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Linear Programming Performance Bounds for Markov Chains With Polyhedrally Translation Invariant Probabilities and Applications to Unreliable Manufacturing Systems and Enhanced Wafer Fab Models

[+] Author Affiliations
James R. Morrison

IBM Microelectronics, Burlington, VT

P. R. Kumar

University of Illinois at Urbana-Champaign, Urbana, IL

Paper No. IMECE2002-39274, pp. 69-78; 10 pages
doi:10.1115/IMECE2002-39274
From:
  • ASME 2002 International Mechanical Engineering Congress and Exposition
  • Electronic and Photonic Packaging, Electrical Systems Design and Photonics, and Nanotechnology
  • New Orleans, Louisiana, USA, November 17–22, 2002
  • Conference Sponsors: Electronic and Photonic Packaging Division
  • ISBN: 0-7918-3648-7 | eISBN: 0-7918-1691-5, 0-7918-1692-3, 0-7918-1693-1
  • Copyright © 2002 by ASME

abstract

Our focus is on a class of Markov chains which have a polyhedral translation invariance property for the transition probabilities. This class can be used to model several applications of interest which feature complexities not found in usual models of queueing networks, for example failure prone manufacturing systems which are operating under hedging point policies, or enhanced wafer fab models featuring batch tools and setups or affine index policies. We present a new family of performance bounds which is more powerful both in expressive capability as well as the quality of the bounds than some earlier approaches.

Copyright © 2002 by ASME

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