Some issues in distributed asynchronous routing in virtual circuit data networks

We consider the behavior of distributed asynchronous routing algorithms for optimizing the flows in a virtual circuit data network, with respect to a given convex cost function. The algorithms operate with minimal synchronization of computations and information exchange between different processors and consist of gradient projection iterations which compute a target set of flows for each path. Then, the processors try to make the actual flows equal to the target flows, by appropriately assigning paths to incoming, new virtual circuits. We concentrate on the "many small users" case, in which there is (on the average) a very large number of virtual circuits, each one requiring a small communication rate. This note is a followup to our earlier paper [TsBe] and addresses the limiting behavior when the frequency of iteration becomes infinite relative to the frequency of information exchange between nodes.