Part II: Control Theory for Buffer Sizing
Gaurav Raina
∗
Judge Institute, Cambridge
gr224@cam.ac.uk
Don Towsley
∗
Computer Science, UMass
towsley@cs.umass.edu
Damon Wischik
∗
Computer Science, UCL
D.Wischik@cs.ucl.ac.uk
ABSTRACT
This article describes how control theory has been used to
address the question of how to size the buffers in core In-
ternet routers. Control theory aims to predict whether the
network is stable, i.e. whether TCP flows are desynchro-
nized. If flows are desynchronized then small buffers are
sufficient [14]; the theory here shows that small buffers ac-
tually promote desynchronization—a virtuous circle.
Categories and Subject Descriptors
C.2 [Internetworking]: Routers; C.4 [Performance of
systems]: Modeling techniques
General Terms
Design, Performance, Theory
Keywords
Buffer size, TCP, congestion control, fluid model, control
theory, synchronization
1.
INTRODUCTION
The starting point of control-theoretic analysis is to write
down a set of differential equations for all the rates of all the
flows in a network, and for the drop probabilities at all of
the routers, and then to determine whether this dynamical
system is stable. Stability is simply the control-theoretic
term for desynchronization between TCP flows. The theory
we describe here aims to predict whether and to what extent
there is synchronization.
A network will generally be stable for certain buffer sizes
and unstable for others. We will explain how to choose buffer
sizes to make it stable. Stability is also affected by Active
Queue Management (AQM) parameters, round trip times,
traffic mixes, and the TCP congestion avoidance algorithm
itself. We will go on to describe how certain changes to
TCP’s rules for increasing and decreasing window size make
the entire network less prone to synchronization.
2. FLUID MODEL
We now present differential equations for describing the
network. There is one natural equation for TCP dynamics.
∗Research supported by DARPA, including Buffer Sizing
Grant no. W911NF-05-1-0254. DJW is also supported by