Oscillations with TCP-like Flow Control in Networks of Queues

We consider a set of flows passing through a set of servers. The injection rate into each flow is governed by a flow control that increases the injection rate when all the servers on the flow's path are empty and decreases the injection rate when some server is congested. We show that if each server's congestion is governed by the arriving traffic at the server then the system can *oscillate*. This is in contrast to previous work on flow control where congestion was modeled as a function of the flow injection rates and the system was shown to converge to a steady state that maximizes an overall network utility.