Approximate queue length distribution of a discriminatory processor sharing queue with impatient customers

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Abstract

We consider a two-class processor sharing queueing system with impatient customers. The system operates under the discriminatory processor sharing (DPS) scheduling. The arrival process of each class customers is the Poisson process and the service requirement of a customer is exponentially distributed. The reneging rate of a customer is a constant. To analyze the performance of the system, we develop a time scale decomposition approach to approximate the joint queue-length distribution of each class customers. Via a numerical experiment, we show that the time scale decomposition approach gives a fairly good approximation of the queue-length distribution and the expected queue length.

Original languageEnglish
Pages (from-to)105-118
Number of pages14
JournalJournal of the Korean Statistical Society
Volume43
Issue number1
DOIs
StatePublished - Mar 2014

Keywords

  • Discriminatory processor sharing
  • Impatient customers
  • Primary
  • Queue length distribution
  • Secondary
  • Time scale decomposition method

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