The increase in data storage and power consumption at data-centers has made it imperative to design energy efficient Distributed Storage Systems (DSS). The energy efficiency of DSS is strongly influenced not only by the volume of data, frequency of data access and redundancy in data storage, but also by the heterogeneity exhibited by the DSS in these dimensions. To this end, we propose and analyze the energy efficiency of a heterogeneous distributed storage system in which @math storage servers (disks) store the data of @math distinct classes. Data of class @math is encoded using a @math erasure code and the (random) data retrieval requests can also vary across classes. We show that the energy efficiency of such systems is closely related to the average latency and hence motivates us to study the energy efficiency via the lens of average latency. Through this connection, we show that erasure coding serves the dual purpose of reducing latency and increasing energy efficiency. We present a queuing theoretic analysis of the proposed model and establish upper and lower bounds on the average latency for each data class under various scheduling policies. Through extensive simulations, we present qualitative insights which reveal the impact of coding rate, number of servers, service distribution and number of redundant requests on the average latency and energy efficiency of the DSS.
The latency analysis of (MDS) erasure coded @math homogenous DSS has been well investigated in @cite_19 @cite_39 @cite_33 which provide queuing theoretic bounds on average latency. A related line of work @cite_24 @cite_31 independently showed that sending requests to multiple servers always reduces the (read) latency. Then Liang et. al. @cite_28 extended the latency analysis to a @math DSS, in which @math of a total @math number of independent servers are used to store the @math MDS code. It assumed a constant+exponential'' model for the service time of jobs. The authors in @cite_4 @cite_26 developed load-adaptive algorithms that dynamically vary job size, coding rate and number of parallel connections to improve the delay-throughput tradeoff of key-value storage systems. These solutions were extended for heterogeneous services with mixture of job sizes and coding rate. Recently, Xiang et. al. @cite_8 provided a tight upper bound on average latency, assuming arbitrary erasure code, multiple file types and a general service time distribution. This was then used to solve a joint latency and storage cost optimization problem by optimizing over the choice of erasure code, placement of encoded chunks and the choice of scheduling policy.
@cite_26 @cite_4 @cite_33 @cite_8 @cite_28 @cite_39 @cite_24 @cite_19 @cite_31
2022138967 2051263915 2072019125 2101207956
Our paper presents solutions that can significantly improve the delay performance of putting and retrieving data in and out of cloud storage. We first focus on measuring the delay performance of a very popular cloud storage service Amazon S3. We establish that there is significant randomness in service times for reading and writing small and medium size objects when assigned distinct keys. We further demonstrate that using erasure coding, parallel connections to storage cloud and limited chunking (i.e., dividing the object into a few smaller objects) together pushes the envelope on service time distributions significantly (e.g., 76 , 80 , and 85 reductions in mean, 90th, and 99th percentiles for 2-MB files) at the expense of additional storage (e.g., 1.75x). However, chunking and erasure coding increase the load and hence the queuing delays while reducing the supportable rate region in number of requests per second per node. Thus, in the second part of our paper, we focus on analyzing the delay performance when chunking, forward error correction (FEC), and parallel connections are used together. Based on this analysis, we develop load-adaptive algorithms that can pick the best code rate on a per-request basis by using offline computed queue backlog thresholds. The solutions work with homogeneous services with fixed object sizes, chunk sizes, operation type (e.g., read or write) as well as heterogeneous services with mixture of object sizes, chunk sizes, and operation types. We also present a simple greedy solution that opportunistically uses idle connections and picks the erasure coding rate accordingly on the fly. Both backlog-based and greedy solutions support the full rate region and provide best mean delay performance when compared to the best fixed coding rate policy. Our evaluations show that backlog-based solutions achieve better delay performance at higher percentile values than the greedy solution. In order to scale economically, data centers are increasingly evolving their data storage methods from the use of simple data replication to the use of more powerful erasure codes, which provide the same level of reliability as replication but at a significantly lower storage cost. In particular, it is well known that Maximum-Distance-Separable (MDS) codes, such as Reed-Solomon codes, provide the maximum storage efficiency. While the use of codes for providing improved reliability in archival storage systems, where the data is less frequently accessed (or so-called "cold data"), is well understood, the role of codes in the storage of more frequently accessed and active "hot data", where latency is the key metric, is less clear. In this paper, we study data storage systems based on MDS codes through the lens of queueing theory, and term this the "MDS queue." We analytically characterize the (average) latency performance of MDS queues, for which we present insightful scheduling policies that form upper and lower bounds to performance, and are observed to be quite tight. Extensive simulations are also provided and used to validate our theoretical analysis. We also employ the framework of the MDS queue to analyse different methods of performing so-called degraded reads (reading of partial data) in distributed data storage. Modern distributed storage systems offer large capacity to satisfy the exponentially increasing need of storage space. They often use erasure codes to protect against disk and node failures to increase reliability, while trying to meet the latency requirements of the applications and clients. This paper provides an insightful upper bound on the average service delay of such erasure-coded storage with arbitrary service time distribution and consisting of multiple heterogeneous files. Not only does the result supersede known delay bounds that only work for homogeneous files, it also enables a novel problem of joint latency and storage cost minimization over three dimensions: selecting the erasure code, placement of encoded chunks, and optimizing scheduling policy. The problem is efficiently solved via the computation of a sequence of convex approximations with provable convergence. We further prototype our solution in an open-source, cloud storage deployment over three geographically distributed data centers. Experimental results validate our theoretical delay analysis and show significant latency reduction, providing valuable insights into the proposed latency-cost tradeoff in erasure-coded storage. Polar codes, as the first provable capacity-achieving error-correcting codes, have received much attention in recent years. However, the decoding performance of polar codes with traditional successive-cancellation (SC) algorithm cannot match that of the low-density parity-check or Turbo codes. Because SC list (SCL) decoding algorithm can significantly improve the error-correcting performance of polar codes, design of SCL decoders is important for polar codes to be deployed in practical applications. However, because the prior latency reduction approaches for SC decoders are not applicable for SCL decoders, these list decoders suffer from the long-latency bottleneck. In this paper, we propose a multibit-decision approach that can significantly reduce latency of SCL decoders. First, we present a reformulated SCL algorithm that can perform intermediate decoding of 2 b together. The proposed approach, referred as 2-bit reformulated SCL ( 2b-rSCL ) algorithm , can reduce the latency of SCL decoder from ( @math ) to ( @math ) clock cycles without any performance loss. Then, we extend the idea of 2-b-decision to general case, and propose a general decoding scheme that can perform intermediate decoding of any @math bits simultaneously. This general approach, referred as @math -bit reformulated SCL ( @math b-rSCL ) algorithm , can reduce the overall decoding latency to as short as @math cycles. Furthermore, on the basis of the proposed algorithms, very large-scale integration architectures for 2b-rSCL and 4b-rSCL decoders are synthesized. Compared with a prior SCL decoder, the proposed (1024, 512) 2b-rSCL and 4b-rSCL decoders can achieve 21 and 60 reduction in latency, 1.66 and 2.77 times increase in coded throughput with list size 2, and 2.11 and 3.23 times increase in coded throughput with list size 4, respectively.