On a dynamical system for a reliability model

被引：0
作者：
Geni Gupur
M. W. Wong
机构：
[1] Xinjiang University,College of Mathematics and Systems Science
[2] York University,Department of Mathematics and Statistics
来源：
Journal of Pseudo-Differential Operators and Applications | 2011年 / 2卷
关键词：
Reliable machine; Unreliable machine; Storage buffer; Infinite capacity; -semigroup; Spectrum; 47A10; 47D99; 90B30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
By studying the spectrum on the imaginary axis of the operator corresponding to the system consisting of a reliable machine, an unreliable machine and a storage buffer with infinite capacity described by an infinite-dimensional non-local (pseudo-differential) dynamical system, we prove that the time-dependent solution of the system converges strongly to its steady-state solution as time tends to infinity and we show that our study provides the optimal result on convergence. Then by discussing the monotonicity of the corresponding C0-semigroup, we obtain the asymptotic behavior of the reliability indices for the system.
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页码：509 / 542
页数：33
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共 22 条
  • [1] Arendt W.(1988)Tauberian theorems and stability of one-parameter semigroups Trans. Am. Math. Soc. 306 837-852
  • [2] Batty C.J.K.(1955)The analysis of non-Markovian stochastic process by the inclusion of supplementary variables Proc. Camb. Phil. Soc. 51 433-441
  • [3] Cox D.R.(1991)Analysis of transfer lines of two unreliable machines with random processing times and finite storage buffers AIIE Trans. 13 2-11
  • [4] Gershwin S.B.(1987)Perturbing the boundary conditions of a generator Houston J. Math. 13 213-229
  • [5] Berman O.(2005)Asymptotic stability of the time-dependent solution of a reliability model Acta Anal. Funct. Appl. 7 299-316
  • [6] Greiner G.(2000)Semigroup method for a mathematical model in reliability analysis J. Syst. Sci. Syst. Eng. 10 137-147
  • [7] Gupur G.(2007)A semigroup approach to queueing systems Semigroup Forum 75 610-624
  • [8] Gupur G.(1996)Global solutions of semilinear heat equations in Hilbert spaces Abstr. Appl. Anal. 1 263-276
  • [9] Li X.(1998)Analytic semigroups and semilinear heat equations in Hilbert spaces Appl. Anal. 69 265-283
  • [10] Haji A.(1998)Some performance measures of transfer line consisting of two unreliable machines with reprocess rule J. Syst. Sci. Syst. Eng. 7 283-292
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