<?xml version="1.0" encoding="utf-8"?>
<export-example>
  <doc>
    <id>695</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2002-07-10</completedDate>
    <publishedDate>2002-07-10</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">On the Two-Class M/M/1 System under Preemptive Resume and Impatience of the Prioritized Customers</title>
    <abstract language="eng">The paper deals with the two-class priority M/M/1 system, where the prioritized class-1 customers are served under FCFS preemptive resume discipline and may become impatient during their waiting for service with generally distributed maximal waiting times but finite expectation. The class-2 customers have no impatience. The required mean service times may depend on the class of the customer. As the dynamics of class-1 customers are related to the well analyzed M/M/1+GI system, our aim is to derive characteristics for class-2 customers and for the whole system. The solution of the balance equations for the partial probability generating functions of the detailed system state process is given in terms of the weak solution of a family of boundary value problems for ordinary differential equations. By means of this solution formulae for the joint occupancy distribution and for the sojourn and waiting times of class-2 customers are derived generalizing results recently obtained by Choi et al. in case of deterministic maximal waiting times. For deterministic maximal waiting times partially new explicit formulae are given.</abstract>
    <identifier type="serial">02-28</identifier>
    <identifier type="opus3-id">696</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-6953</identifier>
    <enrichment key="SourceTitle">Appeared in: Queuing Systems, 47 (2004) 147-168</enrichment>
    <author>Andreas Brandt</author>
    <author>Manfred Brandt</author>
    <series>
      <title>ZIB-Report</title>
      <number>02-28</number>
    </series>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>two-class priority M/M/1 system</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>preemptive resume</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>impatient customers</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>occupancy distribution</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>waiting time</value>
    </subject>
    <subject>
      <language>eng</language>
      <type>uncontrolled</type>
      <value>sojourn time</value>
    </subject>
    <collection role="ddc" number="000">Informatik, Informationswissenschaft, allgemeine Werke</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="">ZIB Allgemein</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/695/ZR-02-28.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/695/ZR-02-28.pdf</file>
  </doc>
  <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>
