Knowledge base

The energy model augments the base DLT model with a power-state machine and a load-dependent running-energy function. Every worker passes through four states during a scheduled computation. Idle (power P^I): the worker is powered on but not yet addressed by the originator. Startup (power P^S): the fixed-overhead connection phase before data begins to flow, lasting Sᵢ regardless of chunk size. Networking (power P^N): the worker is actively receiving its chunk over a window of Cᵢ·αᵢ. Running (power P^R): the worker is computing over a window of Aᵢ·αᵢ. Each state draws a distinct power level, so the total energy consumed by worker i is the sum of power-times-duration across all four phases.

The running energy ε(α) is the dominant and most interesting term. It is modelled as a convex piecewise-linear function of the chunk size α. For small chunks that fit entirely within the processor cache (in-core operation, α ≤ Bᵢ), the energy per unit of load is low and nearly flat: data is accessed from fast local memory with minimal cache-miss penalty. Once the chunk exceeds the cache boundary and must be streamed from main memory (out-of-core operation, α > Bᵢ), the energy rate rises steeply because each unit of load now incurs additional memory-bus transfers. The breakpoint is the memory bound Bᵢ, so the two terms of the piecewise function are directly linked to the memory parameter already present in the base model.

With the energy model active, the solvers can minimise total energy subject to a makespan deadline, or trace the time-energy Pareto front: the set of non-dominated schedules where no further time reduction is achievable without increasing energy consumption. A tight deadline forces the scheduler to activate more processors, spreading the load across more idle and startup phases even as each worker’s computation window shrinks. A loose deadline allows consolidation onto fewer, more efficient processors that operate mostly in-core. The Solver Studio’s Pareto view sweeps the deadline from the single-processor baseline down to the optimal makespan and plots each Pareto-optimal point, letting the operator choose the operating point that best matches their power or thermal budget. The isoefficiency and isoenergy maps extend this view to sweeps over the (V, m) plane.