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On classes of Bitcoin-inspired infinite-server queueing systems

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  • Brian Fralix

    (Clemson University)

Abstract

We analyze the time-dependent behavior of various types of infinite-server queueing systems, where, within each system we consider, jobs interact with one another in ways that induce batch departures from the system. One example of such a queue was introduced in the recent paper of Frolkova and Mandjes (Stochastic Models, 2019) in order to model a type of one-sided communication between two users in the Bitcoin network: here we show that a time-dependent version of the distributional Little’s law can be used to study the time-dependent behavior of this model, as well as a related model where blocks are communicated to a user at a rate that is allowed to vary with time. We also show that the time-dependent behavior of analogous infinite-server queueing systems with batch arrivals and exponentially distributed services can be analyzed just as thoroughly.

Suggested Citation

  • Brian Fralix, 2020. "On classes of Bitcoin-inspired infinite-server queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 29-52, June.
    • Handle: RePEc:spr:queues:v:95:y:2020:i:1:d:10.1007_s11134-019-09643-w
    DOI: 10.1007/s11134-019-09643-w
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    References listed on IDEAS

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    1. Joseph Abate & Ward Whitt, 1995. "Numerical Inversion of Laplace Transforms of Probability Distributions," INFORMS Journal on Computing, INFORMS, vol. 7(1), pages 36-43, February.
    2. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
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    Cited by:

    1. Rico-Peña, Juan Jesús & Arguedas-Sanz, Raquel & López-Martin, Carmen, 2023. "Models used to characterise blockchain features. A systematic literature review and bibliometric analysis," Technovation, Elsevier, vol. 123(C).

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