Stability of two families of queueing networks and a discussion of fluid limits

We investigate the stability of two families of queueing networks. The first family consists of a general class of networks, where service is allotted to the lead customer at each buffer. The other generalizes networks considered by Humes [18], and is related to the insertion of "leaky buckets" into the system. The arguments for the stability of the networks in each case rely on the corresponding behavior for the associated fluid models. This connection is employed using the framework established by Dai [10], with some modifications. It is discussed here in a somewhat more general setting, with future applications in mind.