hand, overutilization of a server is caused by a system failure and this can increase SLA violation. To reduce overutilization, we may need to migrate VMs from an overutilized host to an underutilized host. Managing resources efficiently is an interesting issue but VM consolidation is one of the most important solutions for this problem. The energy consumption of a data center can be reduced by a live VM migration and consolidation.

The single VM migration problem
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On a single host or a physical server, multiple VMs can be allocated. In terms of energy and performance awareness, a dynamic VMs consolidation problem and time discretion can be divided into several time frames, where each frame takes one second. The resource service provider pays the energy cost which is consumed by the physical servers. The cost will be calculated by multiplying the cost per unit energy and the time period. The resource usage and resource capacity of a single host is characterised by the CPU usages.\
Though VMs can experience a dynamic workload during an operation, CPU usages varies over time. When the maximum CPU performance that is allowed exceeds, the host is considered to be oversubscribed. In this case, the 