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

Sergio Palomo and Jamol Pender

Statistics & Probability Letters, 2025, vol. 219, issue C

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.

Keywords: Overlap time; Maximum overlap times (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.spl.2024.110322

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