RED PERFORMANCE EVALUATION USING STOCHASTIC MODELLINGANDFLUID-BASED ANALYSIS

Hussein Al-Zubaidy and Tariq OmarlDepartment ofSystems and Computer Engineering, Carleton University,

1125 Colonel By Drive, Ottawa, Canada KIS 5B6{hussein, tomari} @sce.carleton.ca

AbstractRandom Early Detection (RED) is a powerful mechanism

used for queue management. Many studies showed that REDhas advantages over Tail Drop (TD). However, most of thesestudies were based on simulation and does not reflect aconclusive performance evaluation of RED. The needfor ananalytical evaluation that allows better understanding ofREDwas addressed by several researchers. The result was severalapproaches, each partially characterizes RED performance.This work aims to provide a better understanding of the REDalgorithm and to quantify the benefits and limitations of usingRED queue management by using two analytic models,namely. stochastic-based model, using queuing theory andstochastic modeling and fluid-based model, using stochasticdiferential equations. The fluid-based model was modified toincorporate smooth nonconforming traffic (e.g. UDP) as wellas TCP. The model was verified using simulation results.

Our analysis showed that RED outperforms TD most ofthetime. The stochastic based model showed that RED removesthe bias against bursty traffic and helps control the queue sizeand the delay. On the other hand, it increases the variability ofthe queue size and hence the jitter. The results showed thatRED queue can handle the added UDP traffic whilemaintaining its normal operation to some extent. However, theincrease in the UDP traffic share created oscillation in thequeue size and resulted in instability. When the UDP trafficreached 500 of the total capacity the queue starts oscillatingwildly which can cause buffer overflow andjitter. The effect ofthe UDPportion ofthe overall link capacity on the TCP trafficin the RED queue where studied It seems that a high UDP ratewill not starve the TCP traffic under RED. Another observationwas that for higher link capacities the RED performancebecomes highly dependent on the sampling rate (a). Simulationconfirms the above conclusions and matches well with thefindings obtainedfrom analysis.

1. Introduction

Buffers play an important role in today's computernetworks. The existence of buffers created queues that mightcause queuing delay throughout the network. The traditionaltechnique for managing queues is to accept packets while themaximum length is not reached, and drop all packets thatarrive while the queue is full. This technique is called TailDrop (TD). Active queue management (AQM) was proposedto replace the previous TD scheme and improve IP networksperformance. It allows the network to actively control thevolume of traffic forwarded rather than relying on the sources

to do that.Internet uses end-to-end control mechanism to regulate the

traffic passing through the network so as not to exceed the

1-4244-0038-4 2006 14IEEE CCECE/CCGEI, Ottawa, May 2006

available network capacity. This will insure that queues lengthsand loss rates remain reasonable. The most widely deployedcontrol mechanism is the window-based TCP [5, 6]. TCP tendsto keep high queue occupancy and results in discriminationagainst bursty traffic. Another problem is that TCP traffic isbursty in nature, and a drop event will most likely involveseveral packets resulting in the global synchronization problem[7]. The result is reduced throughputs and underutilizedrouters' resources. Finally, the TCP traffic has to share thenetwork resources with other kinds of traffic, which are notnecessarily responsive, i.e., they are not willing to use a controlmechanism, such as UDP traffic. In this case, the UDP sourcewill continue sending packets on the same rate whether there iscongestion or not. While the TCP flows back off, the UDPflows take over which results in unfairness to the TCP traffic.RED, proposed by S. Floyd [3] and recommended by IRTF

document RFC2309 [8], was introduced to alleviate some ofthe above network inefficiencies. The main idea is to startdropping packets randomly before the buffer gets full. Thiswill force the connections to back off before the buffers getfilled and multiple drops occur. Unresponsive flows that keepsending at the same rate will suffer higher loss rates.

In this paper, two analytic approaches, namely stochasticmodeling and fluid-based analysis, and simulation were used toanalyze RED performance. The three approaches were used tocomplement each other and to provide confidence in the resultsobtained. The rest of the paper is organized as follows: section2 introduces the RED queue management algorithm. Section 3defines the two models used for analysis and the simulationsetup. Section 4 presents and discusses the results, and section5 concludes our findings.

2. RED Queue Management SchemeRED congestion control mechanism monitors the average

queue size and randomly chooses connections to be notified ofthat congestion. A temporary queue occupancy increasereflects a transient congestion, while long lasted congestion isreflected by an increase in the average queue length. Theprobability of a connection to be notified is proportional to thatconnection's share of the router's total capacity.The average queue size is estimated using an exponential

weighted moving average, as follows:I I

k - (1-oa)k+ k (1)

Where k is the instantaneous queue size, kis the average

113

queue length estimate and a is a fixed weight factor. Thedropping probability is given as a function of three parametersminh, max,h, and maxp as shown in (2) and Figure 1.

I

d(k):

The queue occupancy defines a Markov chain that has astationary distribution (7t) that can easily be computed. Thestationary distribution is given by equations (3) and (4) for TailDrop and RED respectively.

p k(1 P)(2) 1rTD (k) =I - K+p);1'-p

I

k -minthkxmaxp, otherwise

maxth - minth

V k = O,...,K

p H1 (1 - d(l)) ;V k O,KFRED (A) K k k-1

k p H' (1 - d (1))k=O /=0

(3)

(4)

Where, K is the maximum queue size. Using PASTA property,the drop probability of a packet in a TD queue is given by:

PTD fTD(K)+fTD(K I)jP(B=i) Ji +- * +TD(K-(S-1))

minth maxth

Figure 1. RED drop function as a function of k.

3. RED Analysis

Most of the previous studies agreed that the RED schemehas its advantages over the other previous queue managementschemes [2,3,9]. In order to quantify these benefits, an analyticevaluation is needed. Furthermore, the RED performance gaincan be achieved only when its parameters are tuned.Simulation can provide general guidelines to tune theseparameters but optimal parameters can only be achieved byderiving analytic understanding for RED scheme.

In this work, two analytic approaches were used to analyzeRED performance. The first approach was presented in [1] andit is based on queuing theory and stochastic modeling of REDqueue. We extended the model to incorporate a random burstsize with any given distribution. The second approach is thefluid-based model. In this approach a jump process drivenstochastic differential equations is used to model theinteraction of a set ofTCP flows and RED routers in a networksetting [2]. We derived an extended fluid-based model basedon [2] that handles both TCP and UDP traffic in order to studythe effect of the UDP on TCP performance in a RED queue.

3.1. Stochastic-Based Approach

Following the approach in [1], the router is modeled by asimple queue with a single input stream of bursty traffic. Thepackets arrival process is modeled as a batch Poisson process.We modified the model to support bursty traffic with randomburst size (B) that can have any distribution. Throughout thiswork we assume it is uniformly distributed (i.e., U(1,S)). Thepacket processing time is assumed to be exponentiallydistributed with average 1/[t. The offered load p = E(B) x X / t.

S-1Z zTD (K10o

For B = U(1,S), eq. (5) reduces to:

The drop probability of a packet in a RED router can beapproximated by:

Equation (7) above obtained under the assumption that d(k)is the same for all packets in the same burst [1].To study the effect of nonconforming traffic on dropping

probability for both TD and RED queues, a combination ofsmooth (Poisson process) and bursty traffic (as describedabove) is used as an input to the queue under investigation. Thetotal offered load is given by P=Ps+Pb, and the burst rate6b=Pb/P. Where, Ps and Pb are the smooth and bursty offeredloads respectively. The TD packet drop probability then isgiven by:

(8)PTD = 8b PTD (bursty) + (1- 5b*)PTD (smooth)

Where PTD(smooth)= 2TD(K) and PTD(bursty) is given by (6).The RED on the other hand, has equal packet drop

probability for both smooth and bursty traffic. This suggeststhat RED has no bias against bursty traffic.

KPRED (bursty) = YfFRED (k)d(k) = PRED (smooth) (9)

k=i

RED claimed to solve global synchronization of TCP flows.In order to be able to determine the validity of this claim, weexamine the impact of RED on the distribution of the number

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A

d(k)

max,s

1) Z P(B1=J+l I -J (5)

I S-1 SPTD j-O i= 1TD (K]=j+L

I). (6)

KPRED = 'FRED (k) d(k)

k=i(7)

of consecutive drops (N). This distribution is given byequations (10) and (1 1) for TD and RED [1].

P(NTD > n) = pn;where, =

P(NRED > n)

A p

A+jt p+l

I- (zrRED ( k)d (k ))K-1

FTRED (k)d(k)k=O

(10)

(1 1)

Analytic evaluation:MathCAD was used to evaluate the above model to examine

RED performance and compare it to the TD case. Theparameters used for this evaluation are as follows: buffer size(K) is 100 packets, the burst size is uniformly distributed from1 to S, where S =10. RED thresholds are: minlh 30, maxth80,maxp 0.1, and o 0.0002. Figures 2 through 4 summarizethe results

Figure 2 illustrates the behavior of the TD and RED queues

for different 6b. The drop probability of the bursty traffic ishigher than that of smooth traffic in TD queue, which is not thecase with RED queue. RED achieves a noticeable decrease inthe drop probability for bursty traffic to achieve fairness. Whenthe fraction of the bursty traffic increases, the RED stillachieves fairness not by decreasing the drop probability forbursty traffic, as in the first case, but by increasing the dropprobability for the smooth traffic.

The distribution of the number of consecutive drops in TDand RED for p =2 is shown in Figure 3. The Figure shows thatthe TD is more probably drops large bursts of consecutivepackets than RED. This suggests that RED is more capable ofreducing the global synchronization effect. This will enhancenetwork throughput and result in better resources utilization.RED does that by randomly choosing the connections to benotified about the congestion and always ensures enoughbuffer space to accommodate bursts of traffic.

0.(

0.4

0.'

0 0.5 1

Offered Load1.5 2

K REDf+ -+ Tail Drop (10% Bursty traffic)B Tail Drop (50% Bursty)- - Tail Drop (90 % Bursty )

Figure 2. Drop probability vs. offered load

The queue size distribution for both RED and TD is shown

in Figure 4. For RED, the queue size, and hence the queuingdelay reduced significantly (compared to TD), and can be

AT

controlled by adjusting maxth, however, this is done at theexpense of increasing the delay variance. As a result, REDproduces higher delay jitter.

number ofconsecutive drops (n)Tail DropRED

Figure 3. Distribution of the number of consecutive drops, p=2.

0.4

pi(k)

0.2-

00 20 40 60 80 100

Queue sizeTail Drop

RED

Figure 4. Queue size distribution for an offered load p=2.

3.2. Fluid-Based Analysis

A router with M TCP input flows is modeled by a system ofM+2 differential equations that can be solved numerically. Thewindow size W- of TCP flow i is given by (12).

dWi 1 _ WiWi(t -) p(x(t-,))dt Ri (q ) 2Ri (q (t - ))

(12)

The estimated average queue size is given by (13). It isassumed to be an exponentially weighted moving average withsamples taken every A seconds and weight a. For completederivation, the reader may refer to [2,4].

dx= ln(1 - a) -

dt A

ln(1-a)-A qf(t)

(13)

We modified this model to incorporate UDP as well as TCPflows. Since the UDP flow is smooth in nature, and it has no

end-to-end flow control mechanism, it can be modeled as a

random process with average arrival (X). The UDP traffic willbe dropped by the RED queue according to the dropprobabilityp(x). The UDP contribution to the queue size willbe A- (I -p(x)). The resultant queue size is given by equation(14) below.

1415

~~~~~~~~,/ +

2

n

0.

;^

P.

$,~0

dt + L-c + +2AUDP * (1- p(X)) ... (14)dt R(q) UD

Where w (t) is the dynamic window size for flow i, q(t) isthe average queue size, and x(t) is the estimated averagequeue size. p(x) is the RED dropping probability, XUDP is theaverage arrival rate for the smooth UDP traffic. C is therouter's capacity. The TCP throughput O = Wi/ R-. The roundtrip time (Ri) is a function of the queue size and is given by:

Ri(q(t)) = a- + q(t)/C, for t > 0; i = 1, ...,M.Where, a- is the propagation delay for flow i.

3.3. Simulation SetupThe simulation was conducted using ns-2 simulator. The

network topology, shown in Figure 5, used for this simulationconsists of n source-destination pairs that run n TCP sessionscarrying FTP traffic through one shared bottleneck link. Inaddition, one UDP source-destination pair was used to carryconstant bit rate (CBR) traffic throughout the same link

s0X 10 Mhbs n MhnR (X)20 msec

20 mVsDpS20 msec

Bottleneck

4 Mbps60 msec

so do: UDPsi di: TCP; for i =1, ... n

and n = 40

Figure 5. Simulated network topology and setup.

The parameters used in this simulation are as follows: buffersize (K) is 150 packets, the RED thresholds are; minth = 50,maxth =100,maxp 01.,anda=0.0002.

4. Results and Discussion

The effect of the UDP traffic on the TCP throughput andRED drop probability is shown in Figures 6 and 7 respectively.The results show that RED queue can handle small UDP ratescompared to the link capacity. However, higher UDP rates willinduce instability and cause the drop probability to vary wildly.This will increase the drops and result in unfairness andperformance deterioration, especially to the TCP flows. Thistrend can be seen clearly in Figure 6. The total TCP throughputin these graphs was normalized by 2 Mbps for clarity.

0 20 40 60 80 100 120 140Time (sec)

- no added UDPI/10%UDP200% UDP

- 50% UDPFigure 7. RED drop probability for different (XuDp/C).

Figure 8 shows the effect of the selection of averagingweight a on system performance. The study shows that thereexists a critical a value below which the system is stable.Higher values of a will result in oscillation and performancedegradation. Another observation is that the critical value of ais inversely proportional to the link capacity. For C = 12 Mbps,the critical value is 0.0005, any value above that will result ina-dependence as shown in Figure 8. The total TCP throughputwas normalized by 6 Mbps.

4r---------- ---- ------- --------- -l

The fluid-based differential equations in (12-14) were solvedusing Matlab. The model was validated by comparing theresults obtained to simulation. The simulation was used toobtain additional results to complement the ones obtained fromanalysis. The parameters used in this evaluation are the sameas the ones used in section 3.3 above, and will retain thesevalues unless stated otherwise.

-------------,I

C=2 Mb/secE| C=4 Mb/sec

1.4_

p

3.5

3

2.5

2

1.5

0.50

I1 '' .,'',-/ 1- /-TilkI~I1

a-/

C=6 Mb/secC=12 Mb/secC= 1 8 Mb/secC=24 Mb/sec

0.5alpha

Figure 8. The effect of a on system stability.

1.5

X 10

The evolution of the RED and TD queues with time fordifferent UDP rates is shown in Figures 9 and 10. Bothsimulation and analysis results are presented. The simulationmatches well with the analytic results obtained. The effect of

1.6 increasing UDP rates on the RED stability that we talked about-I earlier is also clear in this comparison. The TD queue tends to*. maintain high average queue occupancy, which can result in

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0 0.2 0.4 0.6 0.8 1 1.2 1.4UDP traffic rate= lamda/C

Figure 6. Normalized TCP throughput vs. XuDp /C

0.4 -- --

2>

1.8

1.6

1.2

0.8

0.6-

CD

r - 17,

higher delay. RED, on the other hand, produces lower queueoccupancy and provides a mean to control the end-to-enddelay; the drawback is the high queue size variability whichincreases the delay jitter.

RED queue, C= 4Mbps, no UDP traffic

50

75

O -E

0 20 40 60 80 100 120 140Time (sec)

RED queue, C = 4Mbps, 10% UDP trafficn,. -.

o 20 4 6 8 0 2 40 20 40 60 80 1 00 120 140

tuu

225

c-

ctC 150In

C2 7-5

Time (sec)

RED queue, C = 4Mbps, 20% UDP traffic

U

U0 20 40 60 80

Time (sec)

Time (sec)Average queue (simulation)Instantaneous queue (simulation)

-- - Instantaneous queue (Fluid based mo

Figure 9. RED queue size for diff

200%

> 150-z

N 100 w

a 50

0;0

200

a 150ct

N 100u 0

a2 50

0 LL0

50 100Time (sec)

50 100

150

150Time (sec)

Average queue sizeInstantanous queue size

Figure 10. TD queue size for 10%(up) and 50%(down) UDP.

_ t . t t

Two analytic approaches were used to quantify the benefitsclaimed that RED has on TD queue. The analysis shows that awell tuned RED outperforms TD and fixes some of itsdeficiencies. Tuning RED parameters is crucial for obtaining

;4.].MXhE the desired performance gain.The analysis shows that RED reduces the bias against bursty

traffic by increasing the drop of smooth traffic. It also showsl that RED decreases queuing delay but increases jitter of non-

100 120 140 bursty flows. Tail Drop queue on the other hand, shows asignificant bias against bursty traffic.

lo UDP traflic Fluid-based analysis provides a closed loop model to capturethe dynamic behavior of a TCP flow in RED queue and itsinteraction with the UDP flow when competing for the sameresources. The model is computationally efficient, models thecomplete system and can easily expanded and scale to networklevel.

9J 1 I T l 1The effect of the UDP traffic on the TCP performance when

sharing RED queue was studied. The results revealed that REDqueue can handle small UDP rates compared to the linkcapacity. For higher UDP rates, RED became unstable and thedrop probability starts oscillating wildly. This increased the

100 1'50 drops and resulted in unfairness and performance deterioration,especially to the TCP flows. The fluid-based model revealedsome RED inefficiency under certain circumstances. Theselection of the averaging weight a depends on the link

del) _ capacity. Higher value of a will result in a-dependence anderent UDP rates.

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performance deterioration. The analysis showed the need fortuning RED parameters in order to gain the benefits we hopefor. Simulation confirms the above conclusions and matcheswell with the findings obtained from analysis.

References

[1] T. Bonald, M. May, and J. Bolot; "Analytic evaluation ofRED performance," Proceedings of IEEE INFOCOM, 2000,Nineteenth Annual Joint Conference of the IEEE Computerand Communications Societies,, pt. 3, vol.3, p 1415-24, 2000[2] V.Misra, W. Gong, and D.Towsley; "Fluid-based analysisof a network of AQM routers supporting TCP flows with anapplication to RED," Computer Communication Review, v 30,n 4, p 151-60, October, 2000,[3] S. Floyd and V. Jacobson. "Random early detectiongateways for congestion avoidance," IEEEIACM Transactionson Networking, vol. 1, no. 4, pp.3997-413, August,1993.

[4] C.V. Holot, V. Misra; "Analysis and design of controllersfor AQM routers supporting TCP flows." IEEE Transactionson Automatic Control, vol.47, no.6, p 945-59, June 2002.[5] W. Stevens. TCPIIP Illustrated, Volume 2. theImplementation, Addison-Wesley, 1995.[6] W. Stevens TCPIIP Illustrated Volume 1, the Protocols,Addison-Wesley, 1994.[7] L. Zhang, S, Shenker and D.D. Clark . "Observations onthe dynamics of a congestion control algorithm: The effects oftwo-way traffic." Proceedings of ACM SIGCOMM91, pp.133-147, September,.1991.[8] B. Braden et al, Recommendations on Queue Managementand Congestion Avoidance in the Internet", RFC2309, April1998.[9] V. Firoiu and M. Borden. "A study of active queuemanagement for congestion control. "Proceedings IEEEINFOCOM 2000, pt. 3, vol. 3, pp. 1435-44, 2000.

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