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The G/M/1 queue revisited

Author

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  • Ivo Adan
  • Onno Boxma
  • David Perry

Abstract

The G/M/1 queue is one of the classical models of queueing theory. The goal of this paper is two-fold: (a) To introduce new derivations of some well-known results, and (b) to present some new results for the G/M/1 queue and its variants. In particular, we pay attention to the G/M/1 queue with a set-up time at the start of each busy period, and the G/M/1 queue with exceptional first service. Copyright Springer-Verlag 2005

Suggested Citation

  • Ivo Adan & Onno Boxma & David Perry, 2005. "The G/M/1 queue revisited," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(3), pages 437-452, December.
    • Handle: RePEc:spr:mathme:v:62:y:2005:i:3:p:437-452
    DOI: 10.1007/s00186-005-0032-6
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    Citations

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    Cited by:

    1. Legros, Benjamin, 2022. "The principal-agent problem for service rate event-dependency," European Journal of Operational Research, Elsevier, vol. 297(3), pages 949-963.
    2. Boxma, Onno & Frostig, Esther & Perry, David & Yosef, Rami, 2017. "A state dependent reinsurance model," Insurance: Mathematics and Economics, Elsevier, vol. 74(C), pages 170-181.
    3. Michael N. Katehakis & Benjamin Melamed & Jim Junmin Shi, 2022. "Optimal replenishment rate for inventory systems with compound Poisson demands and lost sales: a direct treatment of time-average cost," Annals of Operations Research, Springer, vol. 317(2), pages 665-691, October.
    4. Binyamin Oz & Ivo Adan & Moshe Haviv, 2017. "A rate balance principle and its application to queueing models," Queueing Systems: Theory and Applications, Springer, vol. 87(1), pages 95-111, October.
    5. Moshe Haviv & Yoav Kerner, 2011. "The age of the arrival process in the G/M/1 and M/G/1 queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 139-152, February.
    6. Benjamin Legros, 2021. "Age-based Markovian approximation of the G/M/1 queue," Post-Print hal-03605431, HAL.
    7. Esther Frostig & Adva Keren–Pinhasik, 2017. "Parisian ruin in the dual model with applications to the G/M/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 261-275, August.
    8. Jim (Junmin) Shi & Michael N. Katehakis & Benjamin Melamed & Yusen Xia, 2014. "Production-Inventory Systems with Lost Sales and Compound Poisson Demands," Operations Research, INFORMS, vol. 62(5), pages 1048-1063, October.

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