From the perspective of system design and quality of service (QoS), system reliability is one of the essential performance indicators to measure the probable reliability of a network. In terms of a practical cloud computing system (CCS), edges and nodes have various capacities or states due to failure, partial failure, or maintenance. Thus, the CCS is a typical capacitated-flow network. To guarantee a good level of quality and reliability, the CCS should be maintained, so as not to fall into a failed state whereby it cannot provide sufficient capacity to satisfy demand. Thus, system reliability is developed in this paper to evaluate the capability of the CCS to send d units of data from the cloud to the client through two paths under both the maintenance budget and time constraints. An algorithm with an adjusting procedure based on the branch-and-bound approach is proposed to evaluate the system reliability. The relevant proof shows that the proposed algorithm is reasonable and appropriate for measuring the system reliability of the CCS. According to different maintenance budgets and corresponding system reliability, the system supervisor could determine a reasonable maintenance budget to maintain a good level of quality and reliability of the CCS. From the perspective of system design, the system supervisor could further conduct a sensitivity analysis to improve or investigate the most important part in a large CCS based on system reliability.

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