Stability conditions of the $N$-model with a waiting time dependent threshold on the diagonal
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911266127216640 |
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| author | van Kempen, Sanne Anton, Elene Sloothaak, Fiona |
| author_facet | van Kempen, Sanne Anton, Elene Sloothaak, Fiona |
| contents | We consider the $N$-model queueing system with a waiting time dependent threshold on the diagonal: the service discipline is First--Come--First--Served, but type-1 jobs can only be served by server 2 if their waiting time exceeds a deterministic threshold. We prove the necessary and sufficient stability conditions for this model -- an intuitive result that has not been established in literature up to this point. Our proof relies on coupling the queue length process to a carefully constructed upper (and lower) bound system, and establishing stochastic dominance for the queue length process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_11488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability conditions of the $N$-model with a waiting time dependent threshold on the diagonal van Kempen, Sanne Anton, Elene Sloothaak, Fiona Probability We consider the $N$-model queueing system with a waiting time dependent threshold on the diagonal: the service discipline is First--Come--First--Served, but type-1 jobs can only be served by server 2 if their waiting time exceeds a deterministic threshold. We prove the necessary and sufficient stability conditions for this model -- an intuitive result that has not been established in literature up to this point. Our proof relies on coupling the queue length process to a carefully constructed upper (and lower) bound system, and establishing stochastic dominance for the queue length process. |
| title | Stability conditions of the $N$-model with a waiting time dependent threshold on the diagonal |
| topic | Probability |
| url | https://arxiv.org/abs/2511.11488 |