In modern computing systems, job resource requirements are massively heterogenous by default, with thousands or millions of unique resource-requirement combinations. Existing stochastic scheduling theory focuses on class-based scheduling policies, which cannot handle this heterogeneity.
We introduce a new model with continuous resource-requirement distributions, which captures this massive heterogeneity.
We derive the first throughput-optimal family of scheduling policies for the continuous-resource setting, combining workload-driven resource discretization with existing class-based policies. Our approach dramatically shortens mean queue lengths compared to existing standalone class-based policies. We also introduce novel low-complexity variants, in special cases where the requirement distribution has decreasing or symmetric density.