Stability for Network Flow Control against Disturbances and Time Delays

New stability results are presented for Kelly’s algorithm for network traffic control. These are applicable to a broad class of algorithms including most of those previously discussed in the literature. Three types of results are derived; an asymptotic stability result for networks with external disturbances but without time delays, an asymptotic stability result for a class of algorithms with a linear cost with both external disturbances and time-delays, and a gain stability result for more general algorithms with both disturbances and time-delays. The time-delay results are obtained using a gap metric approach.