An Energy-Efficient Dynamic Resource Management Approach Based on Clustering and Meta-Heuristic Algorithms in Cloud Computing IaaS Platforms

Abstract

Cloud computing as an emerging technology, has revolutionized the information technology industry by elastic on-demand provisioning and De-provisioning of computing resources. Due to the huge amount of electrical energy consumption by large-scale Datacenters, it is essential to investigate various approaches in order to decrease simultaneously energy and its impacts on global economic crisis and ecological concerns. This study through virtualization technique applied a hybrid technique for resource management. This technique used k-means clustering for mapping task and dynamic consolidation method, which improved by micro-genetic algorithm. Experimental evaluation performed on CloudSim 3.0.3 and the results were analyzed with Expert-Choice software tools. We found that the proposed KMGA technique could provide a good trade-off between effectively reduce energy consumption of Datacenters and sustained quality of service. In addition, it minimized the number of virtual machine migrations and make-span, in comparison with particle swarm optimization and genetic algorithms in similar hybrid techniques.

Mathematical Appendix

Here we present details of mathematical derivations of the results presented in the text. The broad ideas and intuitions with focusing on the technical aspects are discussed here.

1.1 Power Model

According to several studies that mentioned in text, the utilization of DVFS on CPU results in relatively linear power-to-frequency relationship. The reason lies in the predetermined number of states that can be set to the frequency and voltage of CPU and the way that DVFS isn’t connected to other framework parts separated from CPU. Besides, these examinations demonstrate that in normal an inactive server expends roughly 70% of the power consumed by the server running at full CPU speed. This reality legitimizes the method of turning idle servers off to diminish total power utilization. Therefore, in this study we use bellow power model (11):

$$P\left( {u^{cpu} } \right) = P_{idle} + \left( {P_{busy} - P_{idle} } \right)u^{cpu} ,$$

(11)

Calculating (11) for the VM consolidation case, we see that:

$$P\left( {u^{cpu} } \right) = k_{j} \cdot e_{j}^{max} + \left( {1 - k_{j} } \right) \cdot e_{j}^{max} \cdot u^{cpu} = e_{j}^{max} \cdot \left( {0.7 + 0.3\cdot u^{cpu} } \right),$$

(12)

where ${\text{P}}\left( {u^{cpu} } \right)$, is the CPU power consumption of physical host, ${\text{k}}_{\text{j}}$ is the fraction of the PM power consumption during server idle time, ${\text{e}}_{\text{j}}^{ \hbox{max} } = P_{busy} = P_{max}$ is the maximum amount of power consumption in PM processor during the full utilization of server which is set to 250 W (a usual value for modern computing servers); ${\text{k}}_{\text{j}}\cdot{\text{e}}_{\text{j}}^{ \hbox{max} } =$$P_{idle} ,$ and $u^{cpu}$ is the CPU utilization which is a function of time and represented as $u^{cpu} \left( t \right)$. Therefore, total energy (E) consumption by a

physical host can be defined as an integral of the power consumption function over a period of time (13).

$$E = \int_{t} {P\left( {u^{cpu} \left( t \right)} \right)} dt$$

(13)

1.2 Fitness Function

During the course of the micro-genetic algorithm the best bit patterns which function as representatives of a set of binary strings are gradually selected, i.e., those patterns which minimize/maximize the value of the function to be optimized. In our study we selected those patterns which minimize the energy consumption. As explained in the text, the fitness function of micro-genetic algorithm evaluates different arrangement of allocating VMs to hosts, in order to find the minimum energy consumption based on CPU utilization. The CPU utilization metric is based on average CPU usage over the time period selected for the view. A simple way to calculate CPU utilization is:

$$U = R/C = u^{cpu} = \frac{{h_{u}^{cpu} }}{{h_{c}^{cpu} }}$$

(14)

${\text{U}} = u^{cpu} = {{\rm Utilization}}$, ${\text{R}} = h_{u}^{cpu}$ = Requirements which in simple terms is the BUSY TIME, ${\text{C}} = h_{c}^{cpu}$ = Capacity which is simple terms is BUSY TIME + IDLE TIME.

In order to find the probability that which of the arrangement for the generation of new child strings would be selected and with which they survive the recombination and mutation steps, we assume that f has to be minimized.

The function f is defined over all binary strings of length l and is called the fitness of the strings. The population consists of a set of N binary strings of length l at time t. Two parent strings from the current population are always selected for the creation of a new string. The probability that a parent string $U_{j}^{cpu}$ will be selected from N strings $U_{1}^{cpu} ,\quad U_{2}^{cpu} , \ldots , U_{N}^{cpu}$ is:

$$p \left( {U_{j}^{cpu} } \right) = \frac{{f\left( {U_{j}^{cpu} } \right)}}{{\mathop \sum \nolimits_{i = 1}^{N} P\left( {U_{i}^{cpu} } \right)}}$$

(15)

This means that strings with greater fitness are more likely to be selected than strings with lesser fitness. Let fμ be the average fitness of all strings in the population, i.e.,

$$f\mu = fitness = \frac{1}{N}\mathop \sum \limits_{i = 1}^{N} P\left( {U_{i}^{cpu} } \right).$$

(16)