A hybrid energy-aware algorithm for virtual machine placement in cloud computing

Abstract

Virtual Machine Placement (VMP) plays a significant role in improving efficiency of Cloud Data Center (CDC). With the dramatic increase in the use of cloud computing, it seems necessary to apply effective algorithms to reduce the power consumption of CDC. VMP is known as a NP-Hard problem that cannot be solved by deterministic algorithms in polynomial time. In this paper, an algorithm named Combinated Random Best First Fit (CRBFF) is proposed with the aim of increasing the Quality of Service (QoS), in which Virtual Machines (VMs) are optimally placed on heterogeneous Physical Machines (PMs). The effectiveness of CRBFF is evaluated by different metrics on Google Compute Engine (GCE), Amazon Web Service Elastic Compute Cloud (AWS EC2) and Microsoft Azure scenarios and the results show that CRBFF performs better than other common algorithms.

Appendix A: Illustrative example

In this part, an example is given to trace the steps of the CRBFF algorithm, and how it works is explained by calculating the parameters value of all the equations. We consider a CDC consisting of two PMs with different resource capacities as shown in Table 6. According to the explanations given in Sect. 3, each PM has a maximum and minimum power consumption. In this example, we assume the maximum value of the PM $P_1$ to be 1300 and PM $P_2$ to be 2000, and the minimum value for each of them is obtained by multiplying the maximum value by 0.7. Then, through Eq. 6, the power efficiency of each PM is calculated, which is also shown in Table 6.

Table 6 PMs configurations ($P_i$: PMs number, $C^{cpu}_i$: cpu capacity of $P_i$, $C^{ram}_i$: memory capacity of $P_i$, $P^{max}_i$: maximum power consumption of $P_i$, $P^{min}_i$: minimum power consumption of $P_i$, $P^{PE}_i$: power efficiency of $P_i$)

Also, five VMs are considered with the amount of resource demands in different scales, which can be seen in Table 7.

Table 7 VMs configurations ($V_j$: VMs number, $R^{cpu}_j$: cpu demand of $V_j$, $R^{ram}_j$: memory demand of $V_j$)

According to Algorithm 1, in the first part, PMs are sorted in descending order based on their power efficiency, in which in this example, PM $P_1$ has a higher priority than PM $P_2$, and as long as it has enough capacity, it can be a candidate for the placement process. Next, the number of randomly selected VMs is calculated through Eq. 10. The value of N is obtained based on the number of VMs and PMs, where its value is equal to three, which means that in each step, three VMs are randomly selected. In the next part of the algorithm, for the current PM, the amount of resource wastage when randomly selected VMs can be placed on it is calculated through Eq. 5. After that, each of the VMs that leads to the least amount of resource wastage is placed on the current PM and removed from the list of VMs, and the resource capacity of the current PM is updated. The algorithm continues for the remaining VMs until they are placed on PMs. In Table 8, the amount of resource wastage of the randomly selected VMs in each step is given, which shows that the proposed CRBFF performs placement optimally with minimal resource wastage and the number of PMs used.

Table 8 Tracing the proposed CRBFF algorithm on the example (Steps: steps of the algorithm, $P_i$: PMs number, $C^{cpu}_i$: remaining cpu capacity of $P_i$, $C^{ram}_i$: remaining memory capacity of $P_i$, $V_j$: VMs number, $R^{cpu}_j$: cpu demand of $V_j$, $R^{ram}_j$: memory demand of $V_j$, $R^w_{ij}$: resource wastage of $V_j$ after placed on $P_i$, SV: randomly and uniformly selected VMs for placement on $P_i$, PV: placement of $V_j$ on $P_i$)

According to Table 8, in the first step, three VMs $V_2$, $V_3$ and $V_5$ are randomly and uniformly selected for placement, and for each of them, the amount of resource wastage on the current PM $P_1$ is calculated if $P_1$ has enough resources. Then, among them, $V_3$, which leads to the least waste of resources, is placed on $P_1$ and removed from the list of VMs, and then the resources capacity of $P_1$ is updated. In the second step, among the remaining VMs, three VMs are selected again, where VMs $V_1$, $V_4$ and $V_5$ are candidates. Also, because $P_1$ still has the resource capacity, it is the first priority to place VMs, so the calculation of resource wastage is done for the selected VMs, and then because $V_4$ has the smaller amount, it is placed on $P_1$, and it is removed from the list of VMs. The third step, in which only three VMs are remained, and because the value of N is equal to three, all VMs are selected. At this step, because $P_1$ does not have enough resources for placement, $P_2$ becomes a candidate, and the resource wastage for it is calculated for the selected VMs. Since $V_1$ has the smaller value, it is placed on $P_2$ and the resource capacity of $P_2$ is updated. In the fourth step, the number of remaining VMs is less than the value of N, so all of them are selected, and since $V_5$ wastes less resources, it is placed on $P_2$, and then the resources of $P_2$ are updated. In the fifth step, there is only one VM and since $P_2$ has enough resources, it places $V_2$. When the list of VMs is empty, the execution of the algorithm ends. After the completion of the placement process by CRBFF, all the VMs have been placed efficiently and the remaining CPU and memory resources capacity are 0 MIPS and 536 MB for $P_1$ and 0 MIPS and 128 MB for $P_2$, respectively, which shows that the proposed CRBFF algorithm has used PMs optimally and has provided a significant performance. To obtain the amount of resources utilization, normalized remaining resources, total resource wastage and total power consumption of PMs, the VMs placed on each PM are needed, which is calculated through Eq. 1, and the obtained values for $x_{ij}$ matrix are as follows:

where two VMs $V_3$ and $V_4$ are placed on $P_1$, and three VMs $V_1$, $V_2$ and $V_5$ are placed on $P_2$. Also, the active state of PMs is calculated through Eq. 2 as the following array

where the value of both PMs $P_1$ and $P_2$ is one, and it means that PMs have been used. After placing the VMs by CRBFF, the obtained values are calculated through different equations to analyze the efficiency of the algorithm, which are shown in Table 9. The resources utilization of PMs and the amount of their normalized remaining resources as well as their power consumption and resource wastage are respectively calculated by Eqs. 3, 4, 7 and 5. Also, the total amount of power consumption and resource wastage of PMs are obtained through Eqs. 8 and 9.

Table 9 Obtained values for metrics ($P_i$: PMs number, $u^{cpu}_i$: cpu utilization of $P_i$, $u^{ram}_i$: memory utilization of $P_i$, $R^{cpu}_i$: normalized remaining cpu resource of $P_i$, $R^{ram}_i$: normalized remaining memory resource of $P_i$, $P^{PE}_i$: power efficiency of $P_i$, $P^{Power}_i$: power consumption of $P_i$, $R^w_i$: resource wastage of $P_i$, $P^{Total}$: total power consumption of PMs, $R^{Total}$: total resource wastage of PMs)

The data in Table 9 shows that the utilization rate of the CPU resource of both $P_1$ and $P_2$ is 100%, and the utilization rate of their memory resource is 87% and 96%, respectively. Therefore, the amount of their remaining resource has reached the minimum possible amount, in other words, the amount of their resource wastage is in the best possible state. Focusing on power consumption and resource wastage, $P_1$ has the lower power consumption than $P_2$ in kilowatts, while its resource wastage, which is a unit is higher than $P_2$ because it has more remaining memory resource and cannot be used for other VMs. Finally, the total power consumption and resource wastage of PMs shows that the algorithm has a suitable performance for the VMP problem. The performance of the proposed CRBFF algorithm on this small example also shows that significant results can be obtained for real and large CDCs as well.