This paper presents a preliminary model for managing involuntary technical debt in agile environments by formulating, in an integrated way, the dynamics among backlog, debt, velocity, and economic value. The work distinguishes initiated but unfinished functional debt from a simple defect back log and from rework, interprets productivity degradation as technical-debt interest, and derives the naive maximum-remediation policy in order to show its limitations against an intertemporal value-based decision. On this basis, a dynamic policy uk is proposed to balance new development and remediation; a decreasing marginal-value structure is incorporated; and the model is extended to discrete, inhomogeneous items. Exploratory validation through sensitivity analysis and MonteCarlo simulation shows behavior consistent with the economic intuition of the model. Finally, the limits of the formulation are made explicit: its macroscopic nature, its dependence on organizationally stable parameters, its assumption of intertemporal rationality, and its requirement of weak coupling among stories.

翻译：本文提出了一种在敏捷环境中管理非自愿技术债务的初步模型，该模型以集成方式刻画了待办事项、债务、速度与经济价值之间的动态关系。研究区分了已启动但未完成的功能债务与单纯的缺陷待办事项及返工，将生产率下降解释为技术债务利息，并推导出朴素的最大化修复策略以揭示其相对于跨期价值决策的局限性。在此基础上，提出了动态策略uk以平衡新功能开发与债务修复，引入了递减边际价值结构，并将模型扩展至离散、异质项。通过敏感性分析与蒙特卡洛仿真进行的探索性验证显示，模型行为与其经济直觉一致。最后，明确了该模型的局限性：宏观性、对组织稳定参数的依赖、跨期理性假设，以及用户故事间弱耦合的要求。