Throughput maximization for two station tandem systems: A proof of the Andradóttir-Ayhan conjecture

John J. Hasenbein, Bara Kim

    Research output: Contribution to journalArticlepeer-review

    9 Citations (Scopus)

    Abstract

    We study a tandem queueing network with two stations, M heterogeneous flexible servers, and a finite intermediate buffer. The objective is to dynamically assign the servers to the stations in order to maximize the throughput of the system. The form of the optimal policy for M≤3 was derived in two previous papers. In one of those papers, Andradóttir and Ayhan (Operations Research 53:516-531, 2005) provide a conjecture on the form of the optimal policy for M≥4. We prove their conjecture in this paper, showing that the optimal policy is defined by monotone thresholds and the ratios of the service rates among the servers. For M>1, we also prove that the optimal policy always uses the entire intermediate buffer.

    Original languageEnglish
    Pages (from-to)365-386
    Number of pages22
    JournalQueueing Systems
    Volume67
    Issue number4
    DOIs
    Publication statusPublished - 2011 Apr

    Bibliographical note

    Funding Information:
    Acknowledgements We would like to thank Hayriye Ayhan and Doug Down for useful discussions during the course of this research. John Hasenbein was partially supported by NSF grant 26-1130-32. Bara Kim was supported by LG Yonam Culture Foundation.

    Keywords

    • Flexible servers
    • Markov decision processes
    • Tandem queueing networks
    • Throughput optimality

    ASJC Scopus subject areas

    • Statistics and Probability
    • Computer Science Applications
    • Management Science and Operations Research
    • Computational Theory and Mathematics

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