On Designing Improved Controllers for AQIMRouters Supporting TCP FlowsC.V. Hollot, Vishal Misra, Don Towsley and Wei-Bo GongAbstract— In this paper we study a previously developed linearizedmodel of TCP and AQM. We use classical control system techniques to de-velop controllers weU suited for the application. The controllers are shownto have better theoretical properties than the wetll known RED controller.We present gnidetines for designing stable controllers subject to networkparameters tike load level, propagation delay etc. We also present simpleimplementation techniques wtdch require a minimal change to RED imple-mentations. The performance of the controllers are verified and comparedwith RED using ns simulations, The second ofour designs,the Propor-tional Integral (Pi) controller isshown to outperform RED significantly.I. INTRODUCTIONActive Queue Management (AQM) is a very active researcharea in networking. Specifically, the RED [1] variant of AQMhas generated a lot of research and interest in the community.Understanding the behavior of RED has largely remained a“simulate and observe” exercise, and tuning ofRED has provento be a difficult job. Numerous variants of RED have been pro-posed [2], [3], [4], [5] to work around some of the performanceproblems obvserved with RED. In [6], we performed a controltheoretic analysis of a linearized model of TCP and RED. Theanalysis enabled us to present design guidelines for RED, whichwe verified via simulations using ns -2 [7]. Our investigationsrevealed two limitations of RED. The first limitation deals withthe tradeoff between speed of response and stability. A designthat is fast in its response time, was found to have relatively lowstability margins, while a design that is stable exhibits sluggishresponses. The other limitation of RED is the direct coupling be-tween queue length and loss probability. The steady state queuelength in RED is dependent on the load level. Hence, for anoverloaded system, the flows pay a double penalty of higher de-lay as well as higher loss. The two can be easily decoupled.In this paper we apply classical control system techniques todesign controllers that are better suited for AQM than RED. Wecome up with two simple designs, namely the Proportional andthe Proportional-Integral (PI) controller. We present guidelinesto design these stable linear controllers. ‘We veri$ our guide-lines through non-linear simulations using ns. We also presentguidelines for a simple implementation of the PI filter in a REDcapable router or simulator. The PI controller is shown via sim-Thk work is supported in part by the National :Science FoundationunderGrants ANI-9873328 and by DARPA under Contract DOD F30602-OO-0554.C.V. Hollot and Wei-Bo Gong are with the ECE Department, University ofMassachusetts, Amherst, MAO 1003; {hollot,gong}@ees. umass.eduVishal Misra and Don Towsley are with the Computer ScienceDepartment, University of Massachusetts,Amherst,MA 01003;{misra,towsley} @cs.umass.eduulations to be a robust controller that outperforms tlhe RED con-troller under almost all scenarios considered.The problem of designing controllers for AQM has also beenapproached from an optimization standpoint in a framework de-fined by Kelly et al. [8]. The problem is formulated as a convexprogram, with the aggregate source utility being maximized sub-ject to capacity constraint. In the primal version of the problem,controllers are designed taking a penalty function approach toobtain opt~al source rates [9], [10]; whereas in a dlual formula-tion [11 ] controllers are designed to obtain optimal congestionmeasures (the dual variables). A virtual buffer technique to-wards the design of controllers is taken in the primal approach,with the basic idea being to mark packets when a virtual buffer(smaller incapacity and service rate than the actual buffer) over-flows. Gibbens and Kelly propose a static virtual buffer config-uration [9], whereas Kunniyur and Srikant [10] use an adap-tive virtual buffer, adapting the size and capacity of the virtualbuffer as a function of the incoming rate to both minimize delayand maximize utilization. Athuraliya and Low [11 jl design con-trollers from the duality standpoint, and we note that one versionof their REM controller is very similar in flavor to the PI con-troller we have proposed. The optimization based approacheslargely lead to steady state equilibria, and don’t concentrate toomuch on the transient performance of the controllers. Our ap-proach, on the other hand, utilizes control theory and we can si-multaneously analyze and design for some desired steady stateas well as transient performance.The rest of the paper is organized as follows. In Section II,we present the linearized control system developed in [6]. Sec-tion III develops the Proportional controller, and presents designguidelines. In Section IV we veriti our design guidelines withsimulations and point out a deficiency of the Proplmtional con-troller. In the next Section we develop the PI controller. Sec-tion VI presents simulations using the PI controller and alsocompares its performance with the RED controll~r. Finally wepresent our conclusions in Section VII.II.BACKGROUNDIn [6], we linearized a non-linear dynamic model forTCP/AQM developed in [12]. The non-linear model is shownin Figure 1, while the linearized model is depictedl in Figure 2,see [6] for linearization details.In the model C(s) is the compensator or controller, andP(s)e–’RO is the “plant” or TCP/AQM system vve are tryingto control.R. is the round trip time, which causes ii delay in the0-7803-7018-8/01/$10.00 (C) 2001 IEEE IEEE INFOCOM 2001bottleneck queue6A\c11aF- E’e ‘‘J W+ N-9J’—1TTCP load factorTutuway1-; ~R%.~—TCP window controlFig. 1. Block-diagram of a TCP connation.feedback of losses. P(s) is given by F’tCP(s)PgtieUe(s) whereP@(s) =g.S+*’we..(s) = +.P(1)s+=withRO ~ round-trip time at the operating pointC ~ link capacity (packetslsec)N + load factor (number of TCP sessions)We refer to the two poles –2N/(R~C) and – ljRo aspt.P andPqueue respectively.The compensator which was studied in [6] was the wellknown RED [1] controller. RED consists of a low-pass fil-ter (LPF) and nonlinear gain map as shown in Figure 3. Theform of the LPF was derived in [12]. The poleK is equal tologe (1 – cr)/6, where o! is the averaging weight and 6 is thesampling frequency. Normally RED updates it’s moving aver-age on every packet arrival, and hence 6
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