Queueing Models with Maxima of Service Times

Harrison, Peter G.; Zertal, Soraya

doi:10.1007/978-3-540-45232-4_10

Cited by 27 publications

(16 citation statements)

References 4 publications

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“…In case of deterministic thinning, the random processes X i (m) and Y i (n) are replaced by deterministic functions. A round robin assignment of the jobs of an arrival process A(n) to k servers results in the processes A i (m) given by (17) where…”

Section: B Deterministic Thinningmentioning

confidence: 99%

Non-asymptotic delay bounds for (k, l) fork-join systems and multi-stage fork-join networks

Fidler

Jiang²

2016

IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications

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Parallel systems have received increasing attention with numerous recent applications such as fork-join systems, load-balancing, and l-out-of-k redundancy. Common to these systems is a join or resequencing stage, where tasks that have finished service may have to wait for the completion of other tasks so that they leave the system in a predefined order. These synchronization constraints make the analysis of parallel systems challenging and few explicit results are known. In this work, we model parallel systems using a max-plus approach that enables us to derive statistical bounds of waiting and sojourn times. Taking advantage of max-plus system theory, we also show end-to-end delay bounds for multi-stage fork-join networks. We contribute solutions for basic G|G|1 fork-join systems, parallel systems with load-balancing, as well as general (k, l) fork-join systems with redundancy. Our results provide insights into the respective advantages of l-out-of-k redundancy vs. load-balancing.

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Section: B Deterministic Thinningmentioning

confidence: 99%

Non-asymptotic delay bounds for (k, l) fork-join systems and multi-stage fork-join networks

Fidler

Jiang²

2016

IEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications

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“…In particular, for t = 0, the MDS-Reservation(0) policy is rather simple, as the file request (consisting of a batch of chunk requests) at the head of the line may move forward and enter service only if there are at least k idle servers. When n = k, this becomes identical to a split-merge queue (Harrison and Zertal, 2003). For t = 1, the MDS-Reservation(1) policy is identical to the block-one scheduling policy proposed in (Huang et al, 2012b).…”

Section: Mds-reservation Scheduling Approachmentioning

confidence: 99%

Modeling and Optimization of Latency in Erasure-coded Storage Systems

Aggarwal¹,

Lan²

2020

Preprint

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As consumers are increasingly engaged in social networking and E-commerce activities, businesses grow to rely on Big Data analytics for intelligence, and traditional IT infrastructures continue to migrate to the cloud and edge, these trends cause distributed data storage demand to rise at an unprecedented speed. Erasure coding has seen itself quickly emerged as a promising technique to reduce storage cost while providing similar reliability as replicated systems, widely adopted by companies like Facebook, Microsoft and Google. However, it also brings new challenges in characterizing and optimizing the access latency when erasure codes are used in distributed storage. The aim of this monograph is to provide a review of recent progress (both theoretical and practical) on systems that employ erasure codes for distributed storage.In this monograph, we will first identify the key challenges and taxonomy of the research problems and then give an overview of different approaches that have been developed to quantify and model latency of erasure-coded storage. This includes recent work leveraging MDS-Reservation, Fork-Join, Probabilistic, and Delayed-Relaunch scheduling policies, as well as their applications to characterize access latency (e.g., mean, tail, asymptotic latency) of erasure-coded distributed storage systems. We will also extend the problem to the case when users are streaming videos from erasure-coded distributed storage systems. Next, we bridge the gap between theory and practice, and discuss lessons learned from prototype implementation. In particular, we will discuss exemplary implementations of erasure-coded storage, illuminate key design degrees of freedom and tradeoffs, and summarize remaining challenges in real-world storage systems such as in content delivery and caching. Open problems for future research are discussed at the end of each chapter.

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“…In contrast, in a fork-join system, the start times of tasks are not synchronized. Splitmerge systems are solvable to some extent as they can be expressed as a single server queue where the service process is governed by the service time of the maximal task of each job [9], [15], [20], [21].…”

Section: Introductionmentioning

confidence: 99%

Non-Asymptotic Delay Bounds for Multi-Server Systems with Synchronization Constraints

Fidler

Walker

Jiang

2018

IEEE Trans. Parallel Distrib. Syst.

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Multi-server systems have received increasing attention with important implementations such as Google MapReduce, Hadoop, and Spark. Common to these systems are a fork operation, where jobs are first divided into tasks that are processed in parallel, and a later join operation, where completed tasks wait until the results of all tasks of a job can be combined and the job leaves the system. The synchronization constraint of the join operation makes the analysis of fork-join systems challenging and few explicit results are known. In this work, we model fork-join systems using a max-plus server model that enables us to derive statistical bounds on waiting and sojourn times for general arrival and service time processes. We contribute end-to-end delay bounds for multi-stage fork-join networks that grow in O(h ln k) for h fork-join stages, each with k parallel servers. We perform a detailed comparison of different multiserver configurations and highlight their pros and cons. We also include an analysis of single-queue fork-join systems that are nonidling and achieve a fundamental performance gain, and compare these results to both simulation and a live Spark system.

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Queueing Models with Maxima of Service Times

Cited by 27 publications

References 4 publications

Non-asymptotic delay bounds for (k, l) fork-join systems and multi-stage fork-join networks

Non-asymptotic delay bounds for (k, l) fork-join systems and multi-stage fork-join networks

Modeling and Optimization of Latency in Erasure-coded Storage Systems

Non-Asymptotic Delay Bounds for Multi-Server Systems with Synchronization Constraints

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