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Remaining Loads in a PH/M/c Queue with Impatient Customers

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  • Anders Rygh Swensen

    (University of Oslo)

Abstract

There are three contributions to the literature in this note. Firstly, we point out that under some weak conditions the result in Swensen (1986) on the remaining loads in a GI/M/c queue with impatient customers, derived under the assumption that the distribution of inter-arrival times is Coxian, is also valid for the more general phase type distribution. From this result the distributions of the virtual and the actual waiting time can easily be obtained. Secondly, the relation to an alternative expression for the distribution of the virtual waiting time derived by Kawanishi and Takine (2015) is also clarified. Finally, we explain how the results on the remaining loads can be used to find distributions describing particular fixed servers and provide a couple of numerical examples of how this can be done.

Suggested Citation

  • Anders Rygh Swensen, 2023. "Remaining Loads in a PH/M/c Queue with Impatient Customers," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-15, March.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:1:d:10.1007_s11009-023-10019-0
    DOI: 10.1007/s11009-023-10019-0
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    References listed on IDEAS

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    1. Bong Dae Choi & Bara Kim & Dongbi Zhu, 2004. "MAP/M/c Queue with Constant Impatient Time," Mathematics of Operations Research, INFORMS, vol. 29(2), pages 309-325, May.
    2. D. Perry & W. Stadje, 2022. "Perishable inventories and queues with impatience," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 237-239, April.
    3. Ken’ichi Kawanishi & Tetsuya Takine, 2016. "MAP/M/c and M/PH/c queues with constant impatience times," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 381-420, April.
    4. Avishai Mandelbaum & Sergey Zeltyn, 2009. "Staffing Many-Server Queues with Impatient Customers: Constraint Satisfaction in Call Centers," Operations Research, INFORMS, vol. 57(5), pages 1189-1205, October.
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    Cited by:

    1. Sergei Dudin & Olga Dudina, 2023. "Analysis of a Multi-Server Queue with Group Service and Service Time Dependent on the Size of a Group as a Model of a Delivery System," Mathematics, MDPI, vol. 11(22), pages 1-20, November.
    2. Ciro D’Apice & Maria Pia D’Arienzo & Alexander Dudin & Rosanna Manzo, 2023. "Optimal Hysteresis Control via a Queuing System with Two Heterogeneous Energy-Consuming Servers," Mathematics, MDPI, vol. 11(21), pages 1-34, November.

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