On the Elasticity of Marking Functions: Scheduling, Stability, and Quality-of-Service in the Internet
Yung Yi, Sanjay Shakkottai · 2005
Much of the research on Internet modeling and analysis has focused on the design of end controllers and network algorithms with the objective of stability and convergence of the transmission rate. However, the Internet is composed of a mix- ture of both (controlled) elastic flows and (uncontrolled) real-time flows. Uncontrolled real-time flows do not react to network con- gestion as well as they require a certain level of QoS guarantees. In this paper, we study the effects of marking elasticity (which characterizes how quickly the marking level changes during tran- sients) on the QoS for uncontrolled real-time flows, at a router accessed by both uncontrolled real-time and controlled flows. First, we derive lower and upper bounds on the queue over- flow probability at a router of a single bottleneck system. Using this, we quantify the trade-off between stability for controlled flows and QoS guarantee for uncontrolled real-time flows as a function of marking elasticity. The results indicate that some marking functions may be uniformly better than others. In particular, among the marking functions that we have compared, our bounds indicate that a rate based version of REM seems to provide the largest local-stability region for any given QoS re- quirement. Next, as a function of the marking function elasticity, we quan- tify the excess capacity required at the router with FIFO schedul- ing that results in the same queue overflow probability if priority scheduling was used instead. We show that the difference in the required capacities with FIFO and priority queueing decreases with more elastic marking functions. In other words, the gains due to scheduling decreases with increasing marking elasticity.