Closed-Loop Collapse via Bottleneck Saturation: A Process Engineering Framework for Tumorigenic Phase Transition and Cellular Reset

This paper introduces a novel process engineering framework that models the emergence of cancer not as an exogenous genetic program, but as a phase transition resulting from the systemic collapse of a biological closed-loop control system. By applying control theory, state-space representation, and M/M/c/K queueing theory, we demonstrate how homeostatic tissue transitions into an open-loop exponential divergence triggered by immune bottleneck saturation. Conventional oncology often models tumorigenesis through isolated genetic mutations. In contrast, this framework shifts the paradigm towards capacity management and process control. We define the tumorigenic cellular reset as the mathematical consequence of a saturated inspection operator (Φ_sat) failing to process an accumulated entropic noise vector (Factor X). Key features of this theoretical and computational model include: Nonlinear Saturation Operator: Modeling the absolute capacity limit (C_max) of the immune inspection channel. Pole Migration (Root Locus): Visualizing the critical transition from BIBO stability (left-half plane) to open-loop instability (right-half plane). Queueing Theory Integration: Mapping the uninspected cellular leakage rate against the biological system's utilization factor (ρ). This interdisciplinary approach provides a rigorously quantifiable foundation for understanding tumorigenesis as a deterministic failure of systems dynamics, offering new perspectives for capacity-based therapeutic interventions.