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

Onno Boxma () and Jamol Pender ()
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Onno Boxma: Eindhoven University of Technology
Jamol Pender: Cornell University

Queueing Systems: Theory and Applications, 2025, vol. 109, issue 1, No 10, 20 pages

Abstract: 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.

Keywords: G/G/1 queue; maximum overlap time; minimum overlap time; 60K25; 90B22 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11134-025-09938-1

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