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

• Published in: IEEE communications letters Vol. 9; no. 5; pp. 402 - 404
• Main Authors: Huijun Gao, Lam, J., Changhong Wang, Xinping Guan
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; Communication system control; Delay effects; Exact sciences and technology; Internet; IP networks; Linear matrix inequalities; Loss measurement; Propagation delay; Protocols; Software standards; Stability; Systems, networks and services of telecommunications; Telecommunications; Telecommunications and information theory; Teleprocessing networks. Isdn; Teletraffic; Valuation and optimization of characteristics. Simulation; Stability; local stability; Congestion control algorithm; Teletraffic; time-varying propagation delay; Time varying system; Computer network; Linear matrix inequality; Traffic control; Delay time; Internet; REM; Traffic congestion
• ISSN: 1089-7798; 1558-2558
• DOI: 10.1109/LCOMM.2005.1431152

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/sub m//spl les/d(t)/spl les/d/sub M/), which is more general than the assumption (0<d(t)/spl les/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/sub M/-d/sub 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.