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

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Abstract

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 matrix-analytic analysis and fixed-point solution, for larger instances of the model.

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Authors and Affiliations

  1. Mathematical Sciences Department, IBM Thomas J. Watson Research Center, 1101 Kitchawan Road, Route 134, P.O. Box 218, Yorktown Heights, NY, 10598, USA

    Mark S. Squillante

  2. Department of Electrical and Computer Engineering, Rutgers University, Piscataway, NJ, 08854, USA

    Yanyong Zhang

  3. Department of Computer Science and Engineering, Pennsylvania State University, University Park, PA, 16802, USA

    Anand Sivasubramaniam

  4. Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX, 77843, USA

    Natarajan Gautam

Authors
  1. Mark S. Squillante
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  2. Yanyong Zhang
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  3. Anand Sivasubramaniam
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  4. Natarajan Gautam
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Correspondence to Mark S. Squillante.

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Squillante, M.S., Zhang, Y., Sivasubramaniam, A. et al. Generalized parallel-server fork-join queues with dynamic task scheduling. Ann Oper Res 160, 227–255 (2008). https://doi.org/10.1007/s10479-008-0312-7

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  • DOI: https://doi.org/10.1007/s10479-008-0312-7

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