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The maximum overlap time in the M/M/1 queue

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  • Palomo, Sergio
  • Pender, Jamol

Abstract

In this paper, we analyze the steady state maximum overlap time in the M/M/1 queue. We derive the maximum overlap time tail distribution, its moments and the moment generating function. We also analyze the steady state minimum overlap time of the adjacent customers and compute its moments and moment generating function. Our results provide new insight on how customers become infected in the M/M/1 queue.

Suggested Citation

  • Palomo, Sergio & Pender, Jamol, 2025. "The maximum overlap time in the M/M/1 queue," Statistics & Probability Letters, Elsevier, vol. 219(C).
    • Handle: RePEc:eee:stapro:v:219:y:2025:i:c:s0167715224002918
    DOI: 10.1016/j.spl.2024.110322
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    References listed on IDEAS

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    1. Mohammad Delasay & Aditya Jain & Subodha Kumar, 2022. "Impacts of the COVID‐19 pandemic on grocery retail operations: An analytical model," Production and Operations Management, Production and Operations Management Society, vol. 31(5), pages 2237-2255, May.
    2. Refael Hassin & Isaac Meilijson & Yael Perlman, 2023. "Queueing with Negative Network Effects," Manufacturing & Service Operations Management, INFORMS, vol. 25(5), pages 1984-1998, September.
    3. Kang Kang & Sherwin Doroudi & Mohammad Delasay & Alexander Wickeham, 2023. "A queueing‐theoretic framework for evaluating transmission risks in service facilities during a pandemic," Production and Operations Management, Production and Operations Management Society, vol. 32(5), pages 1453-1470, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Overlap time; Maximum overlap times;

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