A multiclass feedback queueing network with a regular Skorokhod Problem

We consider a four-class two-station network with feedback, with fluid inpu ts and a head-of-the-line generalized processor sharing discipline at each station. We derive the Skorokhod Problem associated with the network and ob tain algebraic sufficient conditions for Lipschitz continuity of the associ ated Skorokhod Map. This provides the first example of a multiclass network with feedback for which the associated Skorokhod Problem has been proved t o be regular. As an elementary application, we show that under the conditio ns which guarantee Lipschitz continuity the network is stable if and only i f the usual load conditions apply.