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Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers

Author

Listed:
  • Yoshiaki Inoue

    (Osaka University)

  • Onno Boxma

    (Eindhoven University of Technology)

  • David Perry

    (Haifa University
    Western Galilee College)

  • Shelley Zacks

    (Binghamton University)

Abstract

This paper considers a batch arrival $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queue with impatient customers. We consider two different model variants. In the first variant, customers in the same batch are assumed to have the same patience time, and patience times associated with batches are i.i.d. according to a general distribution. In the second variant, patience times of customers in the same batch are independent, and they follow a general distribution. Both variants are related to an M/G/1 queue in which the service time of a customer depends on its waiting time. Our main focus is on the virtual and actual waiting times, and on the loss probability of customers.

Suggested Citation

  • Yoshiaki Inoue & Onno Boxma & David Perry & Shelley Zacks, 2018. "Analysis of $$\hbox {M}^{\mathrm {x}}/\hbox {G}/1$$ M x / G / 1 queues with impatient customers," Queueing Systems: Theory and Applications, Springer, vol. 89(3), pages 303-350, August.
    • Handle: RePEc:spr:queues:v:89:y:2018:i:3:d:10.1007_s11134-017-9565-7
    DOI: 10.1007/s11134-017-9565-7
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    References listed on IDEAS

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