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Algorithmic analysis of the Geo/Geo/c retrial queue

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  • Artalejo, Jesus R.
  • Economou, Antonis
  • Gómez-Corral, Antonio

Abstract

In this paper, we consider a discrete-time queue of Geo/Geo/c type with geometric repeated attempts. It is known that its continuous counterpart, namely the M/M/c queue with exponential retrials, is analytically intractable due to the spatial heterogeneity of the underlying Markov chain, caused from the retrial feature. In discrete-time, the occurrence of multiple events at each slot increases the complexity of the model and raises further computational difficulties. We propose several algorithmic procedures for the efficient computation of the main performance measures of this system. More specifically, we investigate the stationary distribution of the system state, the busy period and the waiting time. Several numerical examples illustrate the analysis.

Suggested Citation

  • Artalejo, Jesus R. & Economou, Antonis & Gómez-Corral, Antonio, 2008. "Algorithmic analysis of the Geo/Geo/c retrial queue," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1042-1056, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:1042-1056
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    References listed on IDEAS

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    1. I. Atencia & P. Moreno, 2006. "A Discrete-Time Geo/ G/1 retrial queue with the server subject to starting failures," Annals of Operations Research, Springer, vol. 141(1), pages 85-107, January.
    2. Li, Hui & Yang, Tao, 1998. "Geo/G/1 discrete time retrial queue with Bernoulli schedule," European Journal of Operational Research, Elsevier, vol. 111(3), pages 629-649, December.
    3. Artalejo, J.R. & Economou, A. & Lopez-Herrero, M.J., 2007. "Algorithmic approximations for the busy period distribution of the M/M/c retrial queue," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1687-1702, February.
    4. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
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    Cited by:

    1. Öner-Közen, Miray & Minner, Stefan, 2017. "Impact of priority sequencing decisions on on-time probability and expected tardiness of orders in make-to-order production systems with external due-dates," European Journal of Operational Research, Elsevier, vol. 263(2), pages 524-539.
    2. A. Azadeh & M. S. Naghavi lhoseiny & V. Salehi, 2018. "Optimum alternatives of tandem G/G/K queues with disaster customers and retrial phenomenon: interactive voice response systems," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 68(3), pages 535-562, July.
    3. Kahraman, Aykut & Gosavi, Abhijit, 2011. "On the distribution of the number stranded in bulk-arrival, bulk-service queues of the M/G/1 form," European Journal of Operational Research, Elsevier, vol. 212(2), pages 352-360, July.

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