Short Queue Behavior and Rate Based Marking

摘要

Differential equation models for Internet congestionrncontrol algorithms have been widely used to understand networkrndynamics and the design of router algorithms. These modelsrnuse a fluid approximation for user data traffic, and describernthe dynamics of the router queue and user adaptation throughrncoupled differential equations.rnIn this paper, we show that the randomness due to short andrnunresponsive flows in the Internet is sufficient to decouple therndynamics of the router queues from those of the end controllers.rnWe show that this implies that a time-scale decompositionrnnaturally occurs such that the dynamics of the router manifestrnonly through their statistical steady-state behavior.rnThe interaction between the routers and flows occur throughrnmarking, where routers indicate congestion by appropriatelyrnmarking packets during congestion. In this paper, we show thatrnthe time-scale decomposition implies that a queue-length basedrnmarking function such as Random Early Detection (RED) orrnRandom Exponential Marking (REM) have an equivalent formrnwhich depend only on the data arrival rate from the end-systemsrnand do not depend on the queue dynamics. This leads to muchrnsimpler dynamics of the differential equation models (there is nornqueueing dynamics to consider), which enables easier simulationrn(the state space is reduced) and analysis. We finally validate ourrnanalysis through simulation.