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Overlap times in the G/G/1 queue via Laplace transforms

Author

Listed:
  • Onno Boxma

    (Eindhoven University of Technology)

  • Jamol Pender

    (Cornell University)

Abstract

In this paper, we analyze the steady-state maximum overlap time distribution in the G/G/1 queue. Our methodology exploits Laplace-Stieltjes transforms with a novel decomposition of the maximum overlap time. Explicit expressions are provided for the special cases of the M/G/1 and G/M/1 queues. We also study the steady-state distribution of the minimum overlap time of a customer with its two adjacent customers. We show a novel relationship between the minimum, maximum and the steady-state waiting time.

Suggested Citation

  • Onno Boxma & Jamol Pender, 2025. "Overlap times in the G/G/1 queue via Laplace transforms," Queueing Systems: Theory and Applications, Springer, vol. 109(1), pages 1-20, March.
    • Handle: RePEc:spr:queues:v:109:y:2025:i:1:d:10.1007_s11134-025-09938-1
    DOI: 10.1007/s11134-025-09938-1
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    References listed on IDEAS

    as
    1. Avi Mandelbaum & William A. Massey, 1995. "Strong Approximations for Time-Dependent Queues," Mathematics of Operations Research, INFORMS, vol. 20(1), pages 33-64, February.
    2. William A. Massey, 1985. "Asymptotic Analysis of the Time Dependent M/M/1 Queue," Mathematics of Operations Research, INFORMS, vol. 10(2), pages 305-327, May.
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