A workload-dependent M/G/1M/G/1 queue under a two-stage service policy

We consider an M/G/1M/G/1 queueing system where the speed of the server depends on the amount of work present in the system. As a service policy, we adopt the Pλ,τM release policy in a dam model. By using the level crossing theory and solving the corresponding integral equations, we obtain the stationary distribution of the workload in the system explicitly.