DOI QR코드

DOI QR Code

Sensitivity of M/M/c Retrial Queue with Respect to Retrial Times : Experimental Investigation

M/M/c 재시도대기체계에서 재시도시간의 민감성에 대한 실험적 고찰

  • Shin, Yang-Woo (Department of Statistics, Changwon National University) ;
  • Moon, Dug-Hee (Department of Industrial and Systems Engineering, Changwon National University)
  • 신양우 (창원대학교 통계학과) ;
  • 문덕희 (창원대학교 산업시스템공학과)
  • Received : 2010.12.29
  • Accepted : 2011.05.15
  • Published : 2011.06.01

Abstract

The effects of the moments of the retrial time to the system performance measures such as blocking probability, mean and standard deviation of the number of customers in service facility and orbit are numerically investigated. The results reveal some performance measures related with the number of customers in orbit can be severely affected by the fourth or higher moments of retrial time.

Keywords

References

  1. Artalejo, J. R. and Gomez-Corral, A. (2008), Retrial Queueing Systems, A Computational Approach, Springer-Verlag.
  2. Bobbio, A., Horvath, A., and Telek, M. (2005), Matching Three Moments with Minimal Acyclic Phase Type Distributions, Stochastic Models, 21, 303-326. https://doi.org/10.1081/STM-200056210
  3. Diamond, J. E. and Alfa, A. S. (1999), Approximation Method for M/ PH/ 1 Retrial Queues with Phase Type Inter-retrial Times, European Journal of Operational Research, 113, 620-631. https://doi.org/10.1016/S0377-2217(98)00004-6
  4. Falin, G. I. and Templeton, J. G. C. (1997), Retrial Queues, Chapman and Hall.
  5. He, Q. M. and Zhao, Y. Q. (2000), Ergodicity of the BMAP/PH/s/s+K Retrial Queue with PH-Retrial Times, Queueing Systems, 35, 323-347. https://doi.org/10.1023/A:1019110631467
  6. Johnson, M. A. and Taaffe, M. R. (1989), Matching moments to phase distributions : mixture of Erlang distributions of common order, Stochastic Models, 5, 711-743. https://doi.org/10.1080/15326348908807131
  7. Kelton, W. D., Sadowski, R. P. and Sadowski, D. A. (1998), Simulation with ARENA (2nd Ed.), McGraw-Hill.
  8. Liang, H. M. and Kulkarni, V. G. (1993), Monotonicity Properties of Single Server Retrial Queues, Stochastic Models, 9, 373-400. https://doi.org/10.1080/15326349308807271
  9. Shin, Y. W. (2011), Algorithmic Solution for M/M/c Retrial Queue with $PH_{2}$-Retrial Times, Journal of Applied Mathematics & Informatics, 29, 803-811.
  10. Tijms, H. (1994), Stochastic Models, An Algorithmic Approach, John Wiley and Sons, New York.
  11. Whitt, W. (1982), Approximating a Point Process by a Renewal Process, I : Two Basic Methods, Operations Research, 30, 125-147. https://doi.org/10.1287/opre.30.1.125
  12. Yang, T., Posner, M. J. M., Templeton, J. G. C., and Li, H. (1994), An Approximation Method for the M/G/1 Retrial Queues with General Retrial Times, European Journal of Operational Research, 76, 552-562. https://doi.org/10.1016/0377-2217(94)90286-0

Cited by

  1. ON APPROXIMATIONS FOR GI/G/c RETRIAL QUEUES vol.31, pp.1_2, 2013, https://doi.org/10.14317/jami.2013.311