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An M/G/1 retrial queue with balking and retrials during service

Author

Listed:
  • Xiaoyong Wu
  • Percy Brill
  • Myron Hlynka
  • Jinting Wang

Abstract

We consider an M/G/1 retrial queue with general retrial times. Customers may balk or renege at particular times. The server is subject to breakdown (with repairs). While the server is being repaired, the customer in service can either remain in the service position or leave and return, while maintaining its rights to the server. We find a stability condition for this system. In the steady state, the joint distribution of the server state and queue length is obtained, leading to useful measures of the system, such as the probability of an empty system, the mean number of customers in the retrial queue and the expected retrial time.

Suggested Citation

  • Xiaoyong Wu & Percy Brill & Myron Hlynka & Jinting Wang, 2005. "An M/G/1 retrial queue with balking and retrials during service," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 1(1/2), pages 30-51.
    • Handle: RePEc:ids:ijores:v:1:y:2005:i:1/2:p:30-51
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    Citations

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    Cited by:

    1. Gao, Shan & Wang, Jinting, 2014. "Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers," European Journal of Operational Research, Elsevier, vol. 236(2), pages 561-572.
    2. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    3. Rakesh Kumar & Narendra Kumar Jain & Bhupernder Kumar Som, 2014. "Optimization of an M/M/1/N feedback queue with retention of reneged customers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(3), pages 45-58.
    4. Jesus R. Artalejo & A. Gómez‐Corral, 2007. "Waiting time analysis of the M/G/1 queue with finite retrial group," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 524-529, August.

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