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Zur stationarität eines ḿodifizierten erlangschen bedienungsprozesses

 

作者: Klaus Fleischmann,  

 

期刊: Mathematische Operationsforschung und Statistik  (Taylor Available online 1971)
卷期: Volume 2, issue 4  

页码: 283-290

 

ISSN:0047-6277

 

年代: 1971

 

DOI:10.1080/02331887108801053

 

出版商: Akademie-Verlag

 

数据来源: Taylor

 

摘要:

A generalized Erlang-model is treated. The calls form a Poisson process. If every line is busy the call is lost. Holding times, times of repair a.s.o. are described in terms of signed point processes. On each line the holding time is not assumed to be independent of time of repair or other characteristics. The whole model is described as a Markov process. Then a time-discrete Markov process describes the same system only observed at such times, when call arrive. It is shown that the stationary distributions of both proceses are the same (Theorem 1). A direct proof is given that the so-called “Produktansatz” based on Erland's formula is a stationary distribution for the discrete process (Theorem 2).

 

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