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On $$M^{X}/G(M/H)/1$$ M X / G ( M / H ) / 1 retrial system with vacation: service helpline performance measurement

Author

Listed:
  • Wee Meng Yeo

    (Singapore Institute of Manufacturing Technology (SIMTech))

  • Xue-Ming Yuan

    (Singapore Institute of Manufacturing Technology)

  • Joyce Mei Wan Low

    (Singapore Management University)

Abstract

This paper analyzes an unreliable $$M^{X}/G(M/H)/1$$ M X / G ( M / H ) / 1 retrial system with vacation. We present closed-form expressions for the important performance indicators of the system, and derive the optimal vacation policies for minimizing the average waiting time of orbiting customers. The performance metrics relevant for helpline services are developed. Numerical experiments are conducted to examine the effect of vacation policy on the queue length and busy period of the system.

Suggested Citation

  • Wee Meng Yeo & Xue-Ming Yuan & Joyce Mei Wan Low, 2017. "On $$M^{X}/G(M/H)/1$$ M X / G ( M / H ) / 1 retrial system with vacation: service helpline performance measurement," Annals of Operations Research, Springer, vol. 248(1), pages 553-578, January.
    • Handle: RePEc:spr:annopr:v:248:y:2017:i:1:d:10.1007_s10479-016-2207-3
    DOI: 10.1007/s10479-016-2207-3
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    References listed on IDEAS

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    1. Linn I. Sennott & Pierre A. Humblet & Richard L. Tweedie, 1983. "Technical Note—Mean Drifts and the Non-Ergodicity of Markov Chains," Operations Research, INFORMS, vol. 31(4), pages 783-789, August.
    2. Jau-Chuan Ke, 2003. "Optimal strategy policy in batch arrival queue with server breakdowns and multiple vacations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(1), pages 41-56, September.
    3. Jing-Sheng Song, 1994. "The Effect of Leadtime Uncertainty in a Simple Stochastic Inventory Model," Management Science, INFORMS, vol. 40(5), pages 603-613, May.
    4. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, September.
    5. Quan-Lin Li & Yu Ying & Yiqiang Zhao, 2006. "A BMAP/G/1 Retrial Queue with a Server Subject to Breakdowns and Repairs," Annals of Operations Research, Springer, vol. 141(1), pages 233-270, January.
    6. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
    7. I. Atencia & G. Bouza & P. Moreno, 2008. "An M [X] /G/1 retrial queue with server breakdowns and constant rate of repeated attempts," Annals of Operations Research, Springer, vol. 157(1), pages 225-243, January.
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