UC San Diego

We consider a model of Internet congestion control, introduced by Massoulié and Roberts, as an example of a stochastic network with resource sharing and a non-head-of -the-line service discipline. To describe the evolution of this system, we use a stochastic process that tracks the amount of service that has been given to each document that is still in the system and the time since the last arrival to each route. This is a Borel right process with a locally compact with countable base state space. It is shown that under mild assumptions, stability of a related fluid model for residual document sizes is sufficient for stability (positive Harris recurrence) of the Borel right process