At present, many cloud services are managed by using open source software,\nsuch as OpenStack and Eucalyptus, because of the unification management of data, cost\nreduction, quick delivery and work savings. The operation phase of cloud computing has\na unique feature, such as the provisioning processes, the network-based operation and the\ndiversity of data, because the operation phase of cloud computing changes depending on\nmany external factors. We propose a jump diffusion model with two-dimensional Wiener\nprocesses in order to consider the interesting aspects of the network traffic and big data\non cloud computing. In particular, we assess the stability of cloud software by using\nthe sample paths obtained from the jump diffusion model with two-dimensional Wiener\nprocesses. Moreover, we discuss the optimal maintenance problem based on the proposed\njump diffusion model. Furthermore, we analyze actual data to show numerical examples of\ndependability optimization based on the software maintenance cost considering big data on\ncloud computing.
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