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      • Department of Industrial Engineering
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      Some Markovian Queuing Retrial Systems under light-traffic conditions

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      Author
      Anisimov, V. V.
      Kurtulush, M.
      Date
      2001
      Source Title
      Cybernetics and Systems Analysis
      Print ISSN
      1060-0396
      Electronic ISSN
      1573-8337
      Publisher
      Kluwer Academic Publishers-Plenum Publishers
      Volume
      37
      Issue
      6
      Pages
      876 - 887
      Language
      English
      Type
      Article
      Item Usage Stats
      143
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      93
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      Abstract
      The asymptotic behavior of the time of the first loss of a demand in Markovian single-channel and multichannel queuing retrial systems with a finite buffer and an external Markovian environment is analyzed. Two cases are studied: (a) the ratio of the input rate to the service rate tends to zero and (b) the ratio of the input rate to the service rate and the ratio of the input rate to the retrial rate tend to zero simultaneously. The method of so-called S-sets and the concept of a monotone structure introduced by Anisimov are used to prove the exponential approximation of the time of the first call loss and Poisson approximation of a flow of lost demands for both cases.
      Keywords
      Markovian queuing systems
      Retrials
      Light - traffic conditions
      S-sets
      Markovian environment
      Permalink
      http://hdl.handle.net/11693/49089
      Published Version (Please cite this version)
      https://doi.org/10.1023/A:1014534015782
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      • Department of Industrial Engineering 688
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