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Discrete-Time Markov-Reward Models of Production Systems

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Discrete Event Systems, Manufacturing Systems, and Communication Networks

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 73))

Abstract

In this paper we consider the discrete-time version of performability modeling. The discrete-time approach is well-suited for the performance studies of Automated Manufacturing Systems (AMS) in the presence of failures, repairs and reconfigurations. AMS exist in various configuration states and this transitional behavior is modeled using discrete-time Markov chains. In addition, the performance in each configuration state is modeled by a Markov reward structure, that is similar to the continuous-time versions. In this paper, we derive recursive expressions for the conditional densities and moments of the cumulative reward function, when the underlying Markov chain describing the evolution of the configuration states is homogenous. Examples are used to illustrate the methods obtained in the paper.

Supported under grants from the Department of Economic Development under the Yankee Ingenuity Initiative, The Precision Manufacturing Center at the University of Connecticut, the Office of Naval Research under Contract ONR-N00014-91-J-1950, and AFOSR grant F4960-93-1-0164.

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Author information

Authors and Affiliations

  1. Department of Electrical and Systems Engineering, University of Connecticut, Storrs, CT, 06269-3157, USA

    Ranga Mallubhatla & Krishna R. Pattipati

  2. Department of Computer Science and Automation, Indian Institute of Science, Bangalore, 560012, India

    N. Viswanadham

Authors
  1. Ranga Mallubhatla
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  2. Krishna R. Pattipati
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  3. N. Viswanadham
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Editors and Affiliations

  1. Coordinated Science Library, University of Illinois at Urbana Champaign, 1308 West Main Street, 61801-2307, Urbana, IL, USA

    P. R. Kumar

  2. Department of Electrical and Computer Engineering, University of California at Berkeley, 94720, Berkely, CA, USA

    P. P. Varaiya

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© 1995 Springer-Verlag New York, Inc

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Mallubhatla, R., Pattipati, K.R., Viswanadham, N. (1995). Discrete-Time Markov-Reward Models of Production Systems. In: Kumar, P.R., Varaiya, P.P. (eds) Discrete Event Systems, Manufacturing Systems, and Communication Networks. The IMA Volumes in Mathematics and its Applications, vol 73. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9347-4_6

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  • DOI: https://doi.org/10.1007/978-1-4613-9347-4_6

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9349-8

  • Online ISBN: 978-1-4613-9347-4

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