<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-information-and-optimization-sciences</journal-id>
      <journal-title-group>
        <journal-title>Journal of Information and Optimization Sciences</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0103</issn>
      <issn publication-format="print">0252-2667</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIOS-2175</article-id>
      <title-group>
        <article-title>Stochastic modeling of a retrial queue with server vacations and customer impatience in a multi-level environment</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Pravina</surname>
            <given-names>C. T. Dora</given-names>
          </name>
          <aff>Department of Mathematics, Avadi, Vel Tech Rangarajan Dr. Sagunthala R&amp;D Institute of Science and Technology, Chennai, Tamil Nadu, 600062, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Hemavathi</surname>
            <given-names>G.</given-names>
          </name>
          <aff>Department of Mathematics, Avadi, Vel Tech Rangarajan Dr. Sagunthala R&amp;D Institute of Science and Technology, Chennai, Tamil Nadu, 600062, India</aff>
        </contrib>
        <contrib contrib-type="author">
          <name>
            <surname>Damodaran</surname>
            <given-names>Sukumaran</given-names>
          </name>
          <aff>Department of Mathematics, Avadi, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Chennai, Tamil Nadu, 600062, India</aff>
        </contrib>
      </contrib-group>
      <volume>47</volume>
      <issue>6</issue>
      <fpage>2391</fpage>
      <lpage>2400</lpage>
      <pub-date date-type="pub">
        <day>11</day>
        <month>06</month>
        <year>2026</year>
      </pub-date>
      <abstract>
        <p>This paper analyzes a single-server retrial queue with vacations and customer impatience in a multi-level stochastic environment. Customer arrivals follow a Poisson process whose rate depends on the environment level and receive immediate exponential service if the server is idle. Otherwise, the customer joins an orbit and is queued as per the FCFS discipline, and retries for service follows an exponential distribution. Whenever the system becomes empty, the server takes a vacation during which arrivals enter the orbit but are not served, and orbiting customers may abandon due to impatience. After vacation, the server stays idle until service is triggered by a new arrival or a retrial.</p>
      </abstract>
      <kwd-group>
        <kwd>Single-server retrial queue</kwd>
        <kwd>Vacation policy</kwd>
        <kwd>Customer impatience</kwd>
        <kwd>Multi-level stochastic environment</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
