Stability conditions of the $N$-model with a waiting time dependent threshold on the diagonal
Probability
2025-11-17 v1
Abstract
We consider the -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.
Keywords
Cite
@article{arxiv.2511.11488,
title = {Stability conditions of the $N$-model with a waiting time dependent threshold on the diagonal},
author = {Sanne van Kempen and Elene Anton and Fiona Sloothaak},
journal= {arXiv preprint arXiv:2511.11488},
year = {2025}
}