# A Novel Self-Adaptive VM Consolidation Strategy Using Dynamic Multi-Thresholds in IaaS Clouds
## 2 Preliminaries
### Formulations and Assumptions  
Let us consider that a large cloud data center provides cloud resources in the form of virtual machine instances. Usually, there are three main steps for VM consolidation: Source PM selection, Target VM selection and Target PM selection. For the first step of selecting Source PM, threshold-based method is used to determine whether a PM is overloaded or underloaded. If a PM is considered to be overloaded, which means its resource utilization is over the corresponding upper threshold, then it will be selected as the Source PM and some potential VMs in it will be migrated out to maintain the QoS; if a PM is determined to be underloaded based on the comparation of lower threshold, then all VMs in this PM will be migrated out to minimize energy consumption. To formulate the problem (Table 1), a physical server can be uniquely identified in the form of \(PM(j)=\langle VM_{List},\ P_{j},\ Status\rangle\), where: \(VM_{List}\) is the list of all VMs on \(PM(j)\); \(P_{j}\) represents all resource  
Figure 2: Centralized model of cloud resource management. utilization ratio on \(PM(j)\) and can be divided into different kinds of resources of CPU, RAM and network bandwidth in the form of \(\langle P_{j}^{c},\ P_{j}^{r},\ P_{j}^{b}\rangle\); Status shows the current workload of this PM, such as overloaded, moderate or underloaded; and \(j\) the unique identifier of a server which arrange from 1 to \(n\). Thus, we can denote \(m\) active servers in a cloud center as \(PM=\langle PM(1),\ PM(2),\ \dots,\ PM(m)\rangle\). Similarly, the VM instance is represented in the form of \(VM(i)=\langle PM(j),V_{j}\ \rangle\), where \(PM(j)\) shows the PM where this VM belongs to, \(V_{j}\) represents each resource utilization on it, and \(i\) is the unique id of a VM which arrange from 1 to \(m\). In this paper, what we mainly focus on is to propose a novel strategy for VM consolidation, aiming at saving much energy consumption and reaching high QoS. While in the process of virtual machine integration, a frequent and indispensable step is VM migration, which will affect the actual computing of resource utilization in each PM to some extent. Thus, we made the following assumptions of VM migration in the process of our consolidation strategy:  
Assumption 1: The VM selected to execute migration does not cause significant resource consumption during its migration process. Assumption 2: The time for the dynamic migration of VMs is not counted to compare the efficiency of different strategies. For Assumption 1, in view of the numerous details in the process of VM migration, many scholars specialize in this area to research efficient strategy for dynamic VM migration. Yet this article does not consider too much detail of it and we mainly focus on the VM consolidation strategies. For Assumption 2, the length of the migration time of the each VM is not used as the standard for comparing the advantages or disadvantages of different strategies, as there is no correlation between migration time and consolidation strategies. Based on that, when we calculate the cost of VM migration, we mainly consider the number of VM migrations as an important basis to measure the merits of different consolidation strategies, and the following section will describe more details of our proposed VM consolidation strategy.