Transient Solution for Queueing Delay Distribution in the GI/M/1/K-type Mode with “Queued” Waking up and Balking

  • Wojciech M. Kempa
  • Marcin Woźniak
  • Robert K. Nowicki
  • Marcin Gabryel
  • Robertas Damaševicius
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9693)

Abstract

Time-dependent behavior of queueing delay distribution in the GI/M/1/K-type model with the “queued” server’s waking up and balking is studied. After each idle period the server is being “queued” woken up, i.e. the processing is being started at the moment the number of packets accumulated in the buffer reaches the fixed level N. Moreover, each incoming packet can balk (resign from service) and leave the system irrevocably, with probability \(1-\beta ,\) and join the queue with probability \(\beta ,\) where \(0< \beta \le 1\).

Keywords

Balking Finite-buffer queue N-policy Queueing delay Transient state 

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Wojciech M. Kempa
    • 1
  • Marcin Woźniak
    • 1
  • Robert K. Nowicki
    • 2
  • Marcin Gabryel
    • 2
  • Robertas Damaševicius
    • 3
  1. 1.Institute of MathematicsSilesian University of TechnologyGliwicePoland
  2. 2.Institute of Computational IntelligenceCzestochowa University of TechnologyCzestochowaPoland
  3. 3.Software Engineering DepartmentKaunas University of TechnologyKaunasLithuania

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