Fluid models have become a standard tool for demonstrating stability for queueing networks. It is presently not known, however, when the stability of a fluid model follows from that of the corresponding queueing network. We present an example of a queueing network where such stability does not, in fact, follow. This example also shows that the behavior of the fluid limits and the fluid model solutions for the same queueing network can differ considerably from one another.
"A stable queueing network with unstable fluid model." Ann. Appl. Probab. 9 (3) 818 - 853, August 1999. https://doi.org/10.1214/aoap/1029962815