Local stability of random exponential marking

Random exponential marking (REM) is an attractive adaptive queue management algorithm. It uses the quantity known as ´price´ to measure the congestion in a network. REM can achieve high utilisation, small queue length, and low buffer overflow probability. Many works have used control theory to provide the stable condition of REM without considering the feedback delay. Sufficient conditions for local stability of REM have been provided when the sources have a uniform one- or two-step feedback delay. Nevertheless, no work has been done for the case of arbitrary uniform delay. The authors propose a continuous time model to generalise the local stable condition for REM in a multilink and multisource network with arbitrary uniform feedback delay