A Foreground–Background queueing model with speed or capacity modulation

Two models involving a foreground and a background queue are studied in the steady state. Service is provided either by a single server whose speed depends on the total number of jobs present, or by several parallel servers whose number may be controlled dynamically. Job service times have a two-phase Coxian distribution. Incoming jobs join the foreground queue where they execute phase 1, and then possibly move to the background queue for the second phase at lower priority. The trade-offs between holding and energy consumption costs are examined by means of a suitable cost function. Two different two-dimensional Markov processes are solved exactly. The solutions are used in several numerical experiments, aimed at illustrating different aspects of system behaviour.