A formal approach to the mapping of tasks on an heterogenous multicore, energy-aware architecture

The search for optimal mapping of application (tasks) onto processor architecture (resources) is always an acute issue, as new types of heterogeneous multicore architectures are being proposed constantly. The physical allocation and temporal scheduling can be attempted at a number of levels, from abstract mathematical models and operational research solvers, to practical simulation and run-time emulation. This work belongs to the first category. As often in the embedded domain we take as optimality metrics a combination of power consumption (to be minimized) and performance (to be maintained). One specificity is that we consider a dedicated architecture, namely the big.LITTLE ARM-based platform style that is found in recent Android smartphones. So now tasks can be executed either on fast, energy-costly cores, or slower energy-sober ones. The problem is even more complex since each processor may switch its running frequency, which is a natural trade-off between performance and power consumption. We consider also energy bonus when a full block (big or LITTLE) can be powered down. This dictates in the end a specific set of requirements and constraints, expressed with equations and inequations of a certain size, which must be fed to an appropriate solver (SMT solver in our case). Our original aim was (and still is) to consider whether these techniques would scale up in this case. We conducted experiments on several examples, and we describe more thoroughly a task graph application based on the tiled Cholesky decomposition algorithm, for its relevant size complexity. We comment on our findings and the modeling issues involved.