Asymptotic stability of congestion control systems with multiple sources

Congestion in computer networks is the main reason for reduced performance and poor quality of service; therefore, a good congestion control system is essential. The basic property of any control system is stability. We consider the problem of stability in computer network congestion control systems with multiple sources, which is the most common case in general purpose computer networks. The main result of the note is the proof that for congestion control systems with linear controllers (e.g., ATM-ABR), the stability of the congestion control system with a single source is equivalent to the stability of the one with multiple sources. In other words, for the considered congestion control systems, if the system is stable for a single source it will be stable for an arbitrary large number of sources. The proof is based on a well-known necessary and sufficient stability test.