On the overlap times in queues with dependence under a Farlie-Gumbel-Morgenstern copula
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908544377290752 |
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| author | Dimitriou, Ioannis |
| author_facet | Dimitriou, Ioannis |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_14100 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the overlap times in queues with dependence under a Farlie-Gumbel-Morgenstern copula Dimitriou, Ioannis Probability 60K25, 90B22 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. |
| title | On the overlap times in queues with dependence under a Farlie-Gumbel-Morgenstern copula |
| topic | Probability 60K25, 90B22 |
| url | https://arxiv.org/abs/2509.14100 |