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AN APPROXIMATION FOR THE QUEUE LENGTH DISTRIBUTION IN A MULTI-SERVER RETRIAL QUEUE

  • Kim, Jeongsim (Department of Mathematics Education, Chungbuk National University)
  • Received : 2015.12.30
  • Accepted : 2016.02.05
  • Published : 2016.02.15

Abstract

Multi-server queueing systems with retrials are widely used to model problems in a call center. We present an explicit formula for an approximation of the queue length distribution in a multi-server retrial queue, by using the Lerch transcendent. Accuracy of our approximation is shown in the numerical examples.

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  1. M. S. Aguir, O. Z. Aksin, F. Karaesmen, and Y. Dallery, On the interaction between retrials and sizing of call centers, European Journal of Operational Research 191 (2008), 398-408. https://doi.org/10.1016/j.ejor.2007.06.051
  2. M. S. Aguir, F. Karaesmen, O. Z. Aksin, and F. Chauvet, The impact of retrials on call center performance, OR Spectrum 26 (2004), 353-376. https://doi.org/10.1007/s00291-004-0165-7
  3. J. R. Artalejo, A classified bibliography of research on retrial queues: Progress in 1990-1999, Top 7 (1999), 187-211. https://doi.org/10.1007/BF02564721
  4. J. R. Artalejo, Accessible bibliography on retrial queues, Math. Comput. Model. 30 (1999), 1-6.
  5. J. R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000-2009, Math. Comput. Model. 51 (2010), 1071-1081. https://doi.org/10.1016/j.mcm.2009.12.011
  6. J. R. Artalejo, A. Economou, and A. Gomez-Corral, Applications of maximum queue lengths to call center management, Computers & Operations Research 34 (2007), 983-996. https://doi.org/10.1016/j.cor.2005.05.020
  7. J. R. Artalejo and A. Gomez-Corral, Retrial Queueing Systems, Springer, 2008.
  8. A. Erdelyi, Higher Transcendental Functions, Vol. 1, McGraw-Hill, New York, 1953.
  9. G. I. Falin, A survey of retrial queues, Queueing Systems 7 (1990), 127-168. https://doi.org/10.1007/BF01158472
  10. G. I. Falin and J. G. C. Templeton, Retrial Queues, Chapman & Hall, London, 1997.
  11. J. Kim and J. Kim, An approximation for the distribution of the number of retrying customers in an M/G/1 retrial queue, Journal of the Chungcheong Mathematical Society 27 (2014), 405-411. https://doi.org/10.14403/jcms.2014.27.3.405
  12. J. Kim, J. Kim, and B. Kim, Tail asymptotics of the queue size distribution in the M/M/m retrial queue, Journal of Computational and Applied Mathematics 236 (2012), 3445-3460. https://doi.org/10.1016/j.cam.2012.03.027
  13. V. G. Kulkarni and H. M. Liang, Retrial queues revisited, In: Frontiers in Queueing: Models and Applications in Science and Engineering (J.H. Dshalalow, ed.), CRC Press, Boca Raton, 1997, 19-34.
  14. T. Yang and J. G. C. Templeton, A survey on retrial queues, Queueing Systems 2 (1987), 201-233. https://doi.org/10.1007/BF01158899