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  <doc>
    <id>1141</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-08-31</completedDate>
    <publishedDate>2009-08-31</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Approximations for the second moments of sojourn times in M/GI systems under state-dependent processor sharing</title>
    <abstract language="eng">We consider a system with Poisson arrivals and general service times, where the requests are served according to the State-Dependent Processor Sharing (SDPS) discipline (Cohen's generalized processor sharing discipline), where each request receives a service capacity which depends on the actual number of requests in the system. For this system, denoted by $M/GI/SDPS$, we derive approximations for the squared coefficients of variation of the conditional sojourn time of a request given its service time and of the unconditional sojourn time by means of two-moment fittings of the service times. The approximations are given in terms of the squared coefficients of variation of the conditional and unconditional sojourn time in related $M/D/SDPS$ and $M/M/SDPS$ systems, respectively. The numerical results presented for $M/GI/m-PS$ systems illustrate that the proposed approximations work well.</abstract>
    <identifier type="serial">09-25</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1190</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11414</identifier>
    <author>Andreas Brandt</author>
    <submitter>unknown unknown</submitter>
    <author>Manfred Brandt</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-25</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state-dependent processor sharing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>M/GI/m-PS</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sojourn time</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>moments</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>approximations</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="60K25">Queueing theory [See also 68M20, 90B22]</collection>
    <collection role="msc" number="68M20">Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]</collection>
    <collection role="msc" number="90B22">Queues and service [See also 60K25, 68M20]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1141/ZR_09_25.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1141/ZR_09_25.ps</file>
  </doc>
  <doc>
    <id>1109</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
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    <creatingCorporation/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2009-01-07</completedDate>
    <publishedDate>2009-01-07</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Insensitivity bounds for the moments of the sojourn times in M/GI systems under state-dependent processor sharing</title>
    <abstract language="eng">We consider a system with Poisson arrivals and i.i.d. service times and where the requests are served according to the state-dependent (Cohen's generalized) processor sharing discipline, where each request in the system receives a service capacity which depends on the actual number of requests in the system. For this system we derive asymptotically tight upper bounds for the moments of the conditional sojourn time of a request with given required service time. The bounds generalize corresponding results, recently given for the single-server processor sharing system by Cheung et al. and for the state-dependent processor sharing system with exponential service times by the authors. Analogous results hold for the waiting times.</abstract>
    <identifier type="serial">09-02</identifier>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="opus3-id">1150</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-11092</identifier>
    <enrichment key="SourceTitle">Appeared in: Adv. in Appl. Probab., 42 (2010) 246-267</enrichment>
    <author>Andreas Brandt</author>
    <submitter>unknown unknown</submitter>
    <author>Manfred Brandt</author>
    <series>
      <title>ZIB-Report</title>
      <number>09-02</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>state-dependent processor sharing</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sojourn time</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>moments</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>bounds</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>M/GI/m-PS</value>
    </subject>
    <collection role="ddc" number="510">Mathematik</collection>
    <collection role="msc" number="60E15">Inequalities; stochastic orderings</collection>
    <collection role="msc" number="60G10">Stationary processes</collection>
    <collection role="msc" number="60K25">Queueing theory [See also 68M20, 90B22]</collection>
    <collection role="msc" number="68M20">Performance evaluation; queueing; scheduling [See also 60K25, 90Bxx]</collection>
    <collection role="msc" number="90B22">Queues and service [See also 60K25, 68M20]</collection>
    <collection role="institutes" number="optimization">Mathematical Optimization</collection>
    <collection role="projects" number="PROSCHED">PROSCHED</collection>
    <collection role="institutes" number="aopt">Applied Optimization</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1109/ZR_09_02.pdf</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1109/ZR_09_02.ps</file>
  </doc>
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