IJPAM: Volume 51, No. 3 (2009)

FURTHER RESEARCH OF K-OUT-OF-N:G REDUNDANT
SYSTEM WITH REPAIR AND MULTIPLE CRITICAL
AND NON-CRITICAL ERRORS

Rena Ehmet$^1$, Geni Gupur$^2$
$^{1,2}$College of Mathematics and System Science
Xinjiang University
Urumqi, 830046, P.R. CHINA
$^2$e-mails: [email protected], [email protected]


Abstract.We study properties of the $C_0$-semigroup generated by the operator corresponding to k-out-of-N:G redundant system with repair and multiple critical and non-critical errors. We prove that the $C_0$-semigroup is a quasi-compact operator, thus we obtain that it converges exponentially to a project operator. For a special case, we deduce asymptotic property of the time-dependent solution of the system.

Received: September 12, 2007

AMS Subject Classification: 47A10, 47D99

Key Words and Phrases: $C_0$-semigroup, quasi-compact operator, eigenvalue, k-out-of-N:G redundant system

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 3