This study develops a Markov-based framework for the stochastic modelling of reservoir dynamics under hydrological uncertainty. Complementing the existing literature on water storage management, which predominantly relies on numerical simulation or optimisation-based methods, the proposed approach provides an analytically transparent formulation that yields exact probabilistic and asymptotic results. Stationary distributions and limiting behaviours are derived for storage dynamics driven by both independent and temporally correlated inflows, extending the analytical capabilities of the classical Moran and Lloyd formulations. Discrete-state models are rigorously analysed to assess the long-term performance of finite-capacity reservoirs, while extensions to infinite-capacity systems allow steady-state inflow behaviour to be examined for planning and design. Furthermore, a continuous-state formulation generalises the approach to reservoirs with continuous inflow processes. Within this analytical setting, reliability and resilience metrics are formally defined and quantified, providing exact measures of long-term system robustness. The methodology is illustrated through a case study of the Quiebrajano dam in southern Spain, demonstrating its potential to support adaptive reservoir management. By linking rigorous Markov process modelling with performance metrics, this study provides a robust analytical framework for quantifying uncertainty and informing decision-making in complex storage systems.
To ensure the operational safety of rail-cum-road bridges, it is essential to accurately simulate the coupled vibrations of road vehicles, trains, and long-span bridge systems. Existing methods often simplify the coupled vibration models when considering elastic wheel-rail contact, as the conventional separated iterative method (SIM) requires small time steps to maintain computational stability, which reduces simulation accuracy. To address this, this paper develops a time-varying coupled vibration equation for the system by constructing dynamic interaction matrices, and proposes an efficient computational method for the coupled vibration of a road vehicle-train-long-span bridge system. This method employs a refined spatial coupling model while avoiding the necessity for small time steps imposed by stability requirements in SIM, thereby significantly improving computational efficiency. The reliability of the proposed method is verified through comparison with field-measured data. Furthermore, a case study is conducted on a single-level rail-cum-road bridge to compare the proposed method with SIM in terms of accuracy and efficiency. The results show that the proposed method achieves comparable accuracy to SIM, while its computational efficiency is improved by approximately 7 to 8 times under the scenario of simultaneous road vehicle and train crossings.
