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arXiv · 2509.14100

On the overlap times in queues with dependence under a Farlie-Gumbel-Morgenstern copula

Ioannis Dimitriou
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Abstract

In this work, we analyze the steady-state maximum overlap time distribution in a single-server queue by introducing a dependence structure between service and interarrival times under the Farlie-Gumber-Morgenstern copula. We provide explicit expressions by indicating the effect of dependence. We also focus on the steady-state distribution of the minimum overlap time of a customer with its two adjacent customers. A more general dependence structure is also investigated. A numerical example illustrates the effect of dependence on the maximum/minimum overlap times.

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Ioannis Dimitriou. 2025-09-17. On the overlap times in queues with dependence under a Farlie-Gumbel-Morgenstern copula. https://arxiv.org/abs/2509.14100

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