The cloud computing network (CCN) has become a new paradigm for the business and clients as the development of information technology. To guarantee the CCN keep a good quality of service (QoS), the maintenance action is necessary when the CCN falls to a specific state such that it cannot afford enough capacity to meet demand d. In the CCN, edges and nodes have various capacities due to failure, partial failure, or maintenance; thus, the CCN has several possible states. This paper proposes an algorithm to estimate the performance of a CCN under maintenance budget with nodes failure. Hence, the maintenance reliability is developed to measure the capability that the CCN can send d units of data from the cloud to the client through multiple paths under the maintenance budget and time constraints. Furthermore, the system supervisor can conduct the sensitive analysis to improve/investigate the most important part in a large CCN afterwards.