when the SLA is violated $(v - m \geq T)$. In this case, the duration of SLA violation is 0. In the second case, VM migration starts before the SLA violation , after which the migration starts later, even though the SLA has been violated. Lastly, in the third case, VM migration starts after the SLA violation. According to Beloglazov and Buyya, \[18\], “The optimal offline algorithm for the single VM migration problem incurs the cost of $\frac{T}{s}$, and is achieved when $\frac{(v-m)}{T}=1$ and the competitive ratio of the optimal online deterministic algorithm for the single VM migration problem is $2 + s$, and the algorithm is achieved when $m = v$”.

Problem of Dynamic VM Consolidation
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The resource utilization of cloud data centers could be improved by dynamic VM consolidation, which can also improve energy efficiency. Dynamic VM consolidation can determine when VMs reallocation should be initiated for an overloaded host. The VMs reallocation decision-making influences the proper resource utilization and QoS requirements delivered by the system.\
In our work, we deal with complex problems of dynamic VM consolidation, which requires us to consider multiple VMs and multiple hosts. All VMs confront variable workloads. Every host has a 