A Survey of Studies on Self-Similarity in I/O Workloads

In order to optimize the performance of storage systems and lighten the bottleneck effects of disk-based storage systems in computer systems, the characteristics of I/O workloads need to be studied, so as to create accurate models to describe them. Recently, researchers have found that in many I/O workloads, arrival patterns and access patterns have similar burstiness at different scales. However, traditional Poisson models cannot describe this kind of burstiness. Some researchers then propose self-similarity models to describe I/O workloads. In addition, though self-similarity models describe long-range dependence (LRD) in I/O workloads very well, they are unable to describe local variations and irregularities at relatively small scales. Therefore, some researchers propose multifractal models to make up for the defects of self-similarity models. In this paper, the definitions of self-similar stochastic processes and the estimation methods of self-similarity are first introduced. The self-similarity in I/O workloads is then discussed. After that, several self-similarity models of I/O workloads, such as Sup-FRP models, ON/OFF models, M/G/∞ models, and so on, are introduced. Finally, two multifractal models of I/O workloads, b-models and PQRS models are presented. After analyzing the status of studies, several conclusions are drawn: (a) Self-similarity estimation is still a hard problem that has not been completely solved. This is an aspect that needs further study; (b) From the perspective of storage system design, the significance of self-similarity in I/O workloads is still an important aspect that needs further study; and (c) How to create more accurate multifractal models is also an aspect that needs further study.