We propose a new class of models of queueing networks with load-balanced dynamic routing. The paper extends earlier works, including [FC], [FMcD], [VDK], where systems with no feedback were considered. The main results are: (a) a sufficient condition for positive recurrence of the arising Markov process and (b) a limiting mean-field picture where the process becomes deterministic and is described by a system of non-linear ODEs
