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Some Exact and Asymptotic Solutions to Single Server Models of Dynamic Storage.

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Title: Some Exact and Asymptotic Solutions to Single Server Models of Dynamic Storage.
Authors: Sohn, Eunju1 (AUTHOR), Knessl, Charles2 (AUTHOR) knessl@uic.edu
Source: Stochastic Models. Apr-Jun2012, Vol. 28 Issue 2, p248-280. 33p. 3 Color Photographs, 5 Graphs.
Subjects: Asymptotic distribution, Dynamic storage allocation (Computer science), Poisson processes, Distribution (Probability theory), Mathematical programming, Mathematical analysis
Abstract: We consider models of queue storage, where items arrive accordingly to a Poisson process of rate λ and each item takes up one cell in a linear array of cells, which are numbered {1, 2, 3,…}. The arriving item is placed in the lowest numbered available cell. The total service rate provided to the items is the constant μ (with ρ = λ/μ), but service may be provided simultaneously to more than one item. If there are 𝒩 items stored and each is serviced at the rate μ/𝒩, this corresponds to processor-sharing (PS). We analyze several models of this type, which have been shown to provide bounds on the PS model. We shall assume that (1) the server works only on the leftmost item, (2) on the two rightmost items, or (3) on all items by the PS discipline, but with a departure of the rightmost item causing a rearrangement of the items within the cells, so that the wasted space remains unchanged. The set of occupied cells at any time is {i 1, i 2,…, i 𝒩} where i 1 < i 2 < …
Copyright of Stochastic Models is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Some Exact and Asymptotic Solutions to Single Server Models of Dynamic Storage.
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  Data: &lt;searchLink fieldCode=&quot;JN&quot; term=&quot;%22Stochastic+Models%22&quot;&gt;Stochastic Models&lt;/searchLink&gt;. Apr-Jun2012, Vol. 28 Issue 2, p248-280. 33p. 3 Color Photographs, 5 Graphs.
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  Data: We consider models of queue storage, where items arrive accordingly to a Poisson process of rate λ and each item takes up one cell in a linear array of cells, which are numbered {1, 2, 3,…}. The arriving item is placed in the lowest numbered available cell. The total service rate provided to the items is the constant μ (with ρ&#160;=&#160;λ/μ), but service may be provided simultaneously to more than one item. If there are &#119977; items stored and each is serviced at the rate μ/&#119977;, this corresponds to processor-sharing (PS). We analyze several models of this type, which have been shown to provide bounds on the PS model. We shall assume that (1) the server works only on the leftmost item, (2) on the two rightmost items, or (3) on all items by the PS discipline, but with a departure of the rightmost item causing a rearrangement of the items within the cells, so that the wasted space remains unchanged. The set of occupied cells at any time is {i 1, i 2,…, i &#119977;} where i 1&#160;&lt;&#160;i 2 &lt; … &lt;i &#119977; and we are interested in the wasted space (W&#160;=&#160;i &#119977; − &#119977;), the maximum occupied cell (i &#119977;), and the joint distribution of W and &#119977;. We study these exactly and asymptotically, especially in the heavy traffic limit where ρ&#160;↑&#160;1. [ABSTRACT FROM PUBLISHER]
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  Data: &lt;i&gt;Copyright of Stochastic Models is the property of Taylor &amp; Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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        Value: 10.1080/15326349.2012.672145
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 33
        StartPage: 248
    Subjects:
      – SubjectFull: Asymptotic distribution
        Type: general
      – SubjectFull: Dynamic storage allocation (Computer science)
        Type: general
      – SubjectFull: Poisson processes
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Mathematical programming
        Type: general
      – SubjectFull: Mathematical analysis
        Type: general
    Titles:
      – TitleFull: Some Exact and Asymptotic Solutions to Single Server Models of Dynamic Storage.
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            NameFull: Sohn, Eunju
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            NameFull: Knessl, Charles
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          Dates:
            – D: 01
              M: 04
              Text: Apr-Jun2012
              Type: published
              Y: 2012
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              Value: 28
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            – TitleFull: Stochastic Models
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