This paper considers an on-off fluid queue model.The on and off states of the system appear alter-nately,and the sojourn times at these two different states are independent,and each one follows an exponential distribution.The fluid flows into the system buffer with some strategies to wait for the system service under the first-come first-served discipline.Here the system can process the fluid in the buffer only when the system is on state.With given utility functions such as an expected average social profit,and an individual expected profit,the equilibrium strategies are characterized under both the fully unobservable case and the partially observable case.