A new model for cloud elastic services efficiency

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. [GRAPHICS] 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. E-R = S-R/p = T(1)/T-R center dot 1/p; E-L = S-L center dot N = T(1)/T-L center dot N; E-RL = S-RL center dot N/p = T(1)/T-RL center dot N/p