Dynamic analysis of Gnedenko system with multiple working vacations

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Abstract

We present a dynamic analysis of the Gnedenko repairable system with multiple working vacations, which is comprised of N operating units and one warm standby unit. The system dynamics are governed by partial differential equations with integral boundary conditions. By applying the C₀-semigroup theory, we establish the well-posedness of the system and the strong convergence of the time-dependent solution to its steady-state solution. Numerical examples illustrate the effect of key parameters on time-dependnet reliability indices, providing practical insights into the system performance.

Keywords

Gnedenko system / multiple working vacations / C₀-semigroup / dynamic solution / asymptotic behavior

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