Summary: A Singular Perturbation Approach to
Analysing a RED queue
Eitan Altman, K. Avrachenkov and B. J. Prabhu
06902 Sophia-Antipolis, France
Several Active Queue Management (AQM) techniques for routers in the Internet have been proposed
and studied during the past few years. One of the widely studied proposals, Random Early Detection (RED),
involves dropping an incoming packet with some probability based on the estimated average queue length
at the router. The analytical approaches to obtaining average drop probabilities in a RED enabled queue
have been either based on using the instantaneous queue size for calculating the drop probability or have
considered averaging with a fluid approximation. In this paper, we use a singular perturbation based approach
to analyse a RED enabled queue with drop probabilities based on the estimated average queue size as has
been proposed in the standard RED. The singular perturbation approach is motivated by the fact that the
instantaneous and the estimated average queue lengths evolve at two different time scales. We present an
analytical method to calculate the average queue size and the average drop probability for the non responsive
flows. We also provide analytical expressions for the Poisson arrivals and exponential service times case.
Our model is derived under several approximations, and is validated through simulations.
Key words - Singular perturbation, RED.