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A probabilistic approach for the analysis of the $$M_n/G/1$$ M n / G / 1 queue

Author

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  • Antonis Economou

    (University of Athens)

  • Athanasia Manou

    (University of Athens)

Abstract

The performance analysis of the classical M / G / 1 queue, under a general mixed joining/balking strategy was carried out recently by Kerner (Stoch Mod 24:364–375, 2008), who used an analytic approach based on the supplementary variable method. The tractability of the corresponding queueing system with state-dependent arrival rates is particularly significant, as it has important applications in situations where the customers are strategic. In this paper, we present an alternative path for the analysis of the same system, using purely probabilistic arguments.

Suggested Citation

  • Antonis Economou & Athanasia Manou, 2022. "A probabilistic approach for the analysis of the $$M_n/G/1$$ M n / G / 1 queue," Annals of Operations Research, Springer, vol. 317(1), pages 19-27, October.
    • Handle: RePEc:spr:annopr:v:317:y:2022:i:1:d:10.1007_s10479-015-1943-0
    DOI: 10.1007/s10479-015-1943-0
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    References listed on IDEAS

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    1. Demetrios Fakinos, 1982. "Technical Note—The Expected Remaining Service Time in a Single Server Queue," Operations Research, INFORMS, vol. 30(5), pages 1014-1018, October.
    2. 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.
    3. Hossein Abouee-Mehrizi & Barış Balcıoğlu & Opher Baron, 2012. "Strategies for a Centralized Single Product Multiclass M/G/ 1 Make-to-Stock Queue," Operations Research, INFORMS, vol. 60(4), pages 803-812, August.
    4. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    5. Kerner, Yoav, 2011. "Equilibrium joining probabilities for an M/G/1 queue," Games and Economic Behavior, Elsevier, vol. 71(2), pages 521-526, March.
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