Module 02 / 04

Measure what the current architecture can still deliver.

The original research question was “which feasible configuration has the best score now?”. That remains useful, but it is no longer the full decision problem.

Measure what the current architecture can still deliver.Open section

Capability

Measure what the current architecture can still deliver.

\[ W=B\,V, \qquad W_j(cfg)=\sum_{i\in R(cfg)} w_{ji}. \] The resource-to-function influence matrix is derived from the architecture through service composition and resource consumption.

\[ \varphi_j(t,cfg)=W_j(cfg)\!\prod_{i\in R(cfg)}\rho_i(t)^{w_{ji}/W_j(cfg)}, \qquad S(t)=\sum_j \alpha_j\,\delta_j(cfg)\,\varphi_j(t,cfg). \] The geometric form is intentionally non-compensatory: a critical resource cannot be hidden by healthier unrelated resources.

The original research question was “which feasible configuration has the best score now?”. That remains useful, but it is no longer the full decision problem.

New question

Which sequence of verified configurations preserves the greatest mission capability over time without violating transition, stability or real-time constraints?

See the turning point →

A stable configuration does not imply a stable sequence of configurations.Open section

Admissibility

A stable configuration does not imply a stable sequence of configurations.

Configurations form a finite, design-time verified graph. A transition is allowed only if the target remains resource-feasible, function-feasible and dynamically admissible.

\[ G_e=(\mathcal C,\mathcal T), \qquad T_{ij}\in\mathcal T \Leftrightarrow Adm_R(C_j,\rho)\wedge Adm_F(C_j)\wedge Stab(C_i,C_j). \]

For switched closed-loop configurations, repeated switching is constrained by a minimum dwell interval.

\[ \tau_d>\frac{\ln\mu}{2\gamma_{\min}}, \qquad f_{\max}<\frac{2\gamma_{\min}}{\ln\mu}. \] The worst-conditioned configuration can determine the whole catalogue. This is why catalogue composition is a design variable, not just a list of fallbacks.

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