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Discrete-Time Informal Queue with an Infinite Number of Groups for Resource Management of a Data Center

Author

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  • Veena Goswami

    (Kalinga Institute of Industrial Technology)

  • G. B. Mund

    (Kalinga Institute of Industrial Technology)

Abstract

We consider the resource management of a data center by using a discrete-time single-server queue with an unlimited-size batch service, where the next queue to be served is the one with the most senior waiting client (the so-called ‘Informal Queue’). Large jobs or tasks are submitted for processing by users from different applications or organizations in a cloud data center setting. There is an endless number of groups in the queue, a very dynamic and diverse workload, and an endless stream of tasks or jobs arriving every day. We analyze the Geo/Geo/1 informal queue with an early arrival system and a late arrival system with delayed access policies. Various key performance measures, such as steady-state distribution of the number of groups in the system, sojourn times and waiting times of a group leader, sojourn times and waiting times of an arbitrary client, and number of sidestep groups, are obtained. Explicit-form expressions are found for both policies. We illustrate several numerical results and present an application of the discussed model in data centers. Finally, it is demonstrated that in the limiting case, the outcomes found in this article tend to the continuous-time counterpart.

Suggested Citation

  • Veena Goswami & G. B. Mund, 2024. "Discrete-Time Informal Queue with an Infinite Number of Groups for Resource Management of a Data Center," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-24, December.
    • Handle: RePEc:spr:metcap:v:26:y:2024:i:4:d:10.1007_s11009-024-10128-4
    DOI: 10.1007/s11009-024-10128-4
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    References listed on IDEAS

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    1. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.
    2. Howard J. Weiss, 1979. "The Computation of Optimal Control Limits for a Queue with Batch Services," Management Science, INFORMS, vol. 25(4), pages 320-328, April.
    3. Nir Perel & Uri Yechiali, 2022. "The Israeli Queue with a general group-joining policy," Annals of Operations Research, Springer, vol. 317(1), pages 179-212, October.
    4. Tuan Phung-Duc & Ken’ichi Kawanishi, 2020. "Delay performance of data-center queue with setup policy and abandonment," Annals of Operations Research, Springer, vol. 293(1), pages 269-293, October.
    5. Muhammad El-Taha & Arunava Majumder, 2023. "A Review of Birth-Death and Other Markovian Discrete-Time Queues," Advances in Operations Research, Hindawi, vol. 2023, pages 1-22, December.
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