The cloud storage service, known for its flexible and expandable nature, often has difficulties managing operating costs while ensuring dependable service and quick response times. This investigation presents a novel approach to optimizing cost efficiency in cloud storage systems by applying particle swarm optimization of the Markovian retrial queueing model in a generic setup by incorporating the working vacation and users’ discouragement behavior. Some users may opt not to enter the system or join the retry pool to wait for their turn if the server is occupied. After returning from working vacation, if there is one user available for service, the server can interrupt the vacation period. The server is subject to breakdown and can be recovered after getting the repair. In the proposed model, the server is prone to catastrophes and can fail at any time, leading to the entire system breaking down, and no users being able to access it during this period. Chapman–Kolmogorov (CK) steady-state equations associated with the quasi-birth-death (QBD) process are constructed to make a mathematical design. The governing equations framed to derive the queue length distributions and various performance indices are solved using the recursive method and difference equation theory. The fuzzified parameters are used to develop the FM/FM/1/WV model, which is analyzed using a parametric nonlinear programming approach. To determine the optimal design parameters, the cost minimization problem has been done using the quasi-Newton method and particle swarm optimization. This model incorporates features such as server failures, retrials, and catastrophes, thereby reflecting the complex nature of cloud storage operations. A suitable illustration of cloud storage is taken for both classical and fuzzified models to facilitate the numerical results of performance indices and optimal decision descriptors.

云存储服务以其灵活和可扩展的特性而闻名，但在确保可靠的服务和快速响应时间的同时，通常难以管理运营成本。这项研究提出了一种优化云存储系统成本效率的新方法，通过在通用设置中应用马尔可夫重审排队模型的粒子群优化，结合工作假期和用户的灰心行为。如果服务器被占用，一些用户可能会选择不进入系统或加入重试池来等待轮到他们。打工度假回来后，如果还有1个用户可以服务，服务器可以中断休假时间。服务器出现故障，修复后即可恢复。在所提出的模型中，服务器很容易发生灾难，随时可能发生故障，导致整个系统崩溃，在此期间没有用户能够访问它。构建与准生死（QBD）过程相关的查普曼-柯尔莫哥洛夫（CK）稳态方程以进行数学设计。使用递归方法和差分方程理论求解用于导出队列长度分布和各种性能指标的控制方程。模糊化参数用于开发 FM/FM/1/WV 模型，并使用参数非线性规划方法对其进行分析。为了确定最佳设计参数，使用拟牛顿法和粒子群优化来完成成本最小化问题。该模型融合了服务器故障、重试和灾难等特征，从而反映了云存储操作的复杂性。对经典模型和模糊模型都采用了云存储的适当说明，以促进性能指标和最佳决策描述符的数值结果。