A new model for cloud elastic services efficiency

ABSTRACT

The speedup measures the improvement in performance when the computational resources are being scaled. The efficiency, on the other side, provides the ratio between the achieved speedup and the number of scaled computational resources (processors). Both parameters (speedup and efficiency), which are defined according to Amdahl’s Law, provide very important information about performance of a computer system with scaled resources compared with a computer system with a single processor. However, as cloud elastic services’ load is variable, apart of the scaled resources, it is vital to analyse the load in order to determine which system is more effective and efficient. Unfortunately, both the speedup and efficiency are not sufficient enough for proper modeling of cloud elastic services, as the assumptions for both the speedup and efficiency are that the system’s resources are scaled, while the load is constant. In this paper, we extend the scaling of resources and define two additional scaled systems by (i) scaling the load and (ii) scaling both the load and resources. We introduce a model to determine the efficiency for each scaled system, which can be used to compare the efficiencies of all scaled systems, regardless if they are scaled in terms of load or resources. We have evaluated the model by using Windows Azure and the experimental results confirm the theoretical analysis. Although one can argue that web services are scalable and comply with Gustafson’s Law only, we provide a taxonomy that classifies scaled systems based on the compliance with both the Amdahl’s and Gustafson’s laws.

For three different scaled systems (scaled resources R, scaled load L and combination RL), we introduce a model to determine the scaling efficiency. Our model extends the current definition of efficiency according to Amdahl’s Law, which assumes scaling the resources, and not the load. $$\begin{array}{c}\hfill E_R=\frac{S_R}{p}=\frac{T(1)}{T_R}·\frac{1}{p};E_L=S_L·N=\frac{T(1)}{T_L}·N;E_{\mathit{RL}}=S_{\mathit{RL}}·\frac{N}{p}=\frac{T(1)}{T_{\mathit{RL}}}·\frac{N}{p}\end{array}$$

GRAPHICAL ABSTRACT

KEYWORDS:

• Efficiency
• load
• optimisation
• performance
• resources
• speedup

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is being accomplished as a part of (i) ENTICE: dEcentralised repositories for traNsparent and efficienT vIrtual maChine opErations, funded by the European Unions Horizon 2020 research and innovation programme [grant agreement number 644179], and (ii) Tiroler Cloud: Energiebewusste Föderierte Cloud für Anwendungen aus Industrie und Forschung, funded by the Österreichische Forschungsförderungsgesellschaft [grant agreement number 848448].