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  <doc>
    <id>1430</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-11-22</completedDate>
    <publishedDate>2011-11-22</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Workload and busy period for M/GI/1 with a general impatience mechanism</title>
    <abstract language="eng">The paper deals with the workload and busy period for the M/GI/1&#13;
system under FCFS discipline, where the customers may become&#13;
impatient during their waiting for service with generally&#13;
distributed maximal waiting times and also during their service&#13;
with generally distributed maximal service times depending&#13;
on the time waited for service. This general impatience mechanism,&#13;
originally introduced by Kovalenko (1961) and considered&#13;
by Daley (1965), too, covers the special cases of impatience&#13;
on waiting times as well as impatience on sojourn times,&#13;
for which Boxma et al. (2010), (2011) gave new results&#13;
and outlined special cases recently. Our unified approach&#13;
bases on the vector process of workload and busy time.&#13;
Explicit representations for the LSTs of workload and&#13;
busy period are given in case of phase-type distributed&#13;
impatience.</abstract>
    <identifier type="issn">1438-0064</identifier>
    <identifier type="serial">11-43</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-14304</identifier>
    <identifier type="doi">10.1007/s11134-013-9373-7</identifier>
    <enrichment key="SourceTitle">Appeared in: Queueing Systems, vol. 75 no. 2-4 (2013), pp. 189-209</enrichment>
    <author>Andreas Brandt</author>
    <submitter>Manfred Brandt</submitter>
    <author>Manfred Brandt</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-43</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>impatient customers</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>workload</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>busy period</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>waiting time dependent service</value>
    </subject>
    <collection role="msc" number="60-XX">PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX)</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/1430/ZIB-11-43.pdf</file>
  </doc>
</export-example>
