Threshold strategies and optimisation of fluid queue with priority customers and mixed vacation

This paper develops a fluid queue model for network nodes operating within a microgrid cluster, incorporating a mixed vacation strategy and a priority policy. Both the individual Nash equilibrium strategies and the optimal control strategies of the system are derived in the fully observable case. The individual balking thresholds for two fluid types are derived by using the conditional expectation theorem, and the expected fluid level is obtained via the Laplace–Stieltjes transform. A linear utility function is constructed to evaluate system performance, leading to the optimal control thresholds. Numerical examples and the seagull optimisation algorithm illustrate the results. These findings provide a theoretical foundation for optimal control design in wireless communication and network transmission systems.