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<!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Publishing DTD v1.3 20210610//EN" "https://jats.nlm.nih.gov/publishing/1.3/JATS-journalpublishing1-3.dtd">
<article article-type="brief-report" dtd-version="1.3" xml:lang="ru">
  <front xmlns:xlink="http://www.w3.org/1999/xlink">
    <journal-meta>
      <journal-title-group>
        <journal-title>St. Petersburg Polytechnic University Journal: Physics and Mathematics</journal-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Научно-технические ведомости СПбГПУ. Физико-математические науки</trans-title>
        </trans-title-group>
      </journal-title-group>
      <issn pub-type="epub">2304-9782, 2618-8686, 2405-7223</issn>
    </journal-meta>
    <article-meta xmlns:xlink="http://www.w3.org/1999/xlink">
      <article-id pub-id-type="publisher-id">2</article-id>
      <article-id pub-id-type="doi">10.5862/JPM.237.2</article-id>
      <title-group>
        <article-title>The semi-markov model for the ‘technological module – storage device’ structure</article-title>
        <trans-title-group xml:lang="ru">
          <trans-title>Полумарковская модель структуры технологическая ячейка – накопитель</trans-title>
        </trans-title-group>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Kopp</surname>
            <given-names>Vadim</given-names>
          </name>
          <email>volkov-and@yandex.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Kartashov</surname>
            <given-names>Aleksey</given-names>
          </name>
          <email>kartashov.alekseyy@rambler.ru</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Zamoryonov</surname>
            <given-names>Michael</given-names>
          </name>
          <email>zamoryonoff@gmail.com</email>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Klyukin</surname>
            <given-names>Valery</given-names>
          </name>
          <email>kljukin@mail.ru</email>
        </contrib>
      </contrib-group>
      <pub-date publication-format="electronic" date-type="pub" iso-8601-date="2016-03-10">
        <day>10</day>
        <month>03</month>
        <year>2016</year>
      </pub-date>
      <issue>1</issue>
      <issue-id pub-id-type="publisher-id">237</issue-id>
      <fpage>16</fpage>
      <lpage>28</lpage>
      <self-uri xmlns:xlink="http://www.w3.org/1999/xlink" content-type="pdf" xlink:href="https://physmath.spbstu.ru/userfiles/files/articles/2016/1/02_16_28_1_237_2016.pdf"/>
      <abstract xml:lang="en">
        <p>The theory of semi-Markov process has been used to design the model of ‘technological module – storage device’ (TM-SD) structure. Stationary characteristics based on obtained equations were determined to find stationary distribution of the Markov embedded chain. Relying upon performed studies the stationary distribution of semi-Markov process was determined. This allowed calculation of the availability ratio of TM-SD structure and the design formula was given. The Markov restoration equations for TM-SD system with taking into account TM and SD failures were solved assuming the exponential behavior of these failures. The obtained expressions describe operating of such a system and allow substitution of TM-SD system with an equivalent element with two factor states. This result significantly simplifies the modeling problem for more complex systems. The legitimacy of using exponential distributions of random variables (error-free periods for TM and SD) was analyzed. The performed simulation modeling disclosed that the hypothesis for an exponential behavior of error-free periods for TM as a whole (and SD as well) can be accepted even in the case that TM (or SD) consists of six nodes.</p>
      </abstract>
      <kwd-group xml:lang="en">
        <kwd>semi-Markov model</kwd>
        <kwd>Markov restoration equation</kwd>
        <kwd>embedded Markov chain</kwd>
        <kwd>stationary distribution</kwd>
      </kwd-group>
    </article-meta>
  </front>
</article>
