Further results on local stability of REM algorithm with time-varying delays

This letter presents some further results on the local stability in equilibrium for Internet congestion control algorithm proposed by Low et al. (IEEE/ACM Transactions on Networking, 1999). The propagation delay d(t) is assumed to be time-varying and have maximum and minimum delay bounds (i.e. d_m ≤ d(t) ≤ d_M), which is more general than the assumption (0 < d(t) ≤ m) made in Long et al.'s work (IEEE Communications Letters, 2003). It is proved that the stability conditions for the Internet congestion control algorithm obtained in Long et al.'s work are in fact dependent on the delay interval (d_M - d_m). Moreover, some new stability conditions are proposed, which are less conservative than Long et al.'s results. The proposed linear matrix inequality based stability conditions can be solved by using standard numerical software. These stability conditions provide a method for selecting the parameters in REM algorithm that ensure stability.