# v-Mapper: An Application-Aware Resource Consolidation Scheme for Cloud Data Centers +
## Data Center Design and the v-Mapper System Model
### VM Placement and the Data Center Model
Each member of the row vector \(\mathrm{v}\) represents the resource usage for its respective element in row vector \(\mathrm{a}\). By considering a case where the number of service requests accepted by the cloud environment does not exceed its aggregate compute nodes, the condition can be expressed mathematically as:

\[\mathrm{a.v}=\sum_{i=1}^{n}\mathrm{a_{c}v_{c}}\leq\mathrm{N} \tag{7}\]

where N shows the number of aggregate compute nodes. Due to the varying allocation models and schemes, workload evaluation for cloud services is increasingly complex. However, applying probability to schemes with varying behavior can address these concerns. Therefore, by employing the recursive methodology approach presented in [27; 28], we can calculate the probability \(\mathrm{p}\) of an individual cloud node capacity \(\mathrm{q}\) as:

\[\mathrm{p(q)}=\sum_{\mathrm{a.av=n}}\frac{\alpha_{1}^{\mathrm{a_{1}}}}{\alpha _{1}!},\ldots,\,\frac{\alpha_{1}^{\mathrm{a_{n}}}}{\alpha_{n}!}\mathrm{n}=0,1, 2,\ldots,\,\mathrm{N} \tag{8}\]

The measured node occupancy probability can be input to the Fuzzy-AHP for fine tuning its decision structuring. Now, the submitted workload occupancy probability in the proposed cloud system can be evaluated. To ensure it upholds the workload occupancy of the entire cloud system, v-Mapper ensures that the resource allocation is made under the cloud's permissible resource threshold limits. The workload admission control algorithm (Algorithm 2) ensures that sufficient resources are available to entertain a request. If resources are scarce, a message about the unavailability of resources is prompted. This conditional approach used in v-Mapper makes it simple yet effective to implement. In this experimental study, the available resources of a cloud are considered as a set containing the cloud's physical resources, the computational resources, the memory and the bandwidth resources. ```
1:Input: Workload admission request
2:Output: Workload admission decision
3: Let \(\text{res}_{\text{ava}}\) denote the available resources for a VM
4: Let \(\text{res}_{\text{req}}\) denote the requested resources by a VM
5: Let queue denote the request queue
6:while(!queue.isEmpty())
7:{
8: req = queue.firstRequestResource();
9:if(\(\text{res}_{\text{req}}\leq\text{res}_{\text{ava}}\))
10:{
11: \(\text{res}_{\text{ava}}\) = \(\text{res}_{\text{ava}}\) - \(\text{res}_{\text{req}}\)
12: queue.pop();
13: }
14: Else
15: {
16: sendMessage(\"resources inadequate\");
17: queue.pop();
18: }
19: }
```
**Algorithm 2** VM workload admission

### VM Scheduling Scheme

v-Mappers' scheduling policy (for admitted applications) involves locating resources that are subject to multiple global optimization constraints and that require searching of a large pool of resources. The proposed scheduler satisfies these requirements by using a fair approach to managing workloads. Our study considered three scenarios (Figure 4) to evaluate v-Mapper's scheduling policy. Scenario 1: The VM hosting the applications is manually scheduled to receive batch processing of the incoming resource demands. The demands accepted by the VCPU of the VMM are synchronized before processing them. Scenario 2: The scheduling strategy for real-time scheduling is set up in such a way that all the VCPUs contain the upcoming scheduling requests based on a load-sharing policy (LSP) [29], which optimally dispatches the incoming workloads according to the current availability of the VMs. The LSP facilitates the scheduling process by permanently engaging the minimal number of available VMs for the incoming workloads. Scenario 3: We developed a load-sharing scheme that manages the VMs on the basis of the incoming workloads, enabling all the VCPUs to be scheduled and synchronized in response to the received workloads. This eases VM scheduling and improves the comprehensive understanding of the virtual infrastructure at both the physical and logical levels. Theoretical analysis: v-Mapper uses a load-sharing concept to improve fairness.