Using correct design metrics and understanding the limitations of the underlying technology is critical to developing effective scheduling algorithms. Unfortunately, existing scheduling techniques used \emph{incorrect} metrics and had \emph{unrealistic} assumptions for fair scheduling of multi-tenant FPGAs where each tenant is aimed to share approximately the same number of resources both spatially and temporally. This paper introduces an enhanced fair scheduling algorithm for multi-tenant FPGA use, addressing previous metric and assumption issues, with three specific improvements claimed First, our method ensures spatiotemporal fairness by considering both spatial and temporal aspects, addressing the limitation of prior work that assumed uniform task latency. Second, we incorporate energy considerations into fairness by adjusting scheduling intervals and accounting for energy overhead, thereby balancing energy efficiency with fairness. Third, we acknowledge overlooked aspects of FPGA multi-tenancy, including heterogeneous regions and the constraints on dynamically merging/splitting partially reconfigurable regions. We develop and evaluate our improved fair scheduling algorithm with these three enhancements. Inspired by the Greek goddess of law and personification of justice, we name our fair scheduling solution THEMIS: \underline{T}ime, \underline{H}eterogeneity, and \underline{E}nergy \underline{Mi}nded \underline{S}cheduling. We used the Xilinx Zedboard XC7Z020 to quantify our approach's savings. Compared to previous algorithms, our improved scheduling algorithm enhances fairness between 24.2--98.4\% and allows a trade-off between 55.3$\times$ in energy vs. 69.3$\times$ in fairness. The paper thus informs cloud providers about future scheduling optimizations for fairness with related challenges and opportunities.
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