Tail Index for a Distributed Storage System with Pareto File Size Distribution

Distributed storage systems often employ erasure codes to achieve high data reliability while attaining space efficiency. Such storage systems are known to be susceptible to long tails in response time. It has been shown that in modern online applications such as Bing, Facebook, and Amazon, the long tail of latency is of particular concern, with $99.9$th percentile response times that are orders of magnitude worse than the mean. Taming tail latency is very challenging in erasure-coded storage systems since quantify tail latency (i.e., $x$th-percentile latency for arbitrary $x\in[0,1]$) has been a long-standing open problem. In this paper, we propose a mathematical model to quantify {\em tail index} of service latency for arbitrary erasure-coded storage systems, by characterizing the asymptotic behavior of latency distribution tails. When file size has a heavy tailed distribution, we find tail index, defined as the exponent at which latency tail probability diminishes to zero, in closed-form, and further show that a family of probabilistic scheduling algorithms are (asymptotically) optimal since they are able to achieve the exact tail index.Comment: Theorem 1 proof was replaced with a proof that uses the result in [21], thus simplifying the analysis and making the paper concis

Taming Tail Latency for Erasure-coded, Distributed Storage Systems

Distributed storage systems are known to be susceptible to long tails in response time. In modern online storage systems such as Bing, Facebook, and Amazon, the long tails of the service latency are of particular concern. with 99.9th percentile response times being orders of magnitude worse than the mean. As erasure codes emerge as a popular technique to achieve high data reliability in distributed storage while attaining space efficiency, taming tail latency still remains an open problem due to the lack of mathematical models for analyzing such systems. To this end, we propose a framework for quantifying and optimizing tail latency in erasure-coded storage systems. In particular, we derive upper bounds on tail latency in closed form for arbitrary service time distribution and heterogeneous files. Based on the model, we formulate an optimization problem to jointly minimize the weighted latency tail probability of all files over the placement of files on the servers, and the choice of servers to access the requested files. The non-convex problem is solved using an efficient, alternating optimization algorithm. Numerical results show significant reduction of tail latency for erasure-coded storage systems with a realistic workload.Comment: 11 pages, 8 figure

Resource Allocation in Multigranular Optical Networks

Thesis Statement: Cost-effective switching and spectrum utilization efficiency have become critical design considerations in optical networks. This dissertation provides in-depth exploration of these important aspects, and proposes effective techniques for low-cost switching architectures and resource allocation algorithms to facilitate the adoption of optical networks in the near future. The dramatic growth of Internet traffic brings challenges for optical network designers. The increasing traffic and bandwidth requirements mean that various resource allocation schemes to achieve different network design goals assume great importance. The general problem of resource allocation to lightpath requests is a challenging problem. An emerging technology of flexible and more fine-grained grid through the use of Optical Orthogonal Frequency Division Multiplexing (OOFDM) allows fiber bandwidth to be more suitably matched up with application requirements, thereby making the network more elastic than the conventional Wavelength Division Multiplexing (WDM) optical networks. Despite the advances of employing OOFDM technology in elastic optical networks (EONs), imminent fiber capacity exhaustion due to the ever-increasing demands means that multiple fibers per link will be inevitable. While increasing the number of fibers boosts the capacity of networks, there is a price to pay for it in the form of increased number of switch ports / complexity of switches. The huge amount of traffic demands and thus high hardware requirements motivate multigranularity (such as wavebanding) to save costs in optical networks. This dissertation aims to tackle several types of resource allocation challenges in multi-granular optical networks to either improve the spectrum utilization or provide cost-effective switching techniques