Global stability with time-delay in network congestion control

This paper concerns the global stability of recently proposed laws for network congestion control. In earlier work it was shown that such laws were able to maintain local dynamic stability on networks of arbitrary delay, capacity and topology. In this paper we give conditions under which the stability can be shown to be global, focusing on the case of a single bottleneck network. The results include: a general boundedness result; a theorem on global asymptotic stability for the case of a single source, or many homogeneous ones, under quite sharp conditions; an a somewhat weaker asymptotic stability theorem for the heterogeneous source case.