Knowledge base

Two classical metrics from parallel computing carry over directly into DLT. Speedup S(m) = T(1) / T(m) is the ratio of the single-processor completion time to the m-processor makespan. Perfect speedup is S(m) = m, meaning every added processor contributes its full capacity. Efficiency E(m) = S(m) / m normalises speedup by the processor count, with perfect efficiency equal to 1. In the startup-free star model, the DLT closed form delivers near-perfect efficiency for any m: every additional processor reduces the makespan, and the allocated fraction shrinks proportionally.

When startup latencies Sᵢ are nonzero, the picture changes qualitatively. Each processor incurs a fixed Sᵢ overhead regardless of how small its assigned chunk is. For large m and small V, the communication startup cost per processor can exceed the computation time saved by adding it, and speedup saturates: there exists a crossover processor count mbeyond which adding workers increases the makespan rather than reducing it. The saturation threshold m depends on the ratio of startup to computation parameters and is computable in closed form from the DLT system. Understanding this threshold is the primary practical output of a speedup analysis.

Isoefficiency analysis asks: how fast must the problem size V grow, as m increases, to hold efficiency above a target threshold? The answer is the isoefficiency function V(m). A sub-linear isoefficiency function (V needs to grow slower than m) means the system scales well; a super-linear function signals that startup overhead dominates at the chosen scale and the hardware is a poor match for small workloads. The Solver Studio’s isoefficiency map evaluates E(m) over a grid of (V, m) pairs and colour-codes the result, giving an at-a-glance view of the region where adding processors remains beneficial.

The isoenergy map is the energy-aware counterpart: it evaluates total energy consumption over the same (V, m) grid and identifies the combinations where adding a processor reduces energy (because computation time drops faster than idle and startup energy rises). The Pareto front synthesises the two objectives into a single curve in the time-energy plane: the set of non-dominated schedules where no improvement in makespan is possible without a penalty in energy, or vice versa. Together, the speedup curve, the isoefficiency map, the isoenergy map, and the Pareto front form the interactive analysis toolkit available in the Solver Studio for any configured hardware model.