• DOI:10.1109/TIT.2021.3054385
• Corpus ID: 234356571

Evaluating Load Balancing Performance in Distributed Storage With Redundancy

@article{Akta2019EvaluatingLB,
  title={Evaluating Load Balancing Performance in Distributed Storage With Redundancy},
  author={Mehmet Fatih Aktaş and Amir Behruzi Far and Emina Soljanin and Philip A. Whiting},
  journal={IEEE Transactions on Information Theory},
  year={2019},
  volume={67},
  pages={3623-3644}
}

• M. Aktaş, Amir Behruzi Far, +1 author P. Whiting
• Published 13 October 2019
• Computer Science
• IEEE Transactions on Information Theory

To facilitate load balancing, distributed systems store data redundantly. We evaluate the load balancing performance of storage schemes in which each object is stored at <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> different nodes, and each node stores the same number of objects. In our model, the load offered for the objects is sampled uniformly at random from all the load vectors with a fixed cumulative value. We find that the load balance in a system of <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> nodes improves multiplicatively with <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> as long as <inline-formula> <tex-math notation="LaTeX">${d} = {o}\left ({\log ({n})}\right)$ </tex-math></inline-formula>, and improves exponentially once <inline-formula> <tex-math notation="LaTeX">${d} = \Theta \left ({\log ({n})}\right)$ </tex-math></inline-formula>. We show that the load balance improves in the same way with <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> when the service choices are created with XOR’s of <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> objects rather than object replicas. In such redundancy schemes, storage overhead is reduced multiplicatively by <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>. However, recovery of an object requires downloading content from <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula> nodes. At the same time, the load balance increases additively by <inline-formula> <tex-math notation="LaTeX">$r$ </tex-math></inline-formula>. We express the system’s load balance in terms of the maximal spacing or maximum of <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula> consecutive spacings between the ordered statistics of uniform random variables. Using this connection and the limit results on the maximal <inline-formula> <tex-math notation="LaTeX">$d$ </tex-math></inline-formula>-spacings, we derive our main results.