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

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.