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Asymptotic Distribution of Makespan in Permutation Flowshops

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Proceedings of the 2nd International Conference on Green Communications and Networks 2012 (GCN 2012): Volume 1

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 223))

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Abstract

In this paper, for permutation flowshops with two machines or more than two machines, as the number of jobs tends to infinity, the properties of asymptotic distribution of makespan are proposed. We introduce several conclusions in queuing theory to the scheduling problem, and convert the distribution of makespan to the distribution of waiting time in the queue. In two-machine conditions, the asymptotic distribution of makespan is proved to be the right half of a normal distribution. In m-machine conditions (m > 2), the asymptotic distribution of waiting time is proved under certain assumptions, and the bounds of probability distribution functions of waiting times are given.

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Author information

Authors and Affiliations

  1. Department of Automation, Tsinghua University, 100084, Beijing, China

    Gengcheng Liu, Shiji Song & Cheng Wu

Authors
  1. Gengcheng Liu
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  2. Shiji Song
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  3. Cheng Wu
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Corresponding author

Correspondence to Shiji Song .

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Editors and Affiliations

  1. , Department of Electronic Engineering, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai, 200240, China, People's Republic

    Yuhang Yang

  2. , Electrical & Electronic Engineering, Nanyang Technological University, Nanyang Avenue, Singapore, 639798, Singapore

    Maode Ma

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Liu, G., Song, S., Wu, C. (2013). Asymptotic Distribution of Makespan in Permutation Flowshops. In: Yang, Y., Ma, M. (eds) Proceedings of the 2nd International Conference on Green Communications and Networks 2012 (GCN 2012): Volume 1. Lecture Notes in Electrical Engineering, vol 223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35419-9_25

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  • DOI: https://doi.org/10.1007/978-3-642-35419-9_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-35418-2

  • Online ISBN: 978-3-642-35419-9

  • eBook Packages: EngineeringEngineering (R0)

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