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| THE POINT PROCESS OF STATETRANSITIONS IN AREGULAR MARKOV CHAIN | |
| 引用本文： | 史定华,郭进利. THE POINT PROCESS OF STATETRANSITIONS IN AREGULAR MARKOV CHAIN[J]. 应用数学学报(英文版), 1998, 14(4): 374-380. DOI: 10.1007/BF02683821 |
| 作者姓名： | 史定华 郭进利 |
| 作者单位： | Deportment of Mathematics，Shanghai University，Shanghai 201800，China |
| 摘 要： | 1.IntroductionInreliabilitytheory,inordertocalculatethefailurefrequencyofarepairablesystem,Shily]firstintroducedandstudiedthetransitionfrequencybetweentwodisjointstatesetsforafiniteMarkovchainandavectorMarkovprocesswithfinitediscretestatespaceandobtainedageneralformulaoftransitionfrequency.Then,ontheconditionthatthegeneratormatrixofMarkovchainisuniformlybounded,Shi[8'9]againprovedthetransitionfrequencyformulaandobtainedthreeotherusefulformulas.Obviously,thepoint(orcalledcounting)processofsta… |
| 关 键 词： | 篜oint process， regular Markov chain state transition counting process transition frequency formula queueing theory |
| 收稿时间： | 1994-04-18 |
The point process of state transitions in a regular Markov chain |
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| Shi Dinghua,Guo Jinli. The point process of state transitions in a regular Markov chain[J]. Acta Mathematicae Applicatae Sinica, 1998, 14(4): 374-380. DOI: 10.1007/BF02683821 | |
| Authors: | Shi Dinghua Guo Jinli |
| Affiliation: | (1) Department of Mathematics, Shanghai University, 201800 Shanghai, China |
| Abstract: | In this paper, we study the point process of state transitions in a regular Markov chain. Under a weaker condition, we prove that the point process is a 1-memory self-exciting point process and again obtain four useful formulas of the transition frequency, the absorbing distribution, the renewal distribution and the entering probability. As an application, using these formulas we derive the LS transform of the busy period for theM/M/∞ queue. |
| Keywords: | Point process regular Markov chain state transition counting process transition frequency formula queueing theory |
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