On the Optimal Policies of Time-Inhomogeneous Unreliable Service Systems

This paper investigates the optimal dynamic policies of time-inhomogeneous unreliable multi-server queueing systems with multiple customer sources and differentiated maintenance speeds. Under the criterion of global revenue optimality, we first elaborate the existence of bias-optimal policies and rigorously prove the existence of optimal time-inhomogeneous multi-threshold policies. We further derive two sufficient conditions to solve the monotonicity problem of the optimal time-inhomogeneous multi-threshold policies. Finally, to reduce the computational complexity of deriving optimal policies under the global optimization objective, we propose a heuristic algorithm based on the above theoretical results. The numerical examples not only demonstrate the strong performance of the proposed algorithm, but also indicate that the assumption of the monotonicity of production loss cost with respect to service states is no longer valid when the preset thresholds are differentiated by customer types.