Optimal Control of a Heterogeneous Two Server System With Consideration for Power and Performance

In this thesis we consider a system of two heterogeneous servers with a shared queue, and examine a scheduling policy for the optimal control of such a system. Previous results by Lin and Kumar and Koole found that a threshold policy, i.e., refraining from assigning a job to a slow server until a certain threshold has been exceed in the job queue, is optimal when seeking only to minimize the mean sojourn time of a job in the system. We build upon these results and generalise the analytical proof of the threshold policy's optimality to take into account power consumption as another performance metric, in the setting where the faster server is more efficient. We also obtain preliminary results for a setting where the slower server is more efficient, under the restriction of low arrival rates. We use experimental data from simulations to provide an assessment of the real world applicability of a threshold policy in this setting; a comparison between a threshold policy with optimal thresholds and a first-come-first-serve policy shows that it achieves a cost improvement of up to 29.19% over the naive policy