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  <doc>
    <id>364</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
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    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>1998-07-30</completedDate>
    <publishedDate>1998-07-30</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On a Two-Queue Priority System with Impatience and its Application to a Call Center</title>
    <abstract language="eng">We consider a $s$-server system with two FCFS queues, where the arrival rates at the queues and the service rate may depend on the number $n$ of customers being in service or in the first queue, but the service rate is assumed to be constant for $n&gt;s$. The customers in the first queue are impatient. If the offered waiting time exceeds a random maximal waiting time $I$, then the customer leaves the first queue after time $I$. If $I$ is less than a given deterministic time then he leaves the system else he transits to the end of the second queue. The customers in the first queue have priority. The service of a customer from the second queue will be started if the first queue is empty and more than a given number of servers become idle. For the model being a generalization of the $M(n)/M(n)/s\!+\!GI$ system balance conditions for the density of the stationary state process are derived yielding the stability conditions and the probabilities that precisely $n$ customers are in service or in the first queue. For obtaining performance measures for the second queue a system approximation basing on fitting impatience intensities is constructed. The results are applied to the performance analysis of a call center with an integrated voice-mail-server. For an important special case a stochastic decomposition is derived illuminating the connection to the dynamics of the $M(n)/M(n)/s\!+\!GI$ system.</abstract>
    <identifier type="serial">SC-98-21</identifier>
    <identifier type="opus3-id">365</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-3641</identifier>
    <enrichment key="SourceTitle">Appeared in: Methodology and Computing in Applied Probability 1 (1999) 191-210</enrichment>
    <author>Andreas Brandt</author>
    <author>Manfred Brandt</author>
    <series>
      <title>ZIB-Report</title>
      <number>SC-98-21</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>two queues</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>many server</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>server reservation</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>impatience</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>occupancy distribution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>waiting time distribution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>approximate system</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>$M(n)/M(n)/s+GI</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</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="institutes" number="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/364/SC-98-21.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/364/SC-98-21.pdf</file>
  </doc>
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