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Cost evaluation in M/G/1 queue with T-policy revisited, technical note

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  • Zhang, Zhe George
  • Tadj, Lotfi
  • Bounkhel, Messaoud

Abstract

This note clarifies the concept of regeneration cycle used in evaluating the average operating cost of the M/G/1 queue with T-policy studied in 70s. Two ways of defining the regeneration cycle are compared and advantages and disadvantages of each way are pointed out. In addition, we establish the convexity of the cost function based on the service cycle.

Suggested Citation

  • Zhang, Zhe George & Tadj, Lotfi & Bounkhel, Messaoud, 2011. "Cost evaluation in M/G/1 queue with T-policy revisited, technical note," European Journal of Operational Research, Elsevier, vol. 214(3), pages 814-817, November.
    • Handle: RePEc:eee:ejores:v:214:y:2011:i:3:p:814-817
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    References listed on IDEAS

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    1. Daniel P. Heyman, 1977. "The T-Policy for the M/G/1 Queue," Management Science, INFORMS, vol. 23(7), pages 775-778, March.
    2. 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, April.
    3. Alfa, Attahiru Sule & Frigui, Imed, 1996. "Discrete NT-policy single server queue with Markovian arrival process and phase type service," European Journal of Operational Research, Elsevier, vol. 88(3), pages 599-613, February.
    4. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    5. Daniel P. Heyman, 1968. "Optimal Operating Policies for M / G /1 Queuing Systems," Operations Research, INFORMS, vol. 16(2), pages 362-382, April.
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    Cited by:

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    2. Zhang, Xuelu & Wang, Jinting & Do, Tien Van, 2015. "Threshold properties of the M/M/1 queue under T-policy with applications," Applied Mathematics and Computation, Elsevier, vol. 261(C), pages 284-301.
    3. Tirdad, Ali & Grassmann, Winfried K. & Tavakoli, Javad, 2016. "Optimal policies of M(t)/M/c/c queues with two different levels of servers," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1124-1130.
    4. uit het Broek, Michiel A.J. & Van der Heide, Gerlach & Van Foreest, Nicky D., 2020. "Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs," European Journal of Operational Research, Elsevier, vol. 287(3), pages 916-928.
    5. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.

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