Most priority-based schedulers lack the ability to control the relative execution rates of applications. A recent scheme, called lottery scheduling [WW94], uses randomization to control the execution rates of threads in proportion to the tickets allocated to them. However, randomization does not afford sufficient control over short periods of time; e.g., it would fail to provide the intended ex...

This supplement consists of several parts that refer directly to specific topics in the paper: A Proof of Equation (2) B Proof of Lemma 3.1 (Symmetric biproportional fit) C Technical details on why ”local affinity” is sufficient in Section 4.1 D Proof of Theorem 4.2 (Convergence of PSIPF) E Proof of Lemma 4.4 (L1-monotony) F Proof of Lemma 4.5 (Volume bounds) G Proof of Lemma 4.6 (Limit points)...

Shrinkage and warpage is a leading fact in casting. It is common to compensate shrinkage by scaling the tool by a certain percentage. The transformed 3D CAD model of a final product is used for tool generation. The transformations of CAD model include 3D scaling or external surface offset. Both methods are proportional and uniform in all three axes, and they are already included in a vast varie...

Real quantities can undergo such a wide variety of dynamics that the mean is often a meaningless reference point for measuring variability. Despite their widespread application, techniques like the Coefficient of Variation are not truly proportional and exhibit pathological properties. The non-parametric measure Proportional Variability (PV) [1] resolves these issues and provides a robust way t...

Iterative Proportional Fitting (IPF) generates from an input matrix W a sequence of matrices that converges, under certain conditions, to a specific limit matrix Ŵ . This limit is the relative-entropy nearest solution to W among all matrices of prescribed row marginals r and column marginals c. We prove this known fact by a novel strategy that contributes a pure algorithmic intuition. Then we f...

This paper reviews the arguments that justify the principles of proportional and degressively proportional representation.