Removal of the Noise Source Inherent to AQM Ajay Mansata, Salil Talauliker, Manali Joshi, and Cory Beard, Member, IEEE Abstract—Many Active Queue Management (AQM) 60 implementations drop packets randomly as a function of the average queue fill. Over a short window of time, all packets are 50 dropped with virtually equal probability. This causes the actual number of dropped packets to vary according to a binomial Queue Fill (packets) distribution, and can result in a significant difference between the 40 actual numbers of dropped packets and the expected. As a result, this introduces unnecessary noise to the system which 30 substantially affects variations in queue fill. A new approach to calculating dropping probabilities is proposed here that adapts 20 the dropping probability over a window of packets and ensures that the number of packets that are actually dropped is virtually 10 equal to the number that are expected to be dropped. It is shown here that this substantially reduces unnecessary variance in queue fill. 0 10 11 12 13 14 15 Index Terms—Active queue management, random early Time (sec) dropping. FIGURE 1 – QUEUE FILL VERSUS TIME FOR I. INTRODUCTION CONSTANT RATE TRAFFIC WITHOUT DROPPING The technique of Active Queue Management, as a CORRECTION generalized extension to Random Early Detection can be 60 applied for managing best effort traffic in two ways. 50 1. To provide early congestion feedback information to Queue Fill (packets) adaptive TCP sources. 40 2. To filter out packets from non-adaptive sources (e.g., UDP sources) to avoid unfairness in the queue. 30 When used in the context of multiple interacting 20 classes of traffic within a single queue, such as with the three drop precedence levels within an Assured 10 Forwarding Diffserv class  , AQM can also be used to provide preferential treatment to certain packets (i.e., 0 10 11 12 13 14 15 lower packet dropping probabilities) . This capability Time (sec) can be especially helpful for cases where service providers wish to support emergency traffic  or FIGURE 2 – QUEUE FILL VERSUS TIME WITH provide premium services to particular customers. DROPPING CORRECTION Regardless of the reason for its implementation, will have to be unnecessarily large to avoid tail drops, however, AQM fundamentally acts as a filter. It is used delay variation can be unfavorably large, and in the case to prevent certain packets from entering a queue based of multiple classes of traffic, packets might not be on a combination of QoS, delay, and queue stability dropped in accordance with their priorities. objectives. Therefore, if input traffic has no variation (i.e., is at One of the purposes for AQM, and really the whole a constant rate), one should see very little variation in concept of queueing itself, is to use buffering of packets queue fill. As seen in Figure 1, however, for even the to absorb temporary variations in traffic arrival rates simplest implementation of AQM using Random Early without causing packet drops. Therefore, it is not an Detection, this is not true. This is the first time this overall objective of AQM to minimize variance in queue problem has been identified and a solution proposed. fill, because one would expect and desire some variation Figure 1 shows the instantaneous queue fill for RED if the input traffic has burstiness . However, if with a link rate of 10 Mbps, constant rate input traffic of variation in queue fill is unnecessarily high, queue limits 20 Mpbs, queue size = 100 packets, fixed packet size = 4000 bits, minth=25, maxth=40, maxp=1.0, and 1 wq=0.002. Figure 2 shows results from the method presented in 0.8 this paper. The improvements are visually obvious, but Dropping Probabilty pc can also be seen numerically as a decrease in variance in 0.6 queue fill from 18.9 to 1.1. II. DROPPING CORRECTION 0.4 Many forms of AQM determine a dropping probability, pb, for a packet from some function of 0.2 current queue fill and queue fill history. Then packets are dropped by comparing outputs from a random 0 number generator to the dropping probability value. If, 0 10 20 30 40 50 over a window of N packets the dropping probability is Packet Number essentially constant, then the number of packets that will FIGURE 3 – EXAMPLE VARIATION IN CORRECTED dropped will be distributed according to a binomial DROPPING PROBABILITY distribution. Such variation in the number of packet drops is what causes the queue fill variations in Figure 1, Therefore, the exact number of packets that needs to because for a constant rate source there are no other be dropped will exactly be dropped if Npb is an integer. noise influences. And if Npb is not an integer, the difference will be less When using an averaging function to find average than one packet from Npb. This creates an elimination of queue fill, for example from  with wq=0.002, average the noise caused by the binomial distribution, except for queue fill changes slowly and the packet dropping roundoff errors. These roundoff errors are now the only probability is relatively constant over hundreds of packet cause of the variation seen in Figure 2. With a binomial arrivals. And because AQM is supposed to act as a distribution, however, an example for a 90% confidence filter, one would wish to drop as close as possible to Npb interval shows that the number of packet drops will fall packets over a window size of N. The goal is to drop within a wide interval of [42, 58] if pb = 0.5 and N = 100 Npb packets, not have packets dropped according to a (Npb = 50). binomial random variable. But it is still valuable to use Probability correction was first proposed in , but randomness to some degree to avoid bias or periodicity. there it was used to modify the distribution of times The proposed approach still incorporates between packet drops instead of modifying the variation randomness, but drops the expected number of packets in the number of packet drops. Here the variance in as follows. Given a dropping probability pb, packets are queue fill is now much less dependent on effects from dropped with a corrected probability pc, according to noise internal to AQM. The remaining sections look at Npb − cd the effect of this new approach on UDP variable rate pc = , (1) traffic and look at the dependence of the effectiveness of N − c d − ca this new approach on how the window size N is chosen. where cd is the count of the number of packets dropped III. VARIABLE RATE TRAFFIC so far in a window, and ca is the count of the number of packets accepted. These counters are reset at the As said previously, it is indeed desirable that the beginning of each new window of N arriving packets. queue fill vary in response to variations in input traffic At the beginning of the window, pc = pb, and then pc rates. However, this variation should come only in varies as the counter values change. If at some point response to input traffic, not be influenced also by Npb = cd becomes true, then all of the remaining packets internally generated noise. By implementing the will be dropped with probability zero since the number correction approach proposed here, we can see how that are to be dropped has already been accomplished. much variation is indeed in response to just the input Conversely, pc = 1 will be used for the remainder of the traffic variations. window once Npb = N – ca is reached, meaning the An AQM implementation was simulated with 6 possible number of packets that could be accepted has input sources, each exponential on-off sources with been accomplished. The last packet will always be average on times of 4 msec. and average off times of dropped with probability 1 or 0 if pb does not change 1 msec. All of the other system parameters are the same over the window and Npb is an integer. Figure 3 as for Figures 1 and 2. illustrates and example of how pc might change over a Figure 4 shows the variance in queue fill with window of 50 packets for pb = 0.5. respect to changes in average aggregate input rates. The 50 remaining system parameters are the same as for Figures 1 and 2. First of all, regardless of the choice of 40 window size in the range from 5 to 100, the variance is much lower than it would be without the probability Variance in Queue Fill Uncorrected VBR correction mechanism. Secondly, it shows that better 30 Corrected VBR Corrected CBR variance levels occur when a window size of around 20 is used. And finally, the choice of the best window size 20 appears to lie within a reasonably wide range. It is expected that the choice of window size would 10 depend on the queue averaging approach that is used. Performance will be affected depending on the number 0 of arrivals over which the average queue fill is expected 11 12 13 14 15 16 17 18 19 20 to be relatively constant. If an exponentially weighted Load (Mbps) average is used as in , and the widely used value of FIGURE 4 – VARIANCE WITH RESPECT TO INPUT wq=0.002 is used, then one can expect a rather large LOAD FOR CBR AND VBR range of window sizes to be effective, as seen in 25 Figure 5. Finding the best queue averaging approach, however, is still an open research question  . 20 V. CONCLUSION Variance in Queue Fill Corrected Uncorrected This work has shown that AQM can have 15 substantial, unnecessary queue fill variance, even for 10 constant rate traffic inputs. It presents a window-based probability correction mechanism that all but completely eliminates unnecessary queue variance, except from 5 integer roundoff errors. This simple approach yields substantial improvements in the way that Active Queue 0 Management systems can now perform. 0 20 40 60 80 100 Window Size (packets) REFERENCES FIGURE 5 – VARIANCE WITH RESPECT WINDOW  S. Blake, D. Black, M. Carlson, E. Davies, Z. Wang, W. SIZE Weiss, “An Architecture for Differentiated Service”, RFC improvement in variance that is created by use of this 2475, December 1998.  J. Heinanen, et. al., , “Assured Forwarding PHB Group”, probability correction mechanism is once again shown to RFC 2597, June 1999. be substantial. Also shown, however, is the fact that the  R. Makkar, I. Lamadaris, J. H. Salim, N. Seddigh, B. variance for constant rate traffic is still much lower than Nandy, and J. Babiarz, “Empirical study of buffer for variable rate traffic, so variable rate traffic does have management schemes for diffserv assured forwarding some ability to cause variations in queue fill. This PHB,” International Conference on Computer correction eliminates the noise source inherent to AQM Communications and Networks (ICCCN 2000), October while still allowing variance related to input traffic. 2000, pp. 632-637.  Manali Joshi, Ajay Mansata, Salil Talauliker, and Cory IV. DEPENDENCE ON PROPER CHOICE OF WINDOW SIZE Beard, "Design and Analysis of Multi-Level AQM Use of this window-based probability correction Mechanisms for Emergency Traffic," Technical Report, mechanism introduces an additional control parameter to University of Missouri-Kansas City, available at www.sce.umkc.edu/~beardc. an AQM implementation, that of the window size, N.  S. Floyd and V. Jacobson, “Random early detection Pertinent questions arise, therefore, as to the sensitivity gateways for congestion avoidance,” IEEE/ACM of system performance with respect to the window size. Transactions on Networking, vol. 1, no. 4, pp. 397-413, Of particular importance is to determine whether or not August 1993. improper selection of the window size might cause  C. V. Hollot, Yong Liu, Vishal Misra, Don Towsley, performance to be so poor that it might be better not to “Unresponsive Flows and AQM Performance,” use the correction factor. Proceedings of IEEE INFOCOM ’03, April 2003. Figure 5 shows that none of these issues cause  A. Misra, T. Ott, “Effect of exponential averaging on the substantial concern. It shows the variances in queue fill variability of a RED queue,” Proceedings of IEEE for 18 Mbps constant rate traffic on a 10 Mbps link. The International Conference on Communications (ICC), June 2001.
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