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Infinite-server systems with Coxian arrivals

Author

Listed:
  • Onno Boxma

    (Eurandom
    Eindhoven University of Technology)

  • Offer Kella

    (The Hebrew University of Jerusalem)

  • Michel Mandjes

    (University of Amsterdam)

Abstract

We consider a network of infinite-server queues where the input process is a Cox process of the following form: The arrival rate is a vector-valued linear transform of a multivariate generalized (i.e., being driven by a subordinator rather than a compound Poisson process) shot-noise process. We first derive some distributional properties of the multivariate generalized shot-noise process. Then these are exploited to obtain the joint transform of the numbers of customers, at various time epochs, in a single infinite-server queue fed by the above-mentioned Cox process. We also obtain transforms pertaining to the joint stationary arrival rate and queue length processes (thus facilitating the analysis of the corresponding departure process), as well as their means and covariance structure. Finally, we extend to the setting of a network of infinite-server queues.

Suggested Citation

  • Onno Boxma & Offer Kella & Michel Mandjes, 2019. "Infinite-server systems with Coxian arrivals," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 233-255, August.
    • Handle: RePEc:spr:queues:v:92:y:2019:i:3:d:10.1007_s11134-019-09613-2
    DOI: 10.1007/s11134-019-09613-2
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    Citations

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    Cited by:

    1. Onno Boxma & Offer Kella & Uri Yechiali, 2021. "Workload distributions in ASIP queueing networks," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 81-100, February.
    2. Yiran Liu & Harsha Honnappa & Samy Tindel & Nung Kwan Yip, 2021. "Infinite server queues in a random fast oscillatory environment," Queueing Systems: Theory and Applications, Springer, vol. 98(1), pages 145-179, June.
    3. Onno Boxma & Michel Mandjes, 2021. "Shot-noise queueing models," Queueing Systems: Theory and Applications, Springer, vol. 99(1), pages 121-159, October.

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