Short Queue Behavior and Rate Based Marking

Differential equation models for Internet congestion control algorithms have been widely used to understand network dynamics and the design of router algorithms. These models use a fluid approximation for user data traffic, and describe the dynamics of the router queue and user adaptation through coupled differential equations. In this paper, we show that the randomness due to short and unresponsive flows in the Internet is sufficient to decouple the dynamics of the router queues from those of the end controllers. We show that this implies that a time-scale decomposition naturally occurs such that the dynamics of the router manifest only through their statistical steady-state behavior. The interaction between the routers and flows occur through marking, where routers indicate congestion by appropriately marking packets during congestion. In this paper, we show that the time-scale decomposition implies that a queue-length based marking function such as Random Early Detection (RED) or Random Exponential Marking (REM) have an equivalent form which depend only on the data arrival rate from the end-systems and do not depend on the queue dynamics. This leads to much simpler dynamics of the differential equation models (there is no queueing dynamics to consider), which enables easier simulation (the state space is reduced) and analysis. We finally validate our analysis through simulation.