Lp Stability and Delay Robustness of Network Flow Control

This paper studies robustness of Kelly’s source and link control laws in [1] with respect to disturbances and time-delays. This problem is of practical importance because of unmodeled flows, and propagation and queueing delays, which are ubiquitous in networks. We first show Lp-stability, for p ∈ [1,∞], with respect to additive disturbances. We pursue L∞-stability within the input-to-state stability (ISS) framework of Sontag [2], which makes explicit the vanishing effect of initial conditions. Next, using this ISS property and a loop transformation, we prove that global asymptotic stability is preserved for sufficiently small time-delays in forward and return channels. For larger delays, we achieve global asymptotic stability by scaling down the control gains as in Paganini et al. [3].