Reliability modeling of structured systems: exploring symmetry in state-space generation

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1997
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Somani, Arun
Senior Associate Dean
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Electrical and Computer Engineering

The Department of Electrical and Computer Engineering (ECpE) contains two focuses. The focus on Electrical Engineering teaches students in the fields of control systems, electromagnetics and non-destructive evaluation, microelectronics, electric power & energy systems, and the like. The Computer Engineering focus teaches in the fields of software systems, embedded systems, networking, information security, computer architecture, etc.

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The Department of Electrical Engineering was formed in 1909 from the division of the Department of Physics and Electrical Engineering. In 1985 its name changed to Department of Electrical Engineering and Computer Engineering. In 1995 it became the Department of Electrical and Computer Engineering.

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1909-present

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  • Department of Electrical Engineering (1909-1985)
  • Department of Electrical Engineering and Computer Engineering (1985-1995)

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A large number of systems are implemented using regular interconnected topologies. Markov analysis of such systems results in large state spaces. We explore symmetry, in particular rotational and permutational, of such systems to achieve a significant reduction in the size of the state space required to analyze them. The resulting much smaller state spaces allow analyses of very large systems. We define equivalent classes of states and develop an algorithm to generate small state spaces and the corresponding Markov chain for systems with permutation symmetries. The state space generation process is also simplified. We demonstrate our technique using several examples. Our technique is very useful in the exact analysis of large systems.

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This is a manuscript of a proceeding published as Somani, Arun K. "Reliability modeling of structured systems: Exploring symmetry in state-space generation." In Proceedings Pacific Rim International Symposium on Fault-Tolerant Systems (1997): 78-84. DOI: 10.1109/PRFTS.1997.640129. Posted with permission.

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Wed Jan 01 00:00:00 UTC 1997