Laadfactorma

Laadfactorma is a hypothetical mathematical construct used in the study of load factors in distributed systems and networks. It provides a compact way to compare how different allocations and scheduling policies respond to varying workloads.

Definition and properties: For a positive integer n and a load vector l = (l1, ..., ln) with li ≥ 0, a laadfactorma of order n is a function F_n: R_+^n → R_+ that is symmetric, homogeneous of degree 1, and monotone in each argument. In practice, F_n can be realized as F_n(l) = (sum_{i=1}^n α_i l_i^p)^{1/p} with p ≥ 1 and weights α_i > 0. Special cases include p = 1, giving F_n(l) = sum α_i l_i (a weighted total load), and p → ∞, where F_n(l) approximates max_i l_i (the bottleneck load). These forms show how different fairness or efficiency criteria can be encoded as a single scalar metric.

Interpretation and usage: F_n encodes various design goals by choosing p and weights, enabling comparisons of schemes under a common framework. In theoretical analyses of load balancing, capacity planning, and resource allocation, laadfactorma serves as a parameterization to study sensitivity to workload distributions, identify bottlenecks, and evaluate policy performance.

History and terminology: The term laadfactorma appears in didactic or exploratory contexts to illustrate how a scalar load measure can be constructed from a vector of component loads. It does not have a single formal standardization in published literature.

See also: Load balancing, Norm (mathematics), Resource allocation, Bottleneck analysis.

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