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ASYMPTOTIC PROPERTY OF THE TIME-DEPENDENT SOLUTION OF A RELIABILITY MODEL

GeniGupur、GUOBaozhu

2005系统科学与复杂性：英文版Business, Management and Accounting被引 2

摘要

We discuss a transfer line consisting of a reliable machine, an unreliable machine and a storage buffer. This transfer line can be described by a group of partial differential equations with integral boundary conditions. First we show that the operator corresponding to these equations generates a positive contraction C0-semigroup T(t), and prove that T(t) is a quasi-compact operator. Next we verify that 0 is an eigenvalue of this operator and its adjoint operator with geometric multiplicity one. Last, by using the above results we obtain that the time-dependent solution of these equations converges strongly to their steady-state solution.

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