This paper develops a comprehensive Markov-based framework for modelling reservoir behaviour and assessing key performance measures such as reliability and resilience. We first formulate a stochastic model for a finite-capacity dam, analysing its long-term storage dynamics under both independent and identically distributed inflows, following the Moran model, and correlated inflows represented by an ergodic Markov chain in the Lloyd formulation. For this finite case, we establish stationary water balance relations and derive asymptotic results, including a central limit theorem for storage levels. The analysis is then extended to an infinite-capacity reservoir, for which normal limit distributions and analogous long-term properties are obtained. A continuous-state formulation is also introduced to represent reservoirs with continuous inflow processes, generalizing the discrete-state framework. On this basis, we define and evaluate reliability and resilience metrics within the proposed Markovian context. The applicability of the methodology is demonstrated through a real-world case study of the Quiebrajano dam, illustrating how the developed models can support efficient and sustainable reservoir management under hydrological uncertainty.

翻译：本文构建了一个全面的基于马尔可夫的建模框架，用于模拟水库行为并评估关键性能指标，如可靠性与恢复力。我们首先针对有限容量水坝建立随机模型，在独立同分布入流（遵循Moran模型）以及相关入流（以Lloyd公式中的遍历马尔可夫链表示）两种情形下，分析其长期蓄水动态。对于此有限容量情形，我们建立了稳态水量平衡关系，并推导了渐近结果，包括蓄水水平的中心极限定理。随后将分析推广至无限容量水库，得到了正态极限分布及类似的长期性质。本文还引入了连续状态建模框架，以表征具有连续入流过程的水库，从而推广了离散状态模型。在此基础上，我们在所提出的马尔可夫框架内定义并评估了可靠性与恢复力指标。通过Quiebrajano水坝的实际案例研究，验证了该方法的适用性，展示了所开发模型如何在水文不确定性条件下支持高效且可持续的水库管理。