in the fully observable case. Besides, the steady-state probability distribution and the corresponding expected social benefit are derived based on the renewal process and the standard theory of linear ordinary differential equations. Furthermore, a reasonable entrance fee strategy is discussed under the condition that the fluid accepts the globally optimal strategies. Finally, the effects of the diverse system parameters on the entrance fee and the expected social benefit are explicitly illustrated by numerical comparisons.