Steady-state probability of the randomized server control system with second optional service, server breakdowns and startup

Dong Yuh Yang, Kuo Hsiung Wang*, W.l. Pearn

*Corresponding author for this work

Research output: Contribution to journalArticle

7 Scopus citations

Abstract

This paper deals with the 〈N,p〉-policy M/G/1 queue with server breakdowns and general startup times, where customers arrive to demand the first essential service and some of them further demand a second optional service. Service times of the first essential service channel are assumed to follow a general distribution and that of the second optional service channel are another general distribution. The server breaks down according to a Poisson process and his repair times obey a general distribution in the first essential service channel and second optional service channel, respectively. The server operation starts only when N (N≥1) customers have accumulated, he requires a startup time before each busy period. When the system becomes empty, turn the server off with probability p (p [0,1]) and leave it on with probability (1-p). The method of maximum entropy principle is used to develop the approximate steady-state probability distribution of the queue length in the M/G(G, G)/1 queueing system. A study of the derived approximate results, compared to the established exact results for three different 〈N,p〉-policy queues, suggests that the maximum entropy principle provides a useful method for solving complex queueing systems.

Original languageEnglish
Pages (from-to)39-58
Number of pages20
JournalJournal of Applied Mathematics and Computing
Volume32
Issue number1
DOIs
StatePublished - 1 Feb 2010

Keywords

  • 〈N,p〉-policy
  • Comparison
  • Maximum entropy principle
  • Second optional service
  • Startup

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