On the Connection-Level Stability of Congestion-Controlled Communication Networks

In this paper, we are interested in the connection-level stability of a network employing congestion control. In particular, we study how the stability region of the network (i.e., the set of offered loads for which the number of active users in the network remains finite) is affected by congestion control. Previous works in the literature typically adopt a time-scale separation assumption, which assumes that, whenever the number of users in the system changes, the data rates of the users are adjusted instantaneously to the optimal and fair rate allocation. Under this assumption, it has been shown that such rate assignment policies can achieve the largest possible stability region. In this paper, this time-scale separation assumption is removed and it is shown that the largest possible stability region can still be achieved by a large class of control algorithms. A second assumption often made in prior work is that the packets of a source (or user) are offered to each link along its path instantaneously, rather than passing through one queue at a time. We show that connection-level stability is again maintained when this assumption is removed, provided that a back-pressure scheduling algorithm is used jointly with the appropriate congestion controller.