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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