Cloud computing is an emerging technology that greatly shapes our lives, where users run their jobs on virtual machines (VMs). The VMs are hosted in physical machines (PMs) provided by a cloud service provider. Scalability and metering are two popular features among users of commercial cloud computing services, because they allow users to reduce their operating costs and save the investment in upfront infrastructures. As a new paradigm of distributed computing, cloud computing has brought several key advantages into our lives, such as on-demand scaling and pay-as-you-go metered service. As a contribution of virtualization technology, VM migration enables the resource rearrangement on the fly. In that case, the cloud provider can migrate the VM to a separated hardware when more computing resources are required. Improving this migration process is an active area of research. This thesis focuses on the resource management topic in the cloud computing research area. More specifically, we dig into the resource allocation schemes, aiming at harnessing limited infrastructure resources more efficiently. Generally speaking, this thesis mainly focus on VM placement problem with different objectives. In the first part, we focus on maximizing the elasticity of input VMs' resource demands. In the second part, we focus on minimizing the average makespan of input tasks. In the third part, we try to minimizing the total completion time, however, we apply VM migration into our VM placement algorithm.
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