Naveen Kr. Sharma

Tales of the Tail: Hardware, OS, and Application-level Sources of Tail Latency

Interactive services often have large-scale parallel implementations. To deliver fast responses, the median and tail latencies of a services components must be low. In this paper, we explore the hardware, OS, and application-level sources of poor tail latency in high throughput servers executing on multi-core machines. We model these network services as a queuing system in order to establish the best-achievable latency distribution. Using fine-grained measurements of three different servers (a null RPC service, Memcached, and Nginx) on Linux, we then explore why these servers exhibit significantly worse tail latencies than queuing models alone predict. The underlying causes include interference from background processes, request re-ordering caused by poor scheduling or constrained concurrency models, suboptimal interrupt routing, CPU power saving mechanisms, and NUMA effects. We systematically eliminate these factors and show that Memcached can achieve a median latency of 11 μs and a 99.9th percentile latency of 32 μs at 80% utilization on a four-core system. In comparison, a naïve deployment of Memcached at the same utilization on a single-core system has a median latency of 100 μs and a 99.9th percentile latency of 5 ms. Finally, we demonstrate that tradeoffs exist between throughput, energy, and tail latency.

Building consistent transactions with inconsistent replication

Application programmers increasingly prefer distributed storage systems with strong consistency and distributed transactions (e.g., Googles Spanner) for their strong guarantees and ease of use. Unfortunately, existing transactional storage systems are expensive to use -- in part because they require costly replication protocols, like Paxos, for fault tolerance. In this paper, we present a new approach that makes transactional storage systems more affordable: we eliminate consistency from the replication protocol while still providing distributed transactions with strong consistency to applications. We present TAPIR -- the Transactional Application Protocol for Inconsistent Replication -- the first transaction protocol to use a novel replication protocol, called inconsistent replication, that provides fault tolerance without consistency. By enforcing strong consistency only in the transaction protocol, TAPIR can commit transactions in a single round-trip and order distributed transactions without centralized coordination. We demonstrate the use of TAPIR in a transactional key-value store, TAPIR-KV. Compared to conventional systems, TAPIR-KV provides better latency and throughput.

Wheel-throwing in digital space using number-theoretic approach

This paper introduces a novel technique to create digital potteries using certain number-theoretic techniques of digital geometry. Given a digital generatrix, the proposed wheel-throwing procedure works with a few primitive integer computations only, wherein lies its strength and novelty. The digital surface created out of the digital wheel-throwing is digitally connected and irreducible when the digital generatrix is an irreducible digital curve segment, which ensures its successful rendition with a realistic finish, whatsoever may be the zoom factor. The proposed technique is also bestowed with the desired quality of producing a monotone or a non-monotone digital surface of revolution depending on whether or not the digital generatrix is monotone with respect to the axis of revolution. Thick-walled potteries, therefore, can be created successfully and efficiently to have the final product ultimately resembling a real-life pottery. Experimental results with some typical generatrices demonstrate its efficiency, elegance and versatility.

Optimizing topology in Bit Torrent based networks

In this paper, we discuss the importance of the network connectivities of the peers in Bit Torrent based systems in determining the download performance of the peers. In this context, assuming that the fraction of the peers of each bandwidth are known, we derive optimal connectivities of the peers that help to improve the average latency of the peers. We represent the topology of a Bit Torrent based system as a weighted graph, where the average edge weight of the graph directly relates to the download latency of the peers. We formulate the average edge weight of the whole system as a linear function of the fraction of the edges that connect peers of different bandwidth and derive the topology that maximizes the average edge weight of the network. Simulation results based on the Bit Torrent protocol validates the fact that in the optimal topology, peers have 13% better download latency as compared to topologies formed in the normal Bit Torrent based systems. Further the obtained topology also improves the fairness of the system as compared to normal Bit Torrent significantly.

Recovering Shared Objects Without Stable Storage.

This paper considers the problem of building fault-tolerant shared objects when processes can crash and recover but lose their persistent state on recovery. This Diskless Crash-Recovery (DCR) model matches the way many long-lived systems are built. We show that it presents new challenges, as operations that are recorded at a quorum may not persist after some of the processes in that quorum crash and then recover. To address this problem, we introduce the notion of crash-consistent quorums, where no recoveries happen during the quorum responses. We show that relying on crash-consistent quorums enables a recovery procedure that can recover all operations that successfully finished. Crash-consistent quorums can be easily identified using a mechanism we term the crash vector, which tracks the causal relationship between crashes, recoveries, and other operations. We apply crash-consistent quorums and crash vectors to build two storage primitives. We give a new algorithm for multi-writer, multi-reader atomic registers in the DCR model that guarantees safety under all conditions and termination under a natural condition. It improves on the best prior protocol for this problem by requiring fewer rounds, fewer nodes to participate in the quorum, and a less restrictive liveness condition. We also present a more efficient single-writer, single-reader atomic set - a virtual stable storage abstraction. It can be used to lift any existing algorithm from the traditional Crash-Recovery model to the DCR model. We examine a specific application, state machine replication, and show that existing diskless protocols can violate their correctness guarantees, while ours offers a general and correct solution.

A sparse matrix approach to reverse mode automatic differentiation in Matlab

Abstract We review the extended Jacobian approach to automatic differentiation of a user-supplied function and highlight the Schur complement form’s forward and reverse variants. We detail a Matlab operator overloaded approach to construct the extended Jacobian that enables the function Jacobian to be computed using Matlab’s sparse matrix operations. Memory and runtime costs are reduced using a variant of the hoisting technique of Bischof (Issues in Parallel Automatic Differentiation, 1991). On five of the six mesh-based gradient test problems from The MINPACK2 Test Problem Collection (Averick et al, 1992) the reverse variant of our extended Jacobian technique with hoisting outperforms the sparse storage forward mode of the MAD package (Forth, ACM T. Math. Software. 32, 2006). For increasing problems size the ratio of gradient to function cpu time is seen to be bounded, if not decreasing, in line with Griewank and Walther’s (Evaluating Derivatives, SIAM, 2008) cheap gradient principle.