Analysis of a variable service speed single server queue with batch arrivals and general setup time

In this paper, we consider an MX/M/1/GSET-VARI queue, which is a single server queue with a variable service speed, batch arrivals and general setup times. The service speed of the server is proportional to the number of jobs in the system. Our model is motivated by power-aware servers in data centers where dynamic scaling techniques are used. In this paper, we obtain the necessary and sufficient condition for the stability of the system and derive an expression for the probability generating function of the number of jobs in the system. In addition, we present some numerical results in order to show the energy-performance trade-off of our queueing system.