Introducing Repository Stability
Giuseppe Destefanis, Silvia Bartolucci, Daniel Graziotin, Rumyana Neykova, Marco Ortu
TL;DR
This work argues that software repositories can be analyzed through a control-theoretic stability lens, modeling them as dynamical systems whose state is captured by four metrics: commit patterns, issue resolution, PR processing, and community engagement. It introduces the Composite Stability Index ($CSI$), a weighted, normalized score that aggregates these metrics into a single health proxy, and defines four stability criteria with initial thresholds to quantify equilibrium maintenance over time. The paper establishes fundamental mathematical properties—boundedness, piecewise continuity, and long-term convergence—to justify the CSI as a robust measure of repository health and stability, and discusses theoretical and practical challenges for empirical validation and tool integration. The contributions lay a theoretical foundation for data-driven, stability-aware repository management and open avenues for future research on non-linear models, socio-technical factors, and cross-context applicability. Overall, the framework provides a rigorous, testable approach to assessing and maintaining sustainable software development practices.
Abstract
Drawing from engineering systems and control theory, we introduce a framework to understand repository stability, which is a repository activity capacity to return to equilibrium following disturbances - such as a sudden influx of bug reports, key contributor departures, or a spike in feature requests. The framework quantifies stability through four indicators: commit patterns, issue resolution, pull request processing, and community engagement, measuring development consistency, problem-solving efficiency, integration effectiveness, and sustainable participation, respectively. These indicators are synthesized into a Composite Stability Index (CSI) that provides a normalized measure of repository health proxied by its stability. Finally, the framework introduces several important theoretical properties that validate its usefulness as a measure of repository health and stability. At a conceptual phase and open to debate, our work establishes mathematical criteria for evaluating repository stability and proposes new ways to understand sustainable development practices. The framework bridges control theory concepts with modern collaborative software development, providing a foundation for future empirical validation.