A single server queue with Markov modulated service rates and impatient customers

Bara Kim, Jeongsim Kim

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

We consider a single server queue in which the customers wait for service for a fixed time and leave the system if the service has not begun within that time. The customers arrive according to a Poisson process and each arriving customer brings in a certain amount of phase-type distributed work. The service rate of a server varies according to the underlying continuous time Markov process with finite states. We construct a Markov process by using the age process and then obtain the stationary distribution of the Markov process. By using the results of the stationary distribution of the Markov process, we obtain the loss probability, the waiting time distribution and the system size distribution.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalPerformance Evaluation
Volume83-84
DOIs
Publication statusPublished - 2014 Jan 1

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Single Server Queue
Markov Process
Markov processes
Servers
Customers
Stationary Distribution
Continuous-time Markov Process
Loss Probability
Waiting Time Distribution
Poisson process
Server
Vary

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Software
  • Modelling and Simulation

Cite this

A single server queue with Markov modulated service rates and impatient customers. / Kim, Bara; Kim, Jeongsim.

In: Performance Evaluation, Vol. 83-84, 01.01.2014, p. 1-15.

Research output: Contribution to journalArticle

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