host is used by VMs, which is characterised by the CPU’s performance parameter. Due to dynamic workload, the CPU usage varies over time and it its usage is considered to be oversubscribed when the request of VMs exceeds the CPU’s maximum performance. The oversubscription issue occurs when the SLA is violated, and the penalty for SLA violation is calculated by $C_vt_v$ ($C_v$ is the SLA violation cost of single unit of time and $t_v$ is the SLA violation time duration). During the VM migration an extra host is accommodated until the migration process is completed and the time needed for migration is $T$ so, total power consumption during migration is $2C_pT$. At some point of time $v$, if SLA violation starts and SLA violation continued until $m$, then the total SLA violation time $r$ will be as Eq. (1).\
$$\label{first}
r=m-v$$

The cost function $C(v,m)$ for SLA violation will be as Eq. (2) for three different cases.

$$\label{2nd}
\footnotesize
C(v,m)=\left\{\begin{array}{l@{\quad}l} (v-m)C_p & \text{if} \ m<v,v-m \geq T, \\ (v-m)C_p+2(m-v+T)C_p+(m-v+T)C_v & \text{if} \ m \leq v,v-m<T, \\ rC_p+(r-m+v)C_p+rC_v & \text{if} \ m>v. \end{array} \right.$$

In the first case, VM migration starts before SLA violation $(m < v)$ and the migration starts 