李文琦.关于M/G/l随机服务系统中L.Takacs引理的证明[J].数学研究及应用,1986,6(3):107~112
关于M/G/l随机服务系统中L.Takacs引理的证明
On the Proof of Takacs Lemma In the Stochastic Service System M/G/I
投稿时间:1982-06-07  
DOI:10.3770/j.issn:1000-341X.1986.03.031
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李文琦 天津师范专科学校 
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      L. Takacs' Lemma (ef [1] PP47-48) is a very important tool for the investigation of the transient behavior of the M/G/1 System. But the original proof contains a gap when γ(s, w) is expanded into Lagrange series by means of Lagrange theorem as given in the appendix of [1]. This is due to the fact that φ(s)=∫0e-sxdH(x), the Laplace transform of the service time distribution , may not be analytic at s=0. An example of such a distrbution function H(x) is gives and a specific Lagrange theorem is proved By using this specific theorem, the gap in the original proof of Takacs′ Lemms is eliminated.
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