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The state-dependent M / G / 1 queue with orbit

Author

Listed:
  • Opher Baron

    (University of Toronto)

  • Antonis Economou

    (National and Kapodistrian University of Athens)

  • Athanasia Manou

    (Koç University)

Abstract

We consider a state-dependent single-server queue with orbit. This is a versatile model for the study of service systems, where the server needs a non-negligible time to retrieve waiting customers every time he completes a service. This situation arises typically when the customers are not physically present at a system, but they have a remote access to it, as in a call center station, a communication node, etc. We introduce a probabilistic approach for the performance evaluation of this queueing system, that we refer to as the queueing and Markov chain decomposition approach. Moreover, we discuss the applicability of this approach for the performance evaluation of other non-Markovian service systems with state dependencies.

Suggested Citation

  • Opher Baron & Antonis Economou & Athanasia Manou, 2018. "The state-dependent M / G / 1 queue with orbit," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 89-123, October.
    • Handle: RePEc:spr:queues:v:90:y:2018:i:1:d:10.1007_s11134-018-9582-1
    DOI: 10.1007/s11134-018-9582-1
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    References listed on IDEAS

    as
    1. 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.
    2. Gabriel R. Bitran & Devanath Tirupati, 1988. "Multiproduct Queueing Networks with Deterministic Routing: Decomposition Approach and the Notion of Interference," Management Science, INFORMS, vol. 34(1), pages 75-100, January.
    3. Athanasia Manou & Antonis Economou & Fikri Karaesmen, 2014. "Strategic Customers in a Transportation Station: When Is It Optimal to Wait?," Operations Research, INFORMS, vol. 62(4), pages 910-925, August.
    4. Jianfu Wang & Opher Baron & Alan Scheller-Wolf, 2015. "M/M/c Queue with Two Priority Classes," Operations Research, INFORMS, vol. 63(3), pages 733-749, June.
    5. Hossein Abouee-Mehrizi & Opher Baron & Oded Berman, 2014. "Exact Analysis of Capacitated Two-Echelon Inventory Systems with Priorities," Manufacturing & Service Operations Management, INFORMS, vol. 16(4), pages 561-577, October.
    6. Moeko Yajima & Tuan Phung-Duc, 2017. "Batch arrival single-server queue with variable service speed and setup time," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 241-260, August.
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    Cited by:

    1. Anatoly Nazarov & Ekaterina Fedorova & Olga Lizyura & Radmir Salimzyanov, 2023. "Asymptotic Diffusion Method for Retrial Queues with State-Dependent Service Rate," Mathematics, MDPI, vol. 11(14), pages 1-10, July.

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