Energy-aware job assignment in server farms with setup delays under LCFS and PS

We consider the job (or task) assignment problem to heterogeneous parallel servers, where servers can be switched off to save energy. However, switching a server back on involves a constant server-specific delay. We will use one step of policy iteration from a starting policy such as Bernoulli splitting, in order to derive efficient job assignment (dispatching) policies that minimize the long-run average cost. In our earlier work, we assumed FCFS scheduling at the servers. In this paper, we focus on LCFS and PS, where the latter in particular serves as an important model, e.g., for server farms where jobs are processed concurrently. LCFS, on the other hand, is a robust policy that works especially well when service times are highly variable, and is easier to implement than the standard alternative policy for high variability, LAS (least attained service time). Our costs include energy related running costs, as well as performance related mean response times. The efficiency of the resulting operating policies is illustrated with numerical examples, where we also compare FCFS to LCFS and PS.