This paper investigates the stability of the primal-dual algorithm for Internet congestion control in the presence of heterogeneous round-trip communication delays. Based on the geometric analysis of frequency response functions of the congestion control system, some sufficient conditions for the local asymptotic stability of the primal-dual algorithm are established. Compared to the existing references, the main contribution of this paper is that in addition to the new sufficient conditions it also obtains some scalability conditions under which the decentralized stability criteria hold for the primal-dual algorithm.
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