English, Article edition: A DISCRETE-TIME Geo/G/1 RETRIAL QUEUE WITH SERVER BREAKDOWNS IVAN ATENCIA; PILAR MORENO

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Bookmark: http://trove.nla.gov.au/version/131666
Physical Description
  • article
Language
  • English

Edition details

Title
  • A DISCRETE-TIME Geo/​G/​1 RETRIAL QUEUE WITH SERVER BREAKDOWNS
Author
  • IVAN ATENCIA
  • PILAR MORENO
Physical Description
  • article
Notes
  • This paper discusses a discrete-time Geo/​G/​1 retrial queue with the server subject to breakdowns and repairs. The customer just being served before server breakdown completes his remaining service when the server is fixed. The server lifetimes are assumed to be geometrical and the server repair times are arbitrarily distributed. We study the Markov chain underlying the considered queueing system and present its stability condition as well as some performance measures of the system in steady-state. Then, we derive a stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions of our system and the corresponding system without retrials. Also, we introduce the concept of generalized service time and develop a recursive procedure to obtain the steady-state distributions of the orbit and system size. Finally, we prove the convergence to the continuous-time counterpart and show some numerical results.
  • Discrete-time retrial queues, recursive formulae, stochastic decomposition, unreliable server
  • RePEc:wsi:apjorx:v:23:y:2006:i:02:p:247-271
Language
  • English
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