The M/G/1 queue with two service speeds (Q2749136)

Consider a single server queue with Poisson arrivals, general service time distribution, and the service speed alternating between a low and a high level. The server's sojourn times in the high speed state are exponentially distributed, the sojourn times in the low speed state have general distribution. The authors derive formulas for the joint state process of the total workload (in steady state) and the (speed) state of the server and study the tail behaviour of the workload. This is done under the assumption that for the high speed sojourn times diffferent specifications are introduced: Rational Laplace-Stieltjes transform or to vary regular at infinity. Here different asymptotics occur, depending on whether the offered load is smaller or larger than the low service speed.