Mean-Field Analysis of Coding Versus Replication in Large Data Storage Systems

Abstract

We study cloud storage systems with a very large number of files stored in a very large number of servers. In such systems, files are either replicated or coded to ensure reliability, i.e., to guarantee file recovery from server failures. This redundancy in storage can further be exploited to improve system performance (mean file-access delay) through appropriate load-balancing (routing) schemes. However, it is unclear whether coding or replication is better from a system performance perspective since the corresponding queueing analysis of such systems is, in general, quite difficult except for the trivial case when the system load asymptotically tends to zero. Here, we study the more difficult case where the system load is not asymptotically zero. Using the fact that the system size is large, we obtain a mean-field limit for the steady-state distribution of the number of file access requests waiting at each server. We then use the mean-field limit to show that, for a given storage capacity per file, coding strictly outperforms replication at all traffic loads while improving reliability. Further, the factor by which the performance improves in the heavy traffic is at least as large as in the light-traffic case. Finally, we validate these results through extensive simulations. Disciplines Electrical and Computer Engineering | Systems and Communications CommentsCopyright ACM, 2018. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published in Li, Bin, Aditya Ramamoorthy, and R. We study cloud-storage systems with a very large number of files stored in a very large number of servers. In such systems, files are either replicated or coded to ensure reliability, i.e., to guarantee file recovery from server failures. This redundancy in storage can further be exploited to improve system performance (mean file access delay) through appropriate load-balancing (routing) schemes. However, it is unclear whether coding or replication is better from a system performance perspective since the corresponding queueing analysis of such systems is, in general, quite difficult except for the trivial case when the system load asymptotically tends to zero. Here, we study the more difficult case where the system load is not asymptotically zero. Using the fact that the system size is large, we obtain a mean-field limit for the steady-state distribution of the number of file access requests waiting at each server. We then use the mean-field limit to show that, for a given storage capacity per file, coding strictly outperforms replication at all traffic loads while improving reliability. Further, the factor by which the performance improves in the heavy-traffic is at least as large as in the light-traffic case. Finally, we validate these results through extensive simulations.

Managing Response Time Tails by Sharding

“…al. address this problem by a form of mean field analysis, whereby any fixed number of queues are assumed to be independent of each other as the number of servers goes to infinity [21]. Simulation results support the validity of the independence assumption, and the mean-field approach certainly looks worthy of further investigation in large scale cloud systems, for example.…”

Latency Optimal Storage and Scheduling of Replicated Fragments for Memory Constrained Servers

“…Two well studied file encoding strategies used in distributed systems with redundant storage are MDS coding [10], [23], [34], [42] and replication [19]- [21], [24]. It has been shown that MDS coding outperforms replication in mean file access latency [4], [10], [44].…”

“…We can compute the sum of mean number of useful servers aggregated over first V (1 − β) downloads. 4 Theorem 6: Consider the heterogeneous B server system with download rates μ b defined in Eq. ( 30), under the random (B, V, R) replication storage defined in Definition 7 and random scheduling defined in Definition 9.…”

Latency-Redundancy Tradeoff in Distributed Read-Write Systems

“…We assume that the read and the write requests for the file arrive as Poisson processes with rates λ r and λ w respectively. This is a widely accepted model for arrivals in distributed storage [11], [14], [22] and caching systems [23]- [25]. This assumption is motivated by analytical tractability, and the fact that this is a good approximation for the arrivals [26]when a large number of independent clients are reading from and writing to the system.…”