Cloud computing has recently garnered significant interests from both industries and academia. The industrial pioneers such as Enomaly therefore offered commercial platforms which enable customer-provided resources for cloud computing. Such systems provide very flexible service especially to the customers who seek to run short-term and customized tasks at minimum costs. In this paper, we investigate the service availability challenges on the customer-provided clouds. We find that their cloud resources are highly heterogeneous and dynamic, the service availability remains a critical problem in such systems. This introduces a severe bottleneck to provide reliable cloud service to support long-term tasks. To mitigate such a problem, we present an optimal resource provisioning algorithm that ensures service availability with minimized lease costs. The trace-based simulation further demonstrates its reliability as a promising complement to the datacenter-based cloud services.