Mathematical Model of Delivery Speed in DevOps: Analysis, Calibration, and Educational Testing

The article presents a formalized, mathematical model of software delivery speed (S-model) in a DevOps environment.It quantitatively describes the interaction between key parameters, including development speed, automation level, CI/CD maturity, resource provisioning, and architectural complexity.The study aims to develop a mathematical structure that can reproduce nonlinear dependencies.The model captures threshold effects and interactions among technical and organizational DevOps factors, demonstrating both practical and educational relevance.The research methodology involves analyzing modern DevOps frameworks, such as DORA, CALMS, SPACE, and Accelerate.We build a functional model using saturation functions and exponential damping.The study also applies scenario modeling and calibrates models using pseudo-real and training empirical data.The results demonstrate that the proposed S-model accurately reproduces the behavior of DevOps processes and describes the influence of technical and organizational factors.Automation and CI/CD have the most significant impact in the early stages of maturity.System complexity exponentially reduces delivery speed.Changes in development speed only affect productivity when the level of automation is sufficient.Model calibration revealed an average deviation of 14.3% between the empirical and model values, confirming the model's applicability even in small learning teams.The scientific novelty of this work lies in creating a formally defined mathematical model of delivery speed in DevOps.