LRED: A Robust and Responsive AQM Algorithm Using Packet Loss Ratio Measurement

Transcription

1 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, TPDS LRED: A Robust and Responsive AQM Algorithm Using Paket Loss Ratio Measurement Chonggang Wang, Member, IEEE, Jianghuan Liu, Member, IEEE, Bo Li, Senior Member, IEEE, Kazem Sohraby, Senior Member, IEEE, and Y. Thomas Hou, Senior Member, IEEE Abstrat Ative queue management (AQM) is an effetive means to enhane ongestion ontrol, and to ahieve tradeoff between link utilization and delay. The de fato standard, Random Early Detetion (RED), and many of its variants employ queue length as a ongestion indiator to trigger paket dropping. Despite their simpliity, these approahes often suffer from unstable behaviors in a dynami network. Adaptive parameter settings, though might solve the problem, remain diffiult in suh a omplex system. Reent proposals based on analytial TCP ontrol and AQM models suggest the use of both queue length and traffi input rate as ongestion indiators, whih effetively enhanes stability. Their response time generally inreases however, leading to frequent buffer overflow and emptiness. In this paper, we propose a novel AQM algorithm that ahieves fast response time and yet good robustness. The algorithm, alled Loss Ratio based RED (LRED), measures the latest paket loss ratio, and uses it as a omplement to queue length for adaptively adjusting the paket drop probability. We develop an analytial model for LRED, whih demonstrates that LRED is responsive even if the number of TCP flows and their persisting times vary signifiantly. It also provides a general guideline for the parameter settings in LRED. The performane of LRED is further examined under various simulated network environments, and ompared to existing AQM algorithms. Our simulation results show that, with omparable omplexities, LRED ahieves shorter response time and higher robustness. More importantly, it trades off the goodput with queue length better than existing algorithms, enabling flexible system onfigurations. Index Terms Ative queue management, ongestion ontrol, TCP, paket loss ratio. 1 INTRODUCTION B Chonggang Wang is with the Department of Eletrial Engineering, University of Arkansas, Fayetteville, AR , gwang@ieee.org; Phone: ; Fax: Jianghuan Liu is with the Shoold of Computer Siene, Simon Fraser University, Burnaby, British Columbia, Canada V5A 1S6. jliu@s.sfu.a; Phone: ; Fax: Bo Li is with the Department of Computer Siene, Hong Kong University of Siene and Tehnology, Hong Kong, P.R.China. bli@s.ust.hk; Phone: ; Fax: The Corresponding Author. Kazem Sohraby is with the Department of Eletrial Engineering, University of Arkansas, Fayetteville, AR , sohraby@uark.edu; Phone: ; Fax: Y. Thomas Hou is with the Bradley Department of Eletrial and Computer Engineering, Virginia Teh, Blaksburg, VA thou@vt.edu; Phone: ; Fax: Manusriptreeived 3, Feb. 5; revised 5 Jan. 6; aepted 8 Feb. 6. An earlier version of this paper was published in IEEE INFOCOM 4. For information on obtaining reprints of this artile, please send to: tpds@omputer.org, and referene IEEECS Log Number TPDS xxxx-xxxx/x/$xx. x IEEE uffer management for Internet routers plays an important role in ongestion ontrol [1][]. However, the two main objetives of buffer management, namely, high link utilization and low paket queuing delay, often onflit with eah other. Speifially, given that most endnodes employ the responsive Additive Inrease and Multipliative Derease (AIMD) TCP ongestion ontrol, a small buffer generally ahieves a low queuing delay, but suffers from exessive paket losses and low link utilization, and vie versa. In addition, a simple poliy like the widely used First-In-First- Out (FIFO) Tail-Drop often auses strong orrelations among paket losses, resulting in the well-known TCP synhronization problem [3]. To mitigate suh problems, Ative Queue Management (AQM) has been introdued in reent years [] [3] [5]-[14]. The basi idea is to atively trigger paket dropping (or marking provided expliit ongestion notifiation (ECN) [4] is enabled) before buffer overflow. Obviously, the drop probability should depend on the degree of ongestion. The de fato AQM standard, Random Early Detetion (RED) [5], and many of its variants employ queue length as a ongestion indiator to trigger paket dropping. Despite their simpliity, these approahes often suffer from unstable behaviors in a dynami network. Adaptive parameter settings, though might solve the problem, remain diffiult in suh a omplex system. Reent proposals based on analytial TCP ontrol and AQM models suggest the use of both queue length and traffi input rate as ongestion indiators, whih effetively enhanes stability. Their response time generally inreases however, leading to frequent buffer overflow and emptiness. In this paper, we argue that paket loss ratio, whih has never been explored in previous AQM studies, is another important index. The paket loss ratio is measured as the fration of the pakets dropped by the router and is updated over time. Intuitively, for a well-designed AQM algorithm, the loss ratio should be lose to the desired drop probability in a steady-state, and it deviates from the desired drop probability if the buffer is (or tends to) overflow

2 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, TPDS or empty. In other words, an inreasing paket loss ratio implies that ongestion ours, and a dereasing implies that the ongestion is relieved. Given the above observations, we propose a novel AQM algorithm, LRED, whih inorporates the paket loss ratio as a omplement to queue length for ongestion estimation. We stress two salient features of this hybrid design: First, the alulation is simple and fast for both measures, whih is desirable for high-throughput routers; seond, it enables a multi-granular update for the paket drop probability: upon eah paket arrival, we an use the instantaneous queue length mismath to update the drop probability, so as to keep the queue length around an expeted value; on a oarser grain, we an adjust the drop probability aording to the paket loss ratio, so as to expedite ontrol response. We have developed an analytial model for LRED, whih suggests that this multi-granular update improves not only the stability of the system, but also its responsiveness. The performane of LRED is further examined under various simulated network environments, and ompared to existing AQM algorithms, inluding Adaptive Virtual Queue (AVQ) [1], Proportional-Integra (PI) [1], and Random Exponentially Marking (REM) [13]. Our simulation results reveal that, with omparable omplexities, LRED ahieves shorter response time and better robustness. More importantly, it enables better tradeoff between the goodput and queue length than existing algorithms, leading to flexible system onfigurations. The remainder of this paper is organized as follows. Setion briefly introdues the existing AQM algorithms. In Setion 3, we offer an overview of the LRED algorithm. Setion 4 develops an analytial model for the ombined TCP/AQM system and disusses its general properties. Based on this model, we analyze the stability and responsiveness of LRED and other AQM algorithms in Setion 5. The simulation results for LRED are presented in Setion 6. Finally, we onlude the paper and give out future works in Setion 7. RELATED WORK There have been numerous proposals on AQM in the past deade, and RED [5] is probably the most widely studied algorithm. RED uses the average queue length to alulate the paket drop probability and to regulate the queue length aordingly. Speifially, when the average queue length is greater than a pre-onfigured threshold (min th ), RED begins to drop newly arrived pakets; the dropping probability inreases linearly to the average queue length with a slope of max p. Despite its simpliity, the optimal parameter onfiguration for RED remains a daunting task. Hene, several enhanements, like S-RED [7] and ARED [8], have been introdued to adaptively onfigure the parameters. Another variation is BLUE [9], whih alulates the paket drop probability based only on two events: buffer overflow and emptiness. When the buffer is overflow, it inreases paket drop probability by d 1, and, when empty, dereases by d. Nevertheless, adaptive settings in suh a omplex system are still diffiult. BLUE an not well regulate the queue length to an expeted value. l( k) k-m+1 k-1 k k+1 On the other hand, AVQ [1] uses input rate x( t) to ontrol paket drop and to ahieve an expeted link utility g. Basially, the paket drop probability is proportional to the mismath between x( t) and g. Through maintaining a virtual queue, AVQ deterministially drops pakets upon eah new paket arrival, realizing the same effet of probabilisti paket drop. AVQ ahieves lower average queue length and higher link utility than RED and its variants [1]. Reently, some advaned algorithms use the queue length and input rate jointly to ahieve better performane. One example is PI [1], whih regulates the queue length to an expeted value q aording to the queue mismath and its integral. The latter is losely related to the input rate mismath. If the network states are known a priori, optimal parameters of PI an be determined through a ontroltheoretial model. However, in dynami networks, PI may have to use a onservative setting to ensure stability, yielding long response time. Another example is REM [13], whih uses a linear ombination of the queue mismath and input rate mismath to alulate the drop probability, and the input rate mismath is equivalently simplified to the queue variane between two adjaent length samples. LRED employs the paket loss ratio as a omplement to the queue length for AQM. To the best of our knowledge, it has never been explored in the previous studies. The use of paket loss ratio enables LRED to ath network dynamis in time, thus ahieving fast ontrol response and better performane in terms of goodput, average queue length, and paket loss ratio. 3 OVERVIEW OF LRED l ( k 1) Fig. 1. Paket loss ratio measurement in LRED. Time Similar to most existing AQM algorithms, LRED keeps a paket drop probability p, whih is adaptively updated upon eah paket arrival, and the inoming pakets are dropped with probability p from the tail of the queue. The alulation of the drop probability is relatively simple, following two design rules: 1) when the queue length is lose to an expeted steady-state length q, the drop probability should be lose to the paket loss ratio; and ) when the queue length beomes larger (or smaller), the drop probability should be inreased (or dereased) to regulate the queue length. To ahieve an adaptive yet stable estimation for the paket loss ratio, LRED estimates the ratio in every measurement period ( t m ). Let l( k) be the paket loss ratio of the k-th measurement, whih is alulated as the number of dropped pakets over the total number of pakets arrived during the latest M periods (see Fig. 1); that is: t m k+

3 C. WANG ET AL.: LRED: A ROBUST AND RESPONSIVE AQM ALGORITHM USING PACKET LOSS RATIO MEASUREMENT 3 Fig. 1. Paket loss ratio measurement in LRED. (a) Time duration from to (b) Time duration from 4 to 43 Fig.. Evolution of paket drop probability ( p ) and paket loss ratio ( l( k ) ) in a simulation. M 1 M 1 N d i i l( k) ( ( k i))/( N ( k i)), (1) where N d( k) is the number of pakets dropped in the k-th measurement period, and Na( k) is the number of pakets arrived in the k-th measurement period. The estimated paket loss ratio l( k) is alulated based on l( k) using an exponential weighted moving average (EWMA), as follows: l( k) l( k 1) w (1 w ) l( k), () m where wm is a weighting fator. In order to promptly ath loss hanges, we set wm to a small value. Given the estimated paket loss ratio and the instantaneous queue length, a straightforward way to meet the design rules (to ontrol the queue length around an expeted steady-state value) is to use a linear funtion, p l( k) a( q q), where p is the paket drop probability and q is the instantaneous queue length. It is however often diffiult to hoose an optimal a. In partiular, if l( k) is large and a is set too small, the paket drop probability for a small queue length q would still be quite high, resulting in low link utility. To avoid this, in LRED, we let p inrease with the measured loss ratio; in other words, we have: p l( k) b l( k)( q q ), (3) where b is a pre-onfigured onstant. Intuitively, the adjustment of the paket drop probability should be related to traffi rate hange, in order to avoid buffer overflow or buffer emptiness. In Eq. (3), this adjustment is set to b l( k)( q q), whih uses square-root funtion of l( k ). This square-root funtion an guarantee that b l( k)( q q ) is proportional to the perentage of traffi rate hange, if we assume traffi flows are TCP. This is beause the TCP throughput is reversely proportional to the square-root of the stable paket loss ratio [15]. Furthermore, given that ( q q ) depends on both the value of stable traffi rate and the perentage of traffi rate hange, the produt of ( q q ) and l( k) depends on the perentage of traffi rate m a hange only. Our analysis in Setion 5 also shows that Eq. (3) ensures stable ontrol. In the ase of non-uniform paket sizes, different drop probabilities may have to be applied to pakets with different sizes. Speifially, larger pakets might have higher drop probabilities. In this ase, we an maintain the expeted queue length ounted in bytes, and therefore improve the fairness among TCP onnetions with different paket size. It an be seen from Eqs. () and (3) that LRED updates l( k) and p at different time sales. l( k) is updated every measurement period (see Fig. 1), while the paket drop probability p is re-alulated eah time a new paket omes. In a steady-state, l( k) ould onverge to a stable value. However, the AIMD mehanism in TCP implies that a TCP sender will always try to derease (or inrease) its sending rate if it detets paket loss (or not); therefore the queue length in routers will unavoidably flutuate and the paket drop probability p thus flutuates around l( k ). This is illustrated in Fig., where we an see l(4) l(41) l(4) l(43).1 ; When t 41., l(41).1 ; When t 41., the paket drop probability flutuates around.1. We an observe from Eq. (3) and Fig. that: 1) In between two adjaent instants k and k 1, when p is updated aording to Eq. (3), l( k) remains onstant and therefore p dependents only on the ontrol error ( q q) ; or more preisely, it is proportional to ( q q ) only; ) In a steady-state, l( k) will be lose to the stable value, and therefore p is still proportional to the ontrol error ( q q ) in this ase. As suh, we believe that LRED is loser to a proportional ontroller. Detailed operations for LRED an be found in Fig. 3 where q is assumed to 1. We will further disuss its parameter settings and prove its stability with the square-root funtion in Setion 5.

4 4 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, TPDS /* Parameters */ q o : the expeted value of queue length; p : the alulated paket drop probability; b : weighting fator (=.1 in this paper); M : the number of the latest periods to measure lossratio ; q : the urrent instantaneous queue length; lossratio: the estimated paket loss ratio; t m : the measurement period; w : the measurement weight; m /* Initialization */ arrpktnum=; droppktnum=; allarrnum=; alldropnum=; index=; q o =1; M=4; w m =.1; b =.1; t m =1.; lossratio=.; LossRatioMeasure() /* Called every t m seonds */ Enqueue() /* Called upon eah paket arrival*/ 1 dropnum[index]=droppktnum; 1 arrpktnum++; arrnum[index]=arrpktnum; p lossratio b lossratio( q q) ; 3 arrpktnum=; 3 p max(, min(1, p)) ; 4 droppktnum=; 4 random=uniformrandom(, 1); 5 index++; 5 if (buffer is full) { 6 if (index==m) index=; 6 Drop the paket; 7 for (i=; i<m; i++) { alldropnum+=dropnum[i]; } 7 droppktnum++; 8 for (i=; i<m; i++) { allarrnum+=arrnum[i]; } 8 } 9 lossratiotemp=alldropnum/allarrnum; 9 else if (random> p ) {Enqueue the paket; } 1 lossratio=lossratio* w m +lossratiotemp*(1- w m ); 1 else { Drop the paket; alldropnum=; droppktnum++; 1 allarrnum=; 1 } Fig. 3. Pseudoode of the LRED algorithm. 4 MODEL OF COMBINED TCP/AQM SYSTEMS In this setion, we first review an analytial model for a ombined TCP/AQM system [][14]. We then make several important observations on the model, whih serve as the basis for designing a stable AQM algorithm, in partiular, for LRED proposed in this paper. 4.1 The Combined TCP/AQM Models We onsider an abstrat network of a single bottlenek with multiple TCP onnetions. Its status an be represented by a 3-tuple ( N, C, R ), where N is the number of TCP flows, C is the bottlenek link apaity, and R is the round trip time (RTT). With the assumption that TCP flows are longlived persistent and paket size is onstant, the system equation for the TCP ongestion window (w ) and the queue length (q ) an be approximated as []: w f( w, p) 1/ R ( w( t) w( t R)/ hr) p ( t R), (4) q g( w, p) ( N / R) w ( t) C, (5) where p is the paket drop probability, and h is a parameter depending on TCP implementations. Let b be the number of pakets aknowledged by a reeived aknowledgement (ACK), we have h 3/b [15]. Eqs. (4) and (5) give a model of ombined TCP/AQM system with long-lived flows and onstant paket size. It is worth noting that the atual traffi mix in real Internet might be more omplex; for example, flows an start and end all the time and the paket sizes may vary for different appliations. Yet, existing studies have shown that this model offers a good approximation [][1][14]. If we let f ( w, p) and g( w, p), the TCP ongestion window w and paket drop probability p in a steady-state an be alulated as: w RC, h h p N 1. (6) N w R C For ease of exposition, we assume eah ACK aknowledges only one paket; therefore b 1 and h 1.5. The steady-state throughput of a single TCP flow given by the above model beomes C / N 3/ /( R p), whih is onsistent with the well-known TCP throughput equations [15]. From Eqs. (4) and (5), it is lear that the ombined TCP/AQM system is non-linear. Let dw w w and dp p p be the mismathes (i.e., the deviations from the steady-state values) for the TCP ongestion window and the paket drop probability, respetively. Eqs. (4) and (5) an be loally linearized around a stable point ( w, p) by assuming w( t) w( t R), as follows: d f f w w p [ K w K1 p( t R)] w d p d d d, (7) g g dq dw dp K1dw, (8) w p where K N /( R C), K 1 RC /( hn ), and K 1 N / R []. All of them are positive onstants related to the network parameters. Applying Laplae transform to Eqs. (7) and (8), we have the following system equations: s W ( s) [ K W ( s) K P ( s) e Rs ], (9) 1 1 s Q ( s) K W( s). (1) In Eqs. (9) and (1), there are three unknown variables: W( s ), P( s ), and Q( s ). Hene, it is neessary to find one more equation to solve the problem. This an be ahieved by bridging P( s) and Q( s) through AQM. As disussed earlier, our proposed LRED is a proportional ontroller; we thus fous on the proportional AQM ontrol in our analysis. Consider an AQM proportional ontrol mehanism that determines p aording to the instantaneous queue length

5 C. WANG ET AL.: LRED: A ROBUST AND RESPONSIVE AQM ALGORITHM USING PACKET LOSS RATIO MEASUREMENT 5 q. Its general ontrol equation an be formulated as: dp H dq. () The orresponding system equation an be written as: P( s) H Q( s), (1) where H is a pre-defined parameter. 4. General Properties of Proportional AQM Control From Eqs. (9), (1), and (1), we an obtain the harateristi equation for suh a system as: s K Rs s K H e, (13) where K K 1K 1 C / hn. The stability of the above system depends on whether the root of Eq. (13), s s j w, lies in the left half-omplex plane. To failitate its stability analysis, we have made the following observations on Eq. (13). First, if the root of Eq. (13) stritly lies in the left halfomplex plane, the ombined system, defined by network parameters ( N, C, R) and AQM ontrol parameter H, is stable. Hene, given ( N, C, R ), we an hoose H to satisfy this ondition. On the other hand, given ontrol parameter H, only some of the system ( N, C, R) an be stably ontrolled. Speifially, when R, the root of Eq. (13) is: s s ( K K 4 K H )/, (14) whih stritly lies in the left half-omplex plane irrespetive of K 4K H or K 4K H. Therefore, the system with zero delay is stable. When R and letting s s j w, the root of Eq. (13) an be alulated as follows: s w K R s KH s e os( Rw), (15) sw w e sin( Rw). (16) K K H R s Clearly, the imaginary part ( w ) of root s is nonzero; otherwise, Eq. (15) will be invalid. Also note that s hanges ontinuously in the omplex plane when N, C, R, or H hanges ontinuously. Assume the first time that s meets the imaginary axis is at R R. When R R, s should stritly lie in the left half-omplex plane, and the system is thus stable. The remaining problem therefore is to find the value of R. We first onsider the absolute imaginary root (s j w ) with w (the ase of w is symmetri). When R, Eq. (13) an be re-written as: T( s) ( e Rs K H )/( s( s K )) 1. (17) Given Eq. (17), the following onditions on magnitude and angles must be met, T( jw) 1, T ( jw) (k 1) p, k, 1,, and w an be alulated as: w( N, C, R, H ) w y( N, C, R, H )/, (18) 4 y( N, C, R, H ) K 4K H K, (19) w p Rw artan( ) (k 1) p, k,1,. () K Sine K is a dereasing funtion of R, and K is independent of R, we have that w( N, C, R, H ) is an inreasing funtion of R, if H is independent of or an inreasing funtion of R. Therefore, R orresponds to the smallest R satisfying Eqs. (13) and (17). Now the problem is to de- termine the value of k that yields the smallest R, whih an be solved through the following Lemma. Lemma 1. When k, Eqs. (18)-() yield the smallest value of R and w, if H is independent of or an inreasing funtion of R. Also Eq. () an be simplified to: Rw artan( w/ K ) p/. (1) Proof. We prove this by ontradition. Assume that k ( Rk, w k ), k, Rk, and wk. Aording to Eq. (), we have: w wk Rkwk R w kp [artan( ) artan( )] K K kp p /. Assume Rk R, we have wk w aording to Eqs. (18) and (19), if H is independent of or an inreasing funtion of R. Sine Rk R and wk w, we have Rkwk R w, whih ontradits to that Rkwk R w. Hene, Rk R, or equivalently, Eqs. (18)-() yield the smallest value of R and w when k. Lemma. Given network parameters( N, C ) and AQM ontrol parameter H. Assume that R satisfies: R w artan( w/ K ) p/, R, () where w is the solution to Eqs. (18) and (19). If funtion y( N, C, R, H ) in Eq. (19) is an inreasing funtion of R, then the system is stable for all R, and R is unique. R Proof. Sine y( N, C, R, H ) is an inreasing funtion of R, aording to Lemma 1, R is the smallest R that satisfy Eqs. (13) and (14), and is unique. It also means that the first time the root meets the imaginary axis is at R R. Therefore the system is stable for all R R. Lemma 3. Given network parameters( C, R) and AQM ontrol parameter H. Assume that N satisfies: Rw artan( w/ K ) p/, N, (3) where w is the solution to Eqs. (18) and (19). If funtion y( N, C, R, H ) in Eq. (18) is an inreasing funtion of R and a dereasing funtion of N, then the system is stable for N N. Proof. Let R( N) be the solution to Eq. (13) with N N. If R R( N), from Lemma, the system is stable for all N N. Sine y( N, C, R, H) in Eq. (18) is a dereasing funtion of N, we have: w( N ) w( N, C, R, H ) w( N, C, R, H ) w( N ). Moreover, K is an inreasing funtion of N, whih implies: Rw( N) artan( w( N)/ K ). Rw( N ) artan( w( N )/ K ) p / Sine R( N) w( N) artan[ w( N)/ K].5p, we have R( N) R, and hene, for all N N, the system is stable. Lemma 4. Given network parameters( N, C, R ), and assume that H satisfies: *

6 6 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, TPDS Rw artan( w/ K ) p/, * H, (4) where w is given by Eqs. (18) and (19). If funtion y( N, C, R, H ) in Eq. (19) is an inreasing funtion of both R and H, then the system is stable for all * H H. Proof. Similar to that of Lemma 3. Theorem 1. Let the network parameters be (, C, N R ) and assume that H satisfies:, R w artan( w / K ) p /, H, (5) where w is given in Eqs. (18) and (19). If funtion y( N, C, R, H ) in Eq. (19) is an inreasing funtion of R, a dereasing funtion of N, and an inreasing funtion of H, then the system is stable for H H, N N, and R. R Proof. Diretly follows Lemmas through 4. 5 ANALYSIS OF LRED AND PARAMETER SETTINGS 5.1 Stability Analysis of LRED We now investigate the stability of LRED and disuss the settings of several important parameters, in partiular, b. Sine the paket loss ratio is lose to the stable paket drop probability p in LRED, i.e., l( k) p, we an approximately rewrite Eq. (3) as: p p b p( q q ), (6) where, aording to Eq. (6), p hn /( R C ). It follows that: dp b dq, (7) or p P( s) b p Q( s), (8) and the system transfer funtion of LRED (see Eq. (1)) is thus given by: H P( s)/ Q( s) b p. (9) Substituting Eq. (9) for have the following Lemma. H in Eqs. (18) and (19), we Lemma 5. For LRED, funtion y( N, C, R, H ) in Eq. (19) is a dereasing funtion of N, and an inreasing funtion of b. 3 3 Moreover, if b h( N) /( R C ), it is an inreasing funtion of R. Proof. For LRED, y( N, C, R, H ) in Eq. (18) an be alulated as: N 4 b C N 4 y( N, C, R, H ) ( ) ( ). (3) R C hr R C It an be easily observed that y( N, C, R, H ) is a dereasing funtion of N and an inreasing funtion of b. We now onsider its relation with R. The derivative of funtion y with respet to R is: 4 8( N) 8b C y R C hr R 4 ( ) R C hr N 4 b C f 1( R) f3( R) f ( R) Theorem. Given network parameters (, C, N R ), and assume that b satisfies: 4( N) 5 R C Note that y is an inreasing funtion of R if y / R, whih is equivalent to: b h N b R C [ ( ) ] [ f ( R) f ( R)] f ( R). h R C 3 3 It follows that b h( N ) /( R C ). R w artan( w / K ) p /, b. (31) where w is defined in Eqs. (18) and (19), and H b p 4 3 in LRED. If b b min( b 3, h( N ) /( R C )), the system is stable for any N and R R. N Proof. Diretly follows Lemma 5 and Theorem 1. Given Theorem, it is easy to find b that guarantees the stability of the system. For example, onsider a network in whih the mean paket size = 5 bytes, C 5 pakets/se (or equivalently, 1 Mbps), N =3, and R =.35 seonds. The AQM parameter b is thus.1, and, for any b b, the system is stable with all N N and R. R 5. Response Time Analysis and Comparison Sine enhaning stability and minimizing response time often onflit with eah other, existing algorithms suh as PI [1] and REM [13] have tried to find a tradeoff between them. If network parameters, in partiular, N and R, are known a priori, these algorithms an ahieve a stable ontrol with minimized response time. In a dynami network, however, it is diffiult to aesses these parameters preisely. Hene, they generally resort to a onservative design that guarantees stability, but may sarifie the orresponding response time. For example, the default parameter for PI in NS Simulator [16] is set based on a small N and large R. When N inreases or R dereases, it will yield a long response time, though the system remains stable. In this subsetion, we provide a simple analysis on the response times of the typial AQM shemes. We fous on a highly dynami senario: at time t, N TCP flows beome ative simultaneously, wheren is large enough suh that the buffer is fully filled before the system onverges to a steady state with paket drop probability p and expeted queue length q. We first onsider PI [1], whih periodially updates its paket drop probability with a sampling frequeny fpi (Hz). Eah update is as follows: p( k) p( k 1) a[ q( k) q ] b [ q( k 1) q ], (3) where a and b are two onstants [1]. We an assume that p() and q( k) Q before reahing a steady-state, where Q is the maximal buffer size. It follows.

7 C. WANG ET AL.: LRED: A ROBUST AND RESPONSIVE AQM ALGORITHM USING PACKET LOSS RATIO MEASUREMENT 7 that: p( k) k( a b)( Q q ). (33) Denote p( k ) p. The lower bound of the response time of PI ( RT PI ) is thus: RT PI k / f PI p/(( Q q )( a b) f PI). (34) In REM [13], paket drop probability is also periodially updated with a sampling frequeny f REM (Hz), as follows [13]: ( ) p( k) 1 f u k, (35) u( k) u( k 1) g[ q( k) (1 a) q( k 1) aq )], (36) u( k) max(, u( k)), (37) where f 1, g, and a are three onstants, and their optimal values are derived in [13]. Similarly, we an also assume that u(), u( k) 1, and q( k) Q before reahing the steady-state, whih follows that: u( k) k ga( Q q ), (38) u ( k) p( k) 1 f 1 {([ u ( k)ln f])/( i!)} i, (39) u( k)ln f kga( Q q )ln f and the lower bound of the response time for REM ( RT REM ) is thus: RT k / f p /( f ga( Q q)ln f). (4) REM REM REM From Eqs. (34) and (4), we an see that the response times of PI or REM mainly depend on the following parameters: buffer size Q, expeted queue length q, and paket drop probability p (whih is an inreasing funtion of TCP flow number N, and a dereasing funtion of round- trip time R and link apaity C ). Consequently, under heavy ongestion or with a high drop probability, PI and REM suffer from long response times. When buffer size Q is small, the responsiveness of PI and REM beomes worse as well. In LRED, the response time is mainly influened by the period ( t m ) to measure the paket loss ratio. In partiular, under heavy traffi (e.g., when N is large and/or R is small), pakets will be dropped frequently and the paket loss ratio an be aurately estimated within a ouple of measurements. As a result, LRED is very responsive in this ase, while PI and REM perform poorly given that p is high. More importantly, when network onditions hange dramatially, LRED an quikly onverge to new steady states. When the traffi load is light (e.g., when N is small and/or R is large), there are few paket losses, and more rounds of measurement are thus needed for aurately estimating the stable paket loss ratio. In this ase, the response time of LRED would slightly inrease, but remain omparable to that of PI and REM, as will be shown in our simulations. In summary, LRED deouples the response time and paket drop probability, making its response time almost independent of the ongestion levels. 6 SIMULATION RESULTS In this setion, we examine the performane of LRED through NS [16] simulations. We also ompare it with existing AQM shemes, in partiular, PI [1] and REM [13]. i 1 5 d1 d d5 1 Mbps Router 1 1 Mbps (d1, d, d3, d4, d5) unit: ms.5 ms Fig. 4. Network topology for simulations. 1 Mbps.5 ms Router Fig. 5. Experiment 1: Response times for the AQM shemes. For loss ratio measurement in LRED, we set w m =.1, t m =1. seond, and M 4; b is set to.1 aording to Theorem. The network topology for the simulation is the ommonly used dumb- bell topology (see Fig. 4). In this topology, 5 lients are linked to router 1, and 5 servers are behind router. The apaity of eah link is 1 Mbps, and the link between router 1 and router thus beomes a bottlenek. The link delay between router and any server is.5 ms, and the delays between the lients (1 through 5) and router 1 are heterogeneous, denoted by a 5-tuple ( d1, d, d3, d4, d 5). All the flows in the network are uniformly distributed among the pairs of lient ( i) and server s(i). The default paket size is 5 bytes. The buffer size of eah router is pakets unless another value is expliitly onfigured suh as in Experiment 6. We run eah simulation for seonds, whih is long enough to observe both transient and steady-state behaviors of an AQM sheme. The following parameter settings are used in our simulations. 1) For REM [13], f 1.1, a.1, g.1, and the sampling interval is ms. These values are adapted from [13] and [16]. ) For PI [1], we use two settings: default and optimal, respetively denoted by PI and PI*. The default values for PI are a =.18, b =.1816, and the sampling frequeny is 17Hz, whih are adapted from [16]; the optimal values for PI* are derived aording to the design rules in [1], whih depend on network parameters ( N, C, R ). Here, N is the minimum number of the TCP flows and R is the maximal round-trip time. Hene, the optimal values for PI* are not fixed for the experiments. In our study, we fous on the following key performane s1 s s5

8 8 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, TPDS (a) light ongestion ( p.5) (b) heavy ongestion ( p.165) Fig. 6. Experiment : Queue length under two extreme ases. Fig. 7. Experiment 3: Comparisons of (a) goodput, (b) average queue length, () average queue deviation, and (d) paket loss ratio. metris: goodput, average queue length, average queue deviation, and paket loss ratio. The goodput is the overall throughput of the system exluding retransmissions; the average queue length is alulated as the arithmeti mean of the instantaneous queue lengths; and the average queue deviation is the average of the absolute deviations of the instantaneous queue lengths from the mean. 6.1 Homogenous Traffi: Long-lived TCP Flows Only In this set of experiments, we fous on a network with homogeneous traffi, i.e., all are persistent TCP flows. Experiment 1: Response time under various ongestion degrees We first investigate the response times for the AQM shemes to reah a steady state. The expeted queue length q is set to 1 pakets, and the vetor for link delays between Clients and Router 1, ( d1, d, d 3, d 4, d 5), is (1, 5, 1, 15, ). The total number of TCP flows, N, varies from 1 to 1, whih leads to 1 senarios with various degrees of ongestion. For PI *, we set N from 1 to 1 for the 1 senarios, R is set to 45 ms for N 5, and 5 ms to 9 ms for N from 6 to 1, whih guarantee that N ( R C )/ aording to the design rule of PI in [1]. The response times as a funtion of the loss ratio are presented in Fig. 5. It an be seen that when the paket loss ratio inreases (whih is a result of an inrease of the number of TCP flows), the response times of PI or REM inrease, for both simulated and analytial results. The mismathes between the simulated and analytial results for PI and REM are relatively small, espeially with high loss ratios. PI * however has a big mismath between its simulated and analytial results. The main reason is that we assume the buffer is always full before reahing a steady-state when analyzing the lower bound of the response time in the Setion 5. Sine PI * uses the optimal parameter aording to the design rules in [1], it has faster response than PI using the default parameters. Nonetheless, the response time of LRED is generally lower than other shemes, and it is nearly independent of the paket loss ratio. As a result, the gaps between LRED and other shemes under a high loss ratio are pretty signifiant. Experiment : Stability under extreme onditions In this experiment, we examine the stability of the AQM

9 C. WANG ET AL.: LRED: A ROBUST AND RESPONSIVE AQM ALGORITHM USING PACKET LOSS RATIO MEASUREMENT 9 Fig. 8. Experiment 3: Queue length for AQM shemes. (a) q (b) q 16 Fig. 9. Experiment 4: Comparisons of (a) goodput, (b) average queue length, () average queue deviation, and (d) paket loss ratio. shemes under two extreme ases: 1) light ongestion with a small number of TCP flows N and large round-trip time R, and ) heavy ongestion with a large N and small R. Fig. 6 presents the instantaneous queue lengths under suh two ases: 1) In the first, we set N =8 and d1 d d 3 d 4 d 5 5 ms. Therefore, we have N =8 and R =55 ms for PI *. ) In the seond, N =8 and d 1 d d 3 d 4 d 5 1 ms, and aordingly, we have N =8 and R =1 ms for PI *. Other parameters are the same as those in Experiment 1. We an see that LRED and PI * have similar response times, but LRED has less overshoots and smaller queue deviations. It an still be seen that, under heavy ongestion, LRED ahieves a shorter response time and better stability than PI and REM. Under light ongestion, the queue length of REM drastially osillates and almost out of ontrol. On the ontrary, LRED and PI an still stably regulate the queue, and LRED is relatively better. Note that the response time of LRED slightly inreases in the light ongestion ase beause it needs more rounds to have a stable loss ratio estimate. Nevertheless, its response time is still omparable to that to PI or PI *. Experiment 3: Varying the expeted queue length This experiment is used to study the performane of AQM shemes when the expeted queue length varies. We fix the number of persistent TCP flows to N =4. The expeted queue length q varies from to 4, 6, 8, 1, 1, 14, and 16. The other parameters are the same as that in the Experiment 1. Aordingly, for PI *, we set N =4 and R =45 ms. We an see from Fig. 7 that PI ahieves higher throughput and lower loss ratio. The reason is that its slow response leads to longer queue length than the other three shemes (as shown in Fig. 8), whih in turn redues the loss ratio and inreases the goodput. On the ontrary, LRED, PI *, and REM effetively realize the expeted average queue length and thus have almost the same paket loss ratio. Compared to PI * and REM, LRED has a higher goodput when q is smaller than 6, as shown in Fig. 7 (a). Moreover, LRED has the smallest queue deviation. Fig. 8 presents the instantaneous queue lengths for the AQM shemes when q equals and 16. It an be seen that LRED ahieves better tradeoff between the average queue length and other QoS performane measures, inluding goodput and loss ratio. 6. Non-Homogenous Traffi: Hybrid Flows Experiment 4: Adding unresponsive UDP flows

10 1 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, TPDS (a) UDP traffi density (r ) is.5 (b) UDP traffi density ( r ) is.9 Fig. 1. Experiment 4: Queue lengths for AQM shemes, where r is UDP traffi density. Fig.. Experiment 5: Comparisons of (a) goodput, (b) average queue lengths, () average queue deviations, and (d) paket loss ratios. In this experiment, we investigate the performane of the AQM shemes with the existene of unresponsive UDP flows. In addition to the 1 persistent TCP flows, we introdue 1 UDP flows arriving in interval [5 se, 15 se]. Eah is an ON/OFF flow, where the durations of the ON and OFF states are exponentially distributed with a mean of 1. seond. The density of the UDP traffi over the total traffi, r, ranges from.1 to.9, and the rate of eah UDP flow is r r 1 Mbps/ 1 during the ON period. Other settings are the same as those in Experiment 1. Aordingly, we hoose N =1 and R =45 ms for PI *. Fig. 9 presents results of the goodput, average queue length, average queue deviation, and paket loss ratio, as funtions of the UDP traffi density. It an be seen that LRED generally outperforms PI, PI *, and REM in all these performane measures, espeially when the UDP traffi density is high. Note that REM ahieves better performane than PI in this experiment; however, it is stable with quite restrited network onditions only, as shown in Experiment. We also present the instantaneous queue lengths for the AQM shemes in Fig. 1. There are two interesting observations. First, when r inreases, LRED an still regulate the queue length to the expeted value with muh smaller under- or over-shoots than PI, PI * and REM. Seond, the buffers of PI, PI * and REM are overflowed (or empty) for a long time when the UDP flows start arriving from 5 seonds (or stops after 15 seonds), espeially if r is large, i.e.,.9. This is due to the slow responsiveness of PI, PI * and REM, whih result in low goodput and high loss ratio. On the ontrary, there is only a short-term inrease (or derease) at time 5 seonds (or 15 seonds), whih implies that LRED has a muh shorter response time. Experiment 5: Adding short-lived TCP flows Besides unresponsive UDP flows, short-lived TCP flows an also affet the performane of an AQM sheme. In this set of experiments, we introdue short-lived TCP flows, whih arrive in intervals [5 se, 15 se] following to a Poisson proess. The mean arrival rate l varies from 1 flows/seond to 1 flows/seond, and the length of eah short-lived TCP flow is uniformly distributed in [1. se,. se]. Other parameters are the same as those in Experiment 4 and N =1 and R =45 ms are still set for PI *. The average queue lengths, average absolute queue deviations, goodputs, and paket loss ratios for the three AQM shemes in this experiment are ompared in Figs.. Clearly, LRED outperforms PI, PI *, and REM in all these

11 C. WANG ET AL.: LRED: A ROBUST AND RESPONSIVE AQM ALGORITHM USING PACKET LOSS RATIO MEASUREMENT (a) l =3 flows/seond Fig. 1. Experiment 5: Queue lengths for the AQM shemes, where l is the short-lived TCP arrival rate. (b) l =1 flows/seond Fig. 13. Experiment 5: Comparisons between LRED and AVQ. (a) goodput, (b) average queue lengths, () average queue deviations, and (d) paket loss ratios. measures. In addition, Fig. 1 shows the instantaneous queue length for PI, PI *, REM, and LRED for l=3 and 1. LRED is again more stable due to its good responsiveness. We also ompare LRED with AVQ [1] in suh a heterogeneous traffi environment. AVQ is known to be effetive in regulating the queue length and ahieving high link utilization [1]. In the design rules of AVQ in [1], a. is required to guarantee stability for this senario (N =1, R 45 ms, and C =5 pakets/seonds). Hene, we let parameter a vary from.1 to.15 and set the expeted utility of AVQ, g, to.98. To make a fair omparison, we also set q in LRED to small values (1 and ), whih math the average queue length in AVQ. The performane measures are presented in Fig. 13. When a dereases, AVQ ahieves higher goodput and lower loss ratio but larger average queue length as well as queue deviation. When l 6, LRED with q = is better than AVQ. When l 6, LRED with q =1 outperforms AVQ. It implies that LRED ahieves better performane than AVQ, if assigned with a small q. Aording to [17] and [18], the Pareto distributions of file sizes and durations ould ontribute to the self-similar harateristis of the Internet traffi. Hene, we have also onduted experiments with the paket inter- arrival time and flow s duration being set to Pareto distributions, with the same means in the previous experiment. The results are Fig. 14. Experiment 5: Queue lengths for the AQM shemes when the short-lived TCP flows follow a Pareto proess (l =1 flows/seond).

12 1 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, TPDS (a) The reverse diretion (Short-lived TCPs) Fig. 15. Experiment 6: Queue lengths for the AQM shemes ( q =1, Q =). (b) The forward diretion (Long-lived TCPs) (a) The reverse diretion (Short-lived TCPs) (b) The forward diretion (Long-lived TCPs) Fig. 16. Experiment 6: Queue lengths for the AQM shemes ( q =1, Q =4). presented in Fig. 14, for PI, PI *, REM, and LRED, respetively. It shows that LRED still has faster response and better performane, and the differene between the results of Poisson and Pareto distributions is generally insignifiant. However, it is worth noting that the Pareto distribution is not neessary the best Internet traffi model, partiularly onsidering that the Internet traffi has always been hanging with suh emerging new tehnologies and appliations as peer-to- peer ommuniations. We expet that, in our future study, more results an be obtained using up-to-date Internet traes or advaned traffi models, e.g., the Frational Gaussian Noise (FGN) distribution [19]. 6.3 Two-Way Traffi: Forward and Reverse Diretion Experiment 6: Two-way traffi and two-way ongestion In this experiment, we introdue two-way traffi: 1) In the reverse diretion, namely, from the lients to the servers (see Fig. 4), only short-lived TCP flows with a Poisson arrival proess of a flows/seond arrival rate are onfigured. The other parameters related to short-lived TCP flows are the same as that in the Experiment 5; ) In the forward diretion, or from the servers to the lients, there are 3 persistent TCP flows. We set N = and R =6 ms for PI *. Note that ongestion will our in both diretions of the link onneting Routers 1 and in Fig. 4. We set the simulation time to 1 seonds, whih enables shortlived TCP flows, and is long enough to disover the performane differene among the AQM shemes (see Figs. 15 and 16). We ollet the queue length for the AQM shemes in both diretions of the ongested link. In Fig. 15 ( q =1 and Q =), we an see that, all the AQM shemes have notieable overshoots in this ase with bi-diretional ongestion on the same link; yet LRED ontrols the queue length better than others. The forward traffi that onsists of persistent TCP flows is influened more notieably than the short-lived TCP flows in the reverse diretion (Fig. 15 (b)). To avoid buffer overflow (see in Fig. 15(b)), we inrease the buffer size from Q = to Q =4. The results are presented in Fig. 16, where both PI and PI * still show slower response and bigger overshoot. Although REM responds more quikly, its queue length is often below the

13 C. WANG ET AL.: LRED: A ROBUST AND RESPONSIVE AQM ALGORITHM USING PACKET LOSS RATIO MEASUREMENT 13 expeted value (1), leading to lower goodput. On the ontrary, LRED still regulates queue length around the expeted value (1) and ahieves better ontrol effet than other shemes. 6.4 Summary Our simulation results suggest that LRED ahieves fast response even under heavy ongestion and its performane is quite good in terms of goodput, queue length and queue deviation, and paket loss ratio. PI and REM however have slower response, whih leads to performane degradation under dynami network environments. Speifially, their paket dropping probability is iteratively omputed (see Eqs. (3) and (35)); if p is high (e.g., when the RTT R is low and the number of TCP flows N is large), PI and REM need a long time for the drop probability p to onverge to p. The onvergene rate and response time of LRED are almost independent of p, as shown in Fig. 5, but mainly influened by the measurement period. More importantly, when the network is highly dynami, LRED an quikly onverge to a new stable state through its multi-granular update. LRED relies on the measured paket loss ratio and therefore the parameters involved in measurement should be arefully onfigured. Speifially, the measurement weight ( w m ) in Eq. () should be set to a small value in order to apture the latest paket loss. Regarding measurement period ( t m ), if it is too small, the measurement ould be inaurate; but if it is too big, the response time an be longer. Our experiene shows that w m =.1 and t m =1. are reasonable hoies in most senarios. Another parameter in LRED is b, whose guideline is given by Theorem. Note that, if b is too big, the paket drop probability alulated by Eq. (3) will be either bigger than 1 (when q q ) or smaller than (when q q ). In this ase, LRED behaves like a virtual Tail-Drop with a virtual buffer size of q. Fig. 17 presents the simulated results for suh a senario, where b =1. It an be seen that the paket drop probability almost equals 1 or, and the queue length stays below 1, like in a traditional Tail- Drop buffer. 7 CONCLUSIONS AND FUTURE WORKS In this paper, we have proposed a novel AQM algorithm, LRED, whih inorporates paket loss ratio as a omplement to queue length for ongestion estimation. In LRED, the paket drop probability is updated over multiple grains: on a fine grain, LRED uses the instantaneous queue length mismath to update the drop probability upon eah paket arrival; on a oarse grain, LRED adjusts the drop probability aording to the paket loss ratio, whih has never been onsidered in existing AQM algorithms. We have developed an analytial model for LRED, whih suggests that this multi-granular update improves not only the stability of the system, but also its responsiveness. Suh observations have been validated by our simulation results under various onfigurations. We have also ompared LRED with existing AQM algorithms, inluding PI, REM, and AVQ. Our results have showed that LRED remains quite stable when the number of TCP flows and round-trip Fig. 17. LRED dynamis with a large b ( N =4, q =1). times vary signifiantly, or when many short-lived flows or unresponsive UDP flows exist in the network. Moreover, it an effetively ontrol the queue to the expeted length, and ahieves a better tradeoff between the goodput and queue length. Finally, LRED ahieves reasonably good performane under two-way traffi. There are many possible future works for enhaning the LRED algorithm. We are partiularly interested in extending LRED to support differentiated QoS, where pakets with different priority may have non-uniform dropping probabilities. Meanwhile a quantitative analysis of LRED s response time is very important to more preisely evaluate LRED s performane. The effet of substituting paket dropping with paket marking is also worth investigating. Another hallenging work is to model LRED s performane for short-lived TCP flows, whih will omplement our existing analytial results with long-lived flows. Finally, we are interested in examining the performane of LRED under more realisti Internet traffi traes, or more sophistiated traffi models that reflets the reent Internet development, e.g., Frational Gaussian Noise (FGN) distribution [19]. ACKNOWLEDGMENT The researh was support in part by grants from RGC under the ontrats HKUST64/3E HKUST614/4E and HKUST6165/5E, a grant from NSFC/RGC under the ontrat N_HKUST65/, grants from National NSF China under the ontrat 649 and J. Liu s work was supported in part by a Canadian NSERC Disovery Grant 8835, an NSERC Researh Tools and Instruments Grant, a Canada Foundation for Innovation (CFI) New Opportunities Grant, and an SFU President s Researh Grant. REFERENCES [1] R. Gurin and V. 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14 14 IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, TPDS [3] B. Braden, et al., Reommendations on Queue Management and Congestion Avoidane in the Internet, IETF RFC39, Apr [4] S. Floyd, TCP and Expliit Congestion Notifiation, ACM Computer Communiation Review, vol. 4, pp. 1-3, Ot [5] S. Floyd and V. Jaobson, Random Early Detetion Gateways for Congestion Avoidane, IEEE/ACM Trans. Networking, vol. 1, no. 4, pp , Aug [6] S. Floyd, Reommendation on Using the Gentle_ Variant of RED, Mar.. [7] W. Feng, D. D. Kandlur, D. Saha, and K. G. Shin, A Self- Configuring RED Gateway, Pro. of IEEE INFOCOMM, vol. 3, pp , Mar [8] S. Floyd, R. Gummadi, and S. Shenker, Adaptive RED: An Algorithm for Inreasing the Robustness of RED s Ative Queue Management, Aug. 1. [9] W. Feng, D. D. Kandlur, D. Saha, and K. G. Shin, The Blue Ative Queue Management Algorithms, IEEE/ACM Trans. Networking, vol. 1, no. 4, pp , Aug.. [1] S. Kunniyur and R. Srikant, Analysis and Design of an Adaptive Virtual Queue (AVQ) Algorithm for Ative Queue Management, Pro. ACM SIGCOMM, pp , Aug. 1. [] C. Hollot, V. Misra, D. Towsley, and W. Gong, A Control Theoreti Analysis of RED, Pro. of IEEE INFOCOM, vol. 3, pp , Apr. 1. [1] C. Hollot, V. Misra, D. Towsley, and W. Gong, On Designing Improved Controllers for AQM Routers Supporting TCP flows, Pro. of IEEE INFOCOM, vol. 3, pp , Apr. 1. [13] S. Athuraliya, S. Low, V. Li, and Q. Yin, REM: Ative Queue Management, IEEE Network Magazine, vol. 15, pp , May 1. [14] Y. Gao and J. C. Hou, A State Feedbak Control Approah to Stabilizing Queues for ECN-enabled TCP Flows, Pro. of IEEE INFOCOM, vol. 3, pp. 31-3, Mar. 3. [15] J. Padhye, V. Firoiu, D. Towsley, and J. Kurose, Modeling TCP Throughput: A Simple Model and Its Empirial Validation, Pro. of ACM SIGCOMM, pp , Aug [16] Network Simulator-NS, 5. [17] M. E. Crovella and A. Bestavros, Self-Similarity in World Wide Web Traffi: Evidene and Possible Causes, IEEE/ACM Trans. Networking, vol. 5, no. 6, pp , De [18] P. Barford and M. Crovella, Generating Representative Web Workloads for Network and Server Performane Evaluation, Pro. of ACM SIGMETRICS, pp , Jun [19] T. Karagiannis, M. Molle, and M. Faloutsos, Long-Range Dependene Ten Years of Internet Traffi Modeling, IEEE Internet Computing, vol. 8, no. 5, pp , Sept.-Ot. 4. Chonggang Wang (S -M 4) reeived the B.Eng. degree (um laude) from Northwestern Polytehni University (NPU), Xi an, China, in 1996, and the M.S. and Ph.D. degrees in ommuniation and information systems from the University of Eletroni Siene and Tehnology of China (UESTC), Chengdu, China, and Beijing University of Posts and Teleommuniations (BUPT), Beijing, China, in 1999 and, respetively. From September to November 3, he was a Researh Assoiate with the Department of Computer Siene, The Hong Kong University of Siene and Tehnology, Hong Kong, P. R. China. Sine then, he has been a onurrent Adjunt Professor with ChongQing University of Posts and Teleommuniations (CQUPT), Chongqing, P. R. China. He has been a Post- Dotoral Researh Fellow with the University of Arkansas, Fayetteville, AR, U.S.A., sine July 4. He is a o-reipient of 4 National Awards for Siene and Tehnology Advanement in Teleommuniations. His urrent researh interests inlude wireless sensor networks, wireless mesh networks, wireless/mobile networks, and ongestion and flow ontrol. He is a member of IEEE. Jianghuan Liu (S 1-M 3) reeived the B.Eng. degree (um laude) from Tsinghua University, Beijing, China, in 1999, and the Ph.D. degree from The Hong Kong University of Siene and Tehnology in 3, both in omputer siene. He is urrently an assistant professor in the Shool of Computing Siene, Simon Fraser University, BC, Canada, and was an assistant professor at The Chinese University of Hong Kong from 3 to 4. He was a reipient of Mirosoft researh fellowship (), a reipient of Hong Kong Young Sientist Award (3), and a o-inventor of one European patents and two US patents. He won first-lass honors in several regional and national programming ontests. His researh interests inlude Internet arhiteture and protools, media streaming, wireless ad ho networks, and servie overlay networks. He serves as TPC member for various networking onferenes, inluding IEEE INFOCOM, IEEE MASS, and IWQoS. He was TPC Co-Chair for The First IEEE International Workshop on Multimedia Systems and Networking (WMSN 5), Information System Co-Chair for IEEE INFOCOM 4, and a guest-editor for ACM/Kluwer Journal of Mobile Networks and Appliations (MONET), Speial Issue on Energy Constraints and Lifetime Performane in Wireless Sensor Networks. He is an editor of IEEE Communiations Surveys and Tutorials. He is a member of IEEE and IEEE Communiations Soiety, and an eleted member of Sigma Xi. Bo Li (S 89-M 9-SM 99) reeived his B. Eng. (summa um laude) and M. Eng. degrees in the Computer Siene from Tsinghua University, Beijing in 1987 and 1989, respetively, and the Ph.D. degree in the Eletrial and Computer Engineering from University of Massahusetts at Amherst in Between 1993 and 1996, he worked on high performane routers and ATM swithes in IBM Networking System Division, Researh Triangle Park, North Carolina. Sine 1996, he has been with the Department of Computer Siene, Hong Kong University of Siene and Tehnology. Sine 1999, he has also held an adjunt researher position at the Mirosoft Researh Asia (MSRA), Beijing, China. His urrent researh interests are on adaptive video multiast, peer-to-peer streaming, resoure management in mobile wireless systems, aross layer design in multihop wireless networks, ontent distribution and repliation. He has published 8 journal papers and held several patents in above areas. He reeived the Outstanding Young Investigator Award by the National Natural Siene Foundation of China (NSFC) in 4. He has been on editorial board for IEEE Transations on Wireless Communiations, IEEE Transations on Mobile Computing, IEEE Transations on Vehiular Tehnology, ACM/Kluwer Journal of Wireless Networks (WINET), IEEE Journal of Seleted Areas in Communiations (JSAC) - Wireless Communiations Series, ACM Mobile Computing and Communiations Review (MCR), Elsevier Ad Ho Networks, SPIE/Kluwer Optial Networking Magazine (ONM), KICS/IEEE Journal of Communiations and Networks (JCN). He served as a guest editor for IEEE Communiations Magazine Speial Issue on Ative, Programmable, and Mobile Code Networking (April ), ACM Performane Evaluation Review Speial Issue on Mobile Computing (Deember ), and SPIE/Kluwer Optial Networks Magazine Speial Issue in Wavelength Routed Networks: Arhiteture, Protools and Experiments (January/February ), IEEE Journal on Seleted Areas in Communiations Speial Issue on Protools for Next Generation Optial WDM Networks (Otober ), Speial Issue on Reent Advanes in Servie-Overlay Network (January 4), and Speial Issue on Quality of Servie Delivery in Variable Topology Networks (September 4), and ACM/Kluwer Mobile Networks and Appliations (MONET) Speial Issue on Energy Constraints and Lifetime Performane in Wireless Sen-

15 C. WANG ET AL.: LRED: A ROBUST AND RESPONSIVE AQM ALGORITHM USING PACKET LOSS RATIO MEASUREMENT 15 sor Networks (nd Quarter of 5). In addition, He has been involved in organizing over 4 onferenes, esp. IEEE Infoom sine He was the Co-TPC Chair for IEEE Infoom 4. Kazem Sohraby reeived B.S. (highest distintion), M.S., and PhD, all in Eletrial Engineering, took graduate ourses in omputer siene at the George Washington University, and reeived an MBA from the Wharton Shool, University of Pennsylvania. He is a Professor and head of department of omputer siene and omputer engineering at University of Arkansas at Fayetteville. He also serves as a Prinipal Consultant on ontrats with the Defense Information Systems Ageny (DISA). Before oming to Arkansas, he served as Chair of interdisiplinary Teleommuniations Management Department at Stevens Institute of Tehnology (1997-), and as adjunt Professor of Eletrial and Computer Engineering, and Computer Siene (1987-). While with Bell Labs, Luent Tehnologies and AT&T Bell Labs (1983-3), he was a Distinguished Member of Tehnial Staff, with the Performane Analysis Department in the Advaned Communiations Tehnologies Center, with the Mathematis of Networks and Systems Department in the Mathematial Sienes Researh Center, and forward looking enter on swith design. His areas of interest inlude omputer networking, signaling, swithing, performane analysis, and traffi theory. Prior to joining Bell Labs, Dr. Sohraby served as the Head of Network Design and Planning Department at Computer Sienes Corporation, Systems Division ( ). He has total of over patent appliations (14 granted) on omputer protools, wireless and optial systems, iruit and paket swithing, and Optial Internet. He has several publiations, inluding a book on the performane and ontrol of omputer ommuniations networks. He is a Distinguished Leturer of the IEEE Communiations Soiety, and Diretor of IEEE Communiations Soiety (on-line ontent), and served as its president's representative on the Committee on Communiations and Information Poliy (CCIP). He served as hair of several onferenes in both IEEE and ACM, ACM Mobiom speial interest group, and is vie hair of the IEEE Infoom exeutive ommittee. He also served on the eduation ommittee of the IEEE Communiations Soiety, is on the editorial boards of several publiations, and panelist and reviewer with the National Siene Foundation. He served as grant referee and reviewer with the US Army, and the Natural Sienes and Engineering Researh Counil of Canada. Y. Thomas Hou (S'91-M'98-SM'4) obtained his B.E. degree from the City College of New York in 1991, the M.S. degree from Columbia University in 1993, and the Ph.D. degree from Polytehni University, Brooklyn, New York, in 1998, all in Eletrial Engineering. From 1997 to, He was a researher at Fujitsu Laboratories of Ameria, IP Networking Researh Department, Sunnyvale, California. Sine fall, he has been an Assistant Professor at Virginia Teh, the Bradley Department of Eletrial and Computer Engineering, Blaksburg, Virginia. His urrent researh interests inlude resoure (spetrum) management and networking issues for SDR-enabled wireless networks, optimization and algorithm design for wireless ad ho and sensor networks, and video ommuniations over dynami ad ho networks. In reent past, he also had work on salable arhitetures, protools, and implementations for differentiated servies Internet, servie overlay networking, video streaming, and network bandwidth alloation poliies and distributed flow ontrol algorithms. He has published over 1 journal and onferene papers in the above areas and is a reipient of the 4 IEEE Communiations Soiety Multimedia Communiations Best Paper Award, the IEEE International Conferene on Network Protools (ICNP) Best Paper Award, and the 1 IEEE Transations on Ciruits and Systems for Video Tehnology (CSVT) Best Paper Award. He is a member of ACM and a senior member of IEEE.