Workload analysis of an M/G /1 queue under the PλM policy with a set-up time

We consider the PλM service policy for an M/G/1 queueing system, in which the service speed is changed from 1 to M after an exponentially distributed set-up time, when the workload has exceeded level λ. The explicit expression for the stationary distribution of the workload is obtained through the level crossing arguments.