Elastic Cloud Services Compliance with Gustafson’s and Amdahl’s Laws

Abstract

The speedup that can be achieved with parallel and distributed architectures is limited at least by two laws: the Amdahl’s and Gustafson’s laws. The former limits the speedup to a constant value when a fixed size problem is executed on a multiprocessor, while the latter limits the speedup up to its linear value for the fixed time problems, which means that it is limited by the number of used processors. However, a superlinear speedup can be achieved (speedup greater than the number of used processors) due to insufficient memory, while, parallel and, especially distributed systems can even slowdown the execution due to the communication overhead, when compared to the sequential one. Since the cloud performance is uncertain and it can be influenced by available memory and networks, in this paper we investigate if it follows the same speedup pattern as the other traditional distributed systems. The focus is to determine how the elastic cloud services behave in the different scaled environments. We define several scaled systems and we model the corresponding performance indicators. The analysis shows that both laws limit the speedup for a specific range of the input parameters and type of scaling. Even more, the speedup in cloud systems follows the Gustafson’s extreme cases, i.e. insufficient memory and communication bound domains.