Queues with service speed adaptations

In this paper, we consider various queueing models in which the server can work at two different service speeds. The speed of the server depends on either the number of customers or the workload. Our main interest is in the model in which service speed adaptations can take place only at the arrival instants of an external Poisson observer. Using insightful probabilistic arguments, we give the structure of the steady-state queue length and workload distributions in the various models. In addition, in case the service speed can only be adapted right after departure instants based on the number of customers, we provide explicit and intuitively appealing expressions for the steady-state distribution of the number of customers present.