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An ASIP model with general gate opening intervals

Author

Listed:
  • Onno Boxma

    (Eindhoven University of Technology)

  • Offer Kella

    (The Hebrew University of Jerusalem)

  • Uri Yechiali

    (Tel Aviv University)

Abstract

We consider an asymmetric inclusion process, which can also be viewed as a model of n queues in series. Each queue has a gate behind it, which can be seen as a server. When a gate opens, all customers in the corresponding queue instantaneously move to the next queue and form a cluster with the customers there. When the nth gate opens, all customers in the nth site leave the system. For the case where the gate openings are determined by a Markov renewal process, and for a quite general arrival process of customers at the various queues during intervals between successive gate openings, we obtain the following results: (i) steady-state distribution of the total number of customers in the first k queues, $$k=1,\dots ,n$$ k = 1 , ⋯ , n ; (ii) steady-state joint queue length distributions for the two-queue case. In addition to the case that the numbers of arrivals in successive gate opening intervals are independent, we also obtain explicit results for a two-queue model with renewal arrivals.

Suggested Citation

  • Onno Boxma & Offer Kella & Uri Yechiali, 2016. "An ASIP model with general gate opening intervals," Queueing Systems: Theory and Applications, Springer, vol. 84(1), pages 1-20, October.
    • Handle: RePEc:spr:queues:v:84:y:2016:i:1:d:10.1007_s11134-016-9492-z
    DOI: 10.1007/s11134-016-9492-z
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    References listed on IDEAS

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    1. Satoru Fujishige & Naoki Katoh & Tetsuo Ichimori, 1988. "The Fair Resource Allocation Problem with Submodular Constraints," Mathematics of Operations Research, INFORMS, vol. 13(1), pages 164-173, February.
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    Cited by:

    1. Ivo Adan & Onno Boxma & Jacques Resing, 2022. "Functional equations with multiple recursive terms," Queueing Systems: Theory and Applications, Springer, vol. 102(1), pages 7-23, October.
    2. Yaron Yeger & Uri Yechiali, 2022. "Performance Measures in a Generalized Asymmetric Simple Inclusion Process," Mathematics, MDPI, vol. 10(4), pages 1-25, February.
    3. 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.
    4. Uri Yechiali & Yaron Yeger, 2022. "Matrix Approach for Analyzing n -Site Generalized ASIP Systems: PGF and Site Occupancy Probabilities," Mathematics, MDPI, vol. 10(23), pages 1-33, December.

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