Active Queue Management A router based control mechanism

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1 Active Queue Management A router based control mechanism Chrysostomos Koutsimanis B.Sc. National Technical University of Athens Pan Gan Park B.Sc. Ajou University Abstract In this report we are going to study and present the efficiency of the most basic Active Queue Management techniques. The study is based on the summary of several research papers from the networks field. Common characteristic of all the papers we reviewed is the simulation based evaluation of the different AQM approaches. Hence, we are not going to cite explicit mathematical models concerning their performance evaluation. Nevertheless, the simulations they use are exhaustive, so safe results can be drawn. From that point of view all the papers we studied describe effectively enough the basic ideas and results of these methods. Last, the metrics we will use in our evaluation is the queue size and the drop probability. I. INTRODUCTION Over the last decade, the flow and congestion control mechanisms of TCP have been used to adaptively control the rates of individual connections sharing IP network links. However, the performance of the TCP congestion control mechanism in networks that implement drop-tail packet discard has some drawbacks. For example, one problem is that the TCP sources reduce their rate only after detecting packet loss due to queue overflow. This is an important error since considerable time may pass between the packet drop at the router and its detection at the source. In the meantime, a large number of packets may be dropped as the sender continues to transmit at a rate that the network cannot support. Therefore, even with end systems equipped with important algorithms such as the TCP congestion avoidance, slow start, fast retransmit, the performance of the TCP congestion control algorithm over current drop-tail networks can still be unsatisfactory. Hence, the most effective detection of congestion can occur in the router itself. The router can reliably distinguish between propagation delay and persistent queueing delay. Moreover, the router has a unified view of the queueing behavior over time and the decisions about the duration and magnitude of transient congestion that can be allowed at the gateway are best made by the router itself. In order to encounter the increasing packet loss rates caused by an exponential increase in network traffic, the Internet Engineering Task Force (IETF) has considered the deployment of active queue management techniques (AQM). The basic idea behind an active queue management algorithm is to convey congestion notification early to the TCP endpoints so that they can reduce their transmission rates before queue overflow and sustained packet loss occur. The main objective of this report is to present a comparative analysis of the performance of the most basic ARQ schemes, namely RED, BLUE, SRED, and DRED. II. OVERVIEW OF AQM ALGORITHMS In this section we will give a short theoretical description of the AQM strategies we will compare. Moreover, some simulation results for each method will be presented. IIa. RED METHOD The Random Early Detection (RED) scheme was initially described and analyzed by Floyd and Jacobson in their article Random Early Detection Gateways for Congestion Avoidance at 993 []. The main idea behind this algorithm is that it starts

2 dropping packets randomly before the buffer gets full. Hence, it forces the connections to back off before the buffer fills up and multiple packets are dropped. Nevertheless, if connections ignore packet drops and keep sending at too-high rates, they will suffer from even higher loss rates. With the RED buffer management scheme, incoming packets are dropped with a probability that is an increasing function of the average queue size k ˆ. This is calculated using an exponentially weighted moving average filter and can be expressed as: kˆ ( w) kˆ + w k () where w is a fixed (small) parameter related to the filter and k is the instantaneous queue size. The reason we use this filter is because we want to limit the effects of bursty traffic or transient congestion to the calculation of queue size. It is shown in [] that we can succeed a very efficient calculation of the queue size when w is a negative power of two. When the average queue size exceeds a minimum threshold min th, the router randomly drops arriving packets with a given drop probability. If the queue continues to build up and the average queue size becomes larger than a maximum threshold max th, then all arriving packets are dropped. Thus, a typical drop function d is defined as follows: kˆ min th d( kˆ) = maxth min th max p if if if kˆ < min min th kˆ max th kˆ < max Next figure illustrates the above drop function. th th () Fig. Drop function of RED The optimal values for max th and min th depend on the desired average queue size. If the typical traffic is fairly bursty, then min th must be correspondingly large to allow the link utilization to be maintained at an acceptably high level. The optimal value for max th depends in part on the maximum average delay that can be allowed by the gateway. The RED algorithm functions most effectively when the difference max th -min th is larger than the typical increase of the calculated average queue size in one roundtrip time. This is true, since if the difference is too small we will cross the max th every time the increase of the average queue size is large. This will result in dropping many packets at the same time, which will cause global synchronization. Next we will present a performance evaluation of this AQM scheme using some basic queuing techniques, as can be found in []. First we will derive a model of a RED router with a single input stream of bursty traffic. We assume that packets arrive according to a bursty (B packets per arrival) Poisson process of rate λ. The processing times of the packets in the router are assumed to be exponentially distributed with mean μ -. We define the offered load by ρ=βλ/μ. Τhis case is illustrated in figure. Fig. Model of RED router with bursty input traffic

3 The number of packets buffered in the queue defines a Markov chain, with π being its stationary distribution. Using the PASTA property, we can approximate the drop probability of a packet in a RED router by: P RED ( drop) = π ( K) + π ( K ) d( K ) +... π () d() (3) In order to reach to the above expression we made two assumptions. First assumption is that the drop rate depends on the instantaneous queue size k rather than on the average queue size k ˆ. Second assumption is that the RED router uses the same drop probability d(k) on all packets in the same burst. Now, we consider the same model as before, except that the traffic is now simply a Poisson process of intensity λ. The number of consecutive drop packets, is: K k= ( N > n) = ( k drop) P π d( k) (4) where π ( k drop) is the stationary distribution of the number of packets in the queue, conditionally to the fact that a drop has occurred. By Bayes formula we have that: π ( k) π ( k drop) = d( k) (5) P( drop) Which gives us: P( N > n) = K k= K π ( k) d( k) k= n+ π ( k) d( k) n, n (6) Moreover, we can evaluate for the above model the stationary distribution of the queue size, hence the distribution of its occupancy. The model we have described is a simple birth-death model, the stationary distribution of which is given by: ( d( l)) π ( k) =, k =,..., K (7) K ρ k= k k l= k k ρ l= ( d( l)) Last, we have to mention that in many papers found in the literature the final dropping probability is given by the next formula instead of the one given in equation (): pb pa = count p (8) b where count is the number of consecutive undropped packets that have arrived since the last dropped packet. In this case the interdropping time X, as shown in [], is a uniform random variable, so we can success better spread of the dropped packets among the different connections. IIb. BLUE METHOD One of the fundamental problems with RED and other active queue management techniques is that they rely on queue length as an estimator of congestion. But this approach has an inherent problem in determining the severity of congestion. For instance, when a large number of TCP sources are active, the aggregate traffic generated is extremely bursty. Bursty traffic often defeats the active queue management techniques used by RED since queue lengths grow and shrink rapidly well before RED can react. Even though RED can achieve an ideal operating point, it can only do so when it has a sufficient amount of buffer space and is correctly parameterized. The key idea behind BLUE, as presented in [3], is to perform queue management based directly on packet loss and link utilization rather than on the instantaneous or average queue lengths. Also, it maintains a single drop probability p which it uses to mark or drop packets upon arrival. If the instantaneous queue length exceeds a predetermined threshold L, BLUE increases p by a very small fixed step size δ which is a system configurable parameter. To avoid dropping packets too aggressively, BLUE keeps a minimum interval,

4 freeze_time, between two successive updates of p. So the freeze_time, should be set based on the effective round-trip times of connections multiplexed across the link in order to allow any changes in the marking probability to reflect back on to the end sources. Conversely, if the link is idle (i.e., the queue is empty), BLUE decreases p by the amount δ periodically (once every freeze_time). By adjusting p with respect to the instantaneous queue length and link utilization (idle periods), BLUE aims to maintain the queue length at a predefined threshold. In order to evaluate the performance of BLUE, the authors in [3] use the following network topology. Fig. 4 Queue Length Fig.4 presents the queue length plots in an experiment using the (freeze_time:ms, δ :., δ :.) configuration of BLUE. In this case, a workload of infinite sources is changed by increasing the number of connections by every s. This plot shows that the queue occupancy remains below the actual capacity, thus allowing room for a burst of packets. Since BLUE manages its marking rate more intelligently, the queue length plot is stable. Hence, the queue occupancy remains below the actual capacity allowing room for a burst of packets. Fig.3 BLUE network topology Using this network, Pareto on/off sources with mean on-times of s and mean off-times of 3s were run from one of the leftmost nodes to one of the right most nodes. In addition, all sources were enabled with ECN support, were randomly started within the first s of simulation, and used kb packets. Packet loss statistics were then measured after s of simulation for s. Fig. 5 BLUE Drop probability Fig.5 shows the marking probability of BLUE. As we can see, the marking probability converges to a value that results in a rate of congestion notification which prevents packet loss and keeps link utilization high throughout the experiment. Actually, the only case where BLUE cannot prevent sustained packet loss is when every packet

5 is being marked, but the offered load still overwhelms the bottleneck link. This occurs at 6 s when the number of sources is increased to 8. As a result, BLUE marks packets randomly and evenly over time. Consequently, it does a better job in avoiding global synchronization. IIc. SRED METHOD As we have mentioned, RED randomly drops an arriving packet with a probability proportional to its average queue length. But this algorithm has a problem that the queue length becomes unstable when the average queue length is large. And another problem is that the average queue length is dependent on the number of active connections. So, the Stabilized Random Early Detection (SRED) algorithm, as proposed in [4], is designed to stabilize the queue size at a level independent of the number of active connections. In SRED, the packet drop probabilities are computed from estimates of the number of active flows and the instantaneous queue size. The key idea of SRED is to estimate the number of active connections using a small cache called "zombie list". The zombie list is equivalent to a list of M recently seen flows augmented with a count and timestamp field. Starting with an empty list, for every arriving packet, the packet flow identifier (source address, destination address, source port number, destination port number, etc.) is added to the list, the count of the zombie is set to zero, and its timestamp is set to the arrival time of the packet. The estimation process works as follows once the list is full. When a packet arrives at the router, SRED compares a randomly chosen entry from the zombie list with the entry corresponding to the arriving packet. If these entries coincide (hit), the counter in the entry is increased by one and the timestamp is reset to the arrival time of the packet in the buffer. Otherwise, the entry is probabilistically replaced by the information on the arriving packet with probability p (no hit). In this no hit case, the count of the zombie is set to, and the timestamp is set to the arrival time at the buffer. Then, we can estimate the relationship between hit and number of active flows. For the tth arriving packet the variable Hit () t is equal to if there is a hit and otherwise. An estimate of the hit frequency P(t) (i.e., an estimate of the frequency of hits for approximately the most recent p/m packets before packet t) is then maintained by the following recursion: Pt () = ( apt ) ( ) + ahit () t (9) a p/ M ( < a < and ) The quantity Pt () is considered a good estimate for the effective number of active flows in the time shortly before the arrival of packet t. Suppose there are flows,, Every time a packet arrives it belongs to flow i with probability πi. Then for every arriving packet the probability that it causes a hit is PHitt { ( ) = } = π i. If there are N active i flows of identical traffic intensity. π i = for i N this gives P{ Hit( t) = } = N N In this symmetrical case, Proposition is exact or at least roughly unbiased. The drop probability function for packet t, when buffer contains q in simple SRED, is as follows: p = p ( q ) min(, ) zap sred (56 Pt ( )) () Next, in proportion to the current queue length q, the packet drop probability p sred ( q) is updated for every packet arrival as Pmax if B qp B 3 psred ( q) = pmax if B qp B () if q p B 6 where B is the buffer size of a router. pmax is the SRED's control parameter, which limits the maximum of the packet drop probability. When we consider the drop probability function of simple SRED, we can notice that drop probability depends on the buffer occupancy. Moreover, p sred insures that the drop probability increases when the buffer occupancy increases. The ratio 4 quadruples the

6 drop probability when the buffer occupancy increases causing long term effect of halving the congestion window. As can be observed from the drop probability function: while Pt ( ) 56 psred psred then pzap = (num of flows) 65,536 ( Pt ( )) 65,536 when however Pt ( ) 56 then pzap = psred Finally, Full SRED drop probability also considers whether the packet caused a hit or not. Full SRED randomly drops an arriving packet with the probability P zap defined by Hit () t Pzap = Psred min(, ) ( + ) () (56 Pt ( )) Pt () This increases the drop probability of overactive flows.(i.e. misbehaving flows) IId. DRED METHOD The Dynamic Early Random Detection (DRED) algorithm, as proposed in [5], uses a simple feedback control approach to randomly discard packets in the queue. The objective of the DRED algorithm is to stabilize the actual queue size q(n) at a predetermined target queue size T, independent of the network traffic load. The actual queue size is sampled every Δt units of time and used to produce an error signal e(n) = q(n) T. This error signal is then used to adapt the drop probability P d, so that e(n) can be kept as small as possible. Figure 6 shows a block diagram of a DRED system in a closed-loop feedback congestion control context. Fig. 6 Basic scheme of a DRED system As we can see from this figure a DRED system consists of a target or reference level (which corresponds to T), an output or controlled variable (which corresponds to the actual occupancy level q), a process (which corresponds to all the TCP data sources), a controller device (which corresponds to the module which computes the packet drop probability), a feedback device (is the one which measures the output and process the information in preparation for comparison with the control target and finally the detector (this is the device which actually compares the recorded output with the target. Taking into account the above elements the model of DRED is like the one shown in figure 7. Fig.7 TCP congestion avoidance as a closed-loop feedback control system Due to the burstiness of the network traffic and other perturbations, the error signal e(n) can be highly fluctuating, so a low pass filtering of e(n) is desirable. Hence, a first-order low-pass filter with a filter gain β is used to generate a filtered error signal. eˆ ( n) = ( β ) eˆ( n ) + β e( n) (3) Then the incremental adaptation of the drop probability p d (n) is proportional to the filtered error signal: pd ( n) = pd ( n ) + α eˆ( n) (4) where α is the control gain, which affects the reaction and stability of the control system. An additional parameter L is used in the control process in order to maintain high link utilization and keep the queue size around the target level. Hence, DRED does not drop packets when q(n)<l. Moreover, with this way we do not further penalize sources which are in the process of backing off in response to previous packet drops.

7 Concluding, the computations in DRED can be summarized as follows: Sample queue size at time n, q(n) Compute current error signal e(n) Compute filtered error signal eˆ ( n) Compute current drop probability: eˆ( n) pd ( n) = min max pd ( n ) + α,, θ (5) B where θ is an upper bound on the drop probability. In the following two figures we present the performance of DRED using a bottleneck network configuration, like the one in figure, for 5 TCP connections. The TCP sources are based on the Reno implementation. First figure shows the instantaneous DRED queue size q(n) and figure 9 shows the DRED drop probability p d (n). which can both minimize packet loss and maximize the link utilization. Moreover, the value of the drop probability tends to be as smooth as possible, indicating that DRED is not too aggressive or too conservative in packet dropping. III. Fig. 9 DRED Drop probability PERFORMANCE EVALUATION In this section we compare the performance of the four active queue management algorithms we presented above. Fig. 8 DRED Queue size From figure 8 we can clearly see that DRED is effective at stabilizing and keeping the queue size around the target value. The initial peak of the queue size is due the slow start phase of the TCP connections. Also, from figure 9 we can observe that the drop probability increases or decreases in order to maintain the queue size at the control target. Actually DRED method searches continuously for the optimal drop probability, IIIa. SIMULATION METHODOLOGY In figure we illustrate the network configuration we will use for our simulation study [6]. Specifically, we can observe a network model representing a simple bottleneck network configuration with two routers and a number of nodes, each representing a TCP source. These TCP sources are based on a TCP-Reno implementation. The Reno version uses the fast retransmit and fast recovery mechanisms. The TCP connections have always data to send as long as their congestion windows permit. The receiver s advertised window size is set sufficiently large so that TCP connections are not constrained at the destination.

8 Fig. Network model bottleneck configuration IIIb. COMPARISON OF AQM METHODS In Figure we compare the instantaneous queue size of the four above mentioned methods. First of all, we can see that the queue sizes are more variable for both the RED and BLUE algorithms than the others. For RED, the queue size oscillates widely across and between the minimum and maximum thresholds. For both RED and BLUE, the queue sizes show periods of buffer underflow and overflow. The queue sizes of SRED and DRED are essentially stable around the target buffer occupancy (denoted by B/3 and T respectively). SRED, however, needs a larger buffer size than DRED in order to achieve the same performance. Fig. (b) (c) (b) (c) (a) (d) Fig. Queue size for connections: a)red, b)blue, c)sred, d)dred The drop probability of each algorithm is shown in

9 figure. As we can see from (a), RED exhibits a highly variable drop probability profile and also the highest numerical values among the four algorithms. The drop probability of DRED adapts faster than those of BLUE and SRED. BLUE s drop probability does not react fast enough, thus leading to periods of buffer overflow and underflow. (c) (a) (b) (d) Fig. Drop probability for connections: a)red, b)blue, c)sred, d)dred From the simulation results, it is obvious that the RED algorithm does not perform as well as the other algorithms in a congested network. In addition to the difficulty in parameterizing the algorithm to provide good and predictable performance under different network scenarios and over a wide range of load levels, it has difficulties in stabilizing the queue size as well. BLUE was also not effective at stabilizing the queue size. It was after some fine-tuning that the results of BLUE were obtained. Even with the fine-tuning, BLUE did not produce good responsiveness when the traffic load changed as compared to SRED and DRED. BLUE reacts slowly and leads to periods of buffer overflow and underflow. On the contrary, DRED and SRED both stabilize queue size very well, thus resulting in a more predictable packet

10 delay in the network. However, the short-term drop probability of SRED is not as smooth as that of DRED. It can reach percent randomly, thus causing a higher packet loss rate than DRED. From a simple queue management perspective, DRED is much simpler to implement than SRED, since it does not require any per-flow accounting mechanism. The flow accounting feature in SRED, however, allows for additional sophisticated capabilities such as misbehaving sources, and so on. IV. CONCLUSIONS In this pape r, we have compared a number of active queue management. An important question is whether active queue management can achieve low delay and high throughput simultaneously. So, we will summarize advantages and disadvantages for these algorithms. First, RED can early detect the congestion and mitigate global synchronization which is one of shortcoming of tail drop policy and alleviate bias against bursty traffic. But this algorithm is hard to set the parameter and has insensitivity to traffic load and drain rate. To be more specific, a small difference on RED parameters can have a large impact on its performance. This result confirms that choosing RED parameters might be a real challenge in an operational router where the traffic fluctuates. A single set of RED parameters may perform very well in certain traffic conditions and can be harmful as the traffic changes in number of flows or offered load. Second, SRED algorithm is designed to stabilize the queue occupancy at a level independent of the number of active connections and protects from misbehaving flows. However it has some per-flow state such as the zombie list and also hard to find proper parameter. Third, BLUE is easy to understand and can give high throughput. But this algorithm can t early detect the congestion and will response slowly, because BLUE updates the drop probability P drop only when queue overflows or the link is idle. Last, DRED stabilizes the queue occupancy at a level independent of the number of active connections and is able to keep the occupancy close to the specified control target, avoiding overflows and underflows. Concluding, it is clear that the complexity of the above methods depends on the quantities they measure, their sampling frequency and the algorithm employed to determine the packet drops. V. REFERENCES [] S. Floyd, V. Jacobson, Random Early Detection Gateways for Congestion Avoidance, IEEE/ACM Trans. Networking, 993, pp [] T. Bonald, M. May, J. Bolot, Analytic Evaluation of RED performance, IEEE INFOCOM [3] W. Feng et al., BLUE: A New Class of Active Queue Management Algorithms, Technical Report CSE-TR , Dept. EECS, Univ. MI, Apr [4] T. J. Ott, T. V. Lakshman, and L. H. Wong, SRED: Stabilized RED, Proc. IEEE INFOCOM 99, Mar. 999, pp [5] J. Aweya, M. Ouellette, and D. Y. Montuno, A Control Theoretic Approach to Active Queue Management, Comp. Net., vol. 36, issue 3, July, pp [6] J. Aweya, M. Ouellette, D. Y. Montuno, et al., A Comparison of Active Queue Management Algorithms Using the OPNET Modeler, IEEE Communications Magazine, June

11 VI. APPENDIX Parameter RED Minimum threshold ( min th ) Maximum threshold ( max th ) Maximum value for pb ( max p ) Queue weight (w) Buffer size (B) description - notes Its optimal value depends on the desired average queue size. If the typical traffic is fairly bursty, then min th must be correspondingly large to allow the link utilization to be maintained at an acceptably high level Its optimal value depends on the desired average queue size and in part on the maximum average delay that can be allowed by the gateway. It can be chosen from a fairly wide range, because it is only an upper bound on the actual marking probability If w is too large, then the averaging procedure will not filter out transient congestion at the gateway and if w is too low then the calculated average responds too slowly to changes in the actual queue size The actual buffer size BLUE Freeze time period Randomized to avoid global synchronization Setting based on effective-rtt Increase, Decrease drop δ f δ probability ( δ, δ ) SRED Number of zombies in the zombie list (M) The maximum drop probability ( ) p max The refresh probability to update the zombie list (P) Feedback gain(α ) Hardly affecting the average queue length, but affects the steady state Hardly affecting the average queue length Hardly affecting the average queue length Affecting to steady state Affecting average queue length than the others DRED Sampling interval ( Δ t ) Control gain (α ) Filter gain ( β ) Control target (T) No-drop threshold (L) Buffer size (B) Sets the sampling rate for the controller Controls the reaction and stability of the control system Controls the reaction speed of the filter Between min-max thresholds of RED It helps to maintain high link utilization Influences packet losses and system utilization level

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