Task assignment in a heterogeneous server farm with switching delays and general energy-aware cost structure

• We model a server farm with switching delays and a general cost structure.
• We derive value functions for M/G/1M/G/1 queues with switching delay.
• Switching (setup) delay shows up as an additional term in the value function.
• We develop energy-aware policies that also control the set of active servers.
• Our heuristics outperform standard policies over a wide range of parameters.

We consider the task assignment problem to heterogeneous parallel servers with switching delay, 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 task assignment (dispatching) policies that minimize the long-run average cost. To evaluate our starting policy, we first analyze a single work-conserving M/G/1M/G/1 queue with a switching delay and derive a value function with respect to a general cost structure. Our costs include energy related switching and processing costs, as well as general performance-related costs, such as costs associated with both means and variability of waiting time and sojourn time. The efficiency of our dispatching policies is illustrated with numerical examples.