Response times in M/M/s fork-join networks

Ko, Sung-Seok; Serfozo, Richard F.

doi:10.1017/s000186780001315x

Cited by 18 publications

(44 citation statements)

References 16 publications

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“…An earlier study dealt with sojourn time distribution with multiserver queues [Ko and Serfozo 2004].…”

Section: Overview: Fork/join and Related Queueing Systemsmentioning

confidence: 99%

Analysis of Fork/Join and Related Queueing Systems

Thomasian¹

2014

ACM Comput. Surv.

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Fork/join (F/J) requests arise in contexts such as parallel computing, query processing in parallel databases, and parallel disk access in RAID. F/J requests spawn K tasks that are sent to K parallel servers, and the completion of all K tasks marks the completion of an F/J request. The exact formula for the mean response time of K = 2-way F/J requests derived under Markovian assumptions (R F/J 2 ) served as the starting point for an approximate expression for R F/J K for 2 < K ≤ 32. When servers process independent requests in addition to F/J requests, the mean response time of F/J requests is better approximated by R max K , which is the maximum of the response times of tasks constituting F/J requests. R max K is easier to compute and serves as an upper bound to R F/J K . We discuss techniques to compute R max K and generally the maximum of K random variables denoting the processing times of the tasks of a parallel computation X max K . Graph models of computations such as Petri nets-a more general form of parallelism than F/J requests-are also discussed in this work. Jobs with precedence constraints may require multiple resources, which are represented by a queueing network model. We also discuss various queueing systems related to F/J queueing systems and outline their analysis. ACM Reference Format:Alexander Thomasian. 2014. Analysis of fork-join and related queueing systems.

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“…An earlier study dealt with sojourn time distribution with multiserver queues [Ko and Serfozo 2004].…”

Section: Overview: Fork/join and Related Queueing Systemsmentioning

confidence: 99%

Analysis of Fork/Join and Related Queueing Systems

Thomasian¹

2014

ACM Comput. Surv.

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“…2, under appropriate configuration, reduces to the classical forkjoin queueing system, which has a rich history and has received considerable attention in the research literature; refer to, e.g., Nelson and Tantawi (1988), Baccelli et al (1989), Varma and Makowski (1994), Tan and Knessl (1996), Chen (2001), Ko and Serfozo (2004) and the references therein. An exact mathematical analysis of the fork-join queue is often limited to relatively small P due to various factors, including the inherent complexity of the underlying stochastic process and the explosive growth of the state space with increasing P .…”

Section: Applicationsmentioning

confidence: 99%

“…An exact mathematical analysis of the fork-join queue is often limited to relatively small P due to various factors, including the inherent complexity of the underlying stochastic process and the explosive growth of the state space with increasing P . Hence, a significant portion of previous research in the area is based on an approximate mathematical analysis; see, e.g., Nelson and Tantawi (1988), Baccelli et al (1989), Varma and Makowski (1994), Tan and Knessl (1996), Chen (2001), Ko and Serfozo (2004). In order to explore the accuracy of our approximate analysis of the generalized parallelserver fork-join queueing systems (cf.…”

Section: Applicationsmentioning

confidence: 99%

“…A wide variety of application domains have a similar fork-join structure and thus forkjoin queueing systems have often played an important role in the modeling and analysis of these diverse applications; refer to, e.g., Nelson and Tantawi (1988), Baccelli et al (1989), Varma and Makowski (1994), Tan and Knessl (1996), Chen (2001), Ko and Serfozo (2004) and the references therein. Over the past decade or so, however, many existing application domains have been evolving and many new application domains have been emerging, each exhibiting important differences in the properties of the tasks comprising every customer.…”

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Generalized parallel-server fork-join queues with dynamic task scheduling

et al. 2008

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This paper introduces a generalization of the classical parallel-server fork-join queueing system in which arriving customers fork into multiple tasks, every task is uniquely assigned to one of the set of single-server queues, and each task consists of multiple iterations of different stages of execution, including task vacations and communication among sibling tasks. Several classes of dynamic polices are considered for scheduling multiple tasks at each of the single-server queues to maintain effective server utilization. The paper presents an exact matrix-analytic analysis of generalized parallel-server fork-join queueing systems, for small instances of the stochastic model, and presents an approximate matrixanalytic analysis and fixed-point solution, for larger instances of the model.

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“…The analysis of fork-join in parallel queues has been studied for at least 30 years [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24], [25], [26]. Exact analysis of this model for M/M/1 HFJ queues was achieved only for K ¼ 2 by Flatto and Hahn [8], [9] in 1984 and 1985.…”

Section: Introductionmentioning

confidence: 99%

An Upper Bound Solution for Homogeneous Fork/Join Queuing Systems

Chen

2011

IEEE Trans. Parallel Distrib. Syst.

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In this paper, we use dynamic-bubblesort technology [4] to analyze general first-in-first-out K-queue homogenous fork/join queuing (HFJ) systems for any K ! 2. Jobs arrive with a mean rate and a general arrival distribution. Upon arrival, a job forks into K tasks. Task k; k ¼ 1; 2; . . . ; K, is assigned to the kth queuing system, which is a first-in-first-out server with a general service distribution and an infinite capacity queue. A job leaves the HFJ system as soon as all its tasks complete their service. We mathematically prove an upper bound solution for the mean response time that we denote by T K . The upper bound solution of general K-queue HFJ systems for any K ! 2 is very simple and practical-one only needs to simulate a small number of queues (e.g., 16 queues). The tightness is evaluated by comparing with the simulation of thousands of queues for three different HFJ cases. The maximum offset for our upper bounds over all the simulations is less than 5 percent. The corresponding source codes (reusable) are offered on our website for others to use.

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Response times in M/M/s fork-join networks

Cited by 18 publications

References 16 publications

Analysis of Fork/Join and Related Queueing Systems

Analysis of Fork/Join and Related Queueing Systems

Generalized parallel-server fork-join queues with dynamic task scheduling

An Upper Bound Solution for Homogeneous Fork/Join Queuing Systems

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