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Stochastic Analysis of a Finite Source Retrial Queue with Spares and Orbit Search

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 7201)

Abstract

This paper aims at presenting an analytic approach for investigating a single server finite-source retrial queue with spares and constant retrial rate. We assume that there is a single repair facility (server) and K independent parts (customers) in the system. The customers’ life times are assumed to be exponentially distributed random variables. Once a customer breaks down, it is sent for repair immediately. If the server is idle upon the failed customer’s arrival, the customer receives repair immediately. The failed customer that finds the server busy upon arrival enters into the retrial orbit. Upon completion of a repair, the server searches for a customer from orbit if any. However, when a new primary customer arrives during the seeking process, the server interrupts the seeking process and serves the new customer. There are some spares for substitution of failed machines and the system is maintained by replacing failed part by spares and by repairing failed parts so that they may become spares when they are repaired. We carry out the steady-state analysis of the model and obtain various steady-state performance measures.

Keywords

  • Quasi-random input
  • orbital search
  • spares
  • busy period
  • waiting time

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Zhang, F., Wang, J. (2012). Stochastic Analysis of a Finite Source Retrial Queue with Spares and Orbit Search. In: Schmitt, J.B. (eds) Measurement, Modelling, and Evaluation of Computing Systems and Dependability and Fault Tolerance. MMB&DFT 2012. Lecture Notes in Computer Science, vol 7201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28540-0_2

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  • DOI: https://doi.org/10.1007/978-3-642-28540-0_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-28539-4

  • Online ISBN: 978-3-642-28540-0

  • eBook Packages: Computer ScienceComputer Science (R0)