Network Working Group B. Braden, USC/ISI Request for Comments: 2309 D. Clark, MIT LCS Category: Informational J. Crowcroft, UCL B. Davie, Cisco Systems S. Deering, Cisco Systems D. Estrin, USC S. Floyd, LBNL V. Jacobson, LBNL G. Minshall, Fiberlane C. Partridge, BBN L. Peterson, University of Arizona K. Ramakrishnan, ATT Labs Research S. Shenker, Xerox PARC J. Wroclawski, MIT LCS L. Zhang, UCLA April 1998 Recommendations on Queue Management and Congestion Avoidance in the Internet Status of Memo This memo provides information for the Internet community. It does not specify an Internet standard of any kind. Distribution of this memo is unlimited. Copyright Notice Copyright (C) The Internet Society (1998). All Rights Reserved. Abstract This memo presents two recommendations to the Internet community concerning measures to improve and preserve Internet performance. It presents a strong recommendation for testing, standardization, and widespread deployment of active queue management in routers, to improve the performance of today's Internet. It also urges a concerted effort of research, measurement, and ultimate deployment of router mechanisms to protect the Internet from flows that are not sufficiently responsive to congestion notification.
1. INTRODUCTION The Internet protocol architecture is based on a connectionless end- to-end packet service using the IP protocol. The advantages of its connectionless design, flexibility and robustness, have been amply demonstrated. However, these advantages are not without cost: careful design is required to provide good service under heavy load. In fact, lack of attention to the dynamics of packet forwarding can result in severe service degradation or "Internet meltdown". This phenomenon was first observed during the early growth phase of the Internet of the mid 1980s [Nagle84], and is technically called "congestion collapse". The original fix for Internet meltdown was provided by Van Jacobson. Beginning in 1986, Jacobson developed the congestion avoidance mechanisms that are now required in TCP implementations [Jacobson88, HostReq89]. These mechanisms operate in the hosts to cause TCP connections to "back off" during congestion. We say that TCP flows are "responsive" to congestion signals (i.e., dropped packets) from the network. It is primarily these TCP congestion avoidance algorithms that prevent the congestion collapse of today's Internet. However, that is not the end of the story. Considerable research has been done on Internet dynamics since 1988, and the Internet has grown. It has become clear that the TCP congestion avoidance mechanisms [RFC2001], while necessary and powerful, are not sufficient to provide good service in all circumstances. Basically, there is a limit to how much control can be accomplished from the edges of the network. Some mechanisms are needed in the routers to complement the endpoint congestion avoidance mechanisms. It is useful to distinguish between two classes of router algorithms related to congestion control: "queue management" versus "scheduling" algorithms. To a rough approximation, queue management algorithms manage the length of packet queues by dropping packets when necessary or appropriate, while scheduling algorithms determine which packet to send next and are used primarily to manage the allocation of bandwidth among flows. While these two router mechanisms are closely related, they address rather different performance issues. This memo highlights two router performance issues. The first issue is the need for an advanced form of router queue management that we call "active queue management." Section 2 summarizes the benefits that active queue management can bring. Section 3 describes a recommended active queue management mechanism, called Random Early Detection or "RED". We expect that the RED algorithm can be used with a wide variety of scheduling algorithms, can be implemented relatively efficiently, and will provide significant Internet
performance improvement. The second issue, discussed in Section 4 of this memo, is the potential for future congestion collapse of the Internet due to flows that are unresponsive, or not sufficiently responsive, to congestion indications. Unfortunately, there is no consensus solution to controlling congestion caused by such aggressive flows; significant research and engineering will be required before any solution will be available. It is imperative that this work be energetically pursued, to ensure the future stability of the Internet. Section 5 concludes the memo with a set of recommendations to the IETF concerning these topics. The discussion in this memo applies to "best-effort" traffic. The Internet integrated services architecture, which provides a mechanism for protecting individual flows from congestion, introduces its own queue management and scheduling algorithms [Shenker96, Wroclawski96]. Similarly, the discussion of queue management and congestion control requirements for differential services is a separate issue. However, we do not expect the deployment of integrated services and differential services to significantly diminish the importance of the best-effort traffic issues discussed in this memo. Preparation of this memo resulted from past discussions of end-to-end performance, Internet congestion, and RED in the End-to-End Research Group of the Internet Research Task Force (IRTF). 2. THE NEED FOR ACTIVE QUEUE MANAGEMENT The traditional technique for managing router queue lengths is to set a maximum length (in terms of packets) for each queue, accept packets for the queue until the maximum length is reached, then reject (drop) subsequent incoming packets until the queue decreases because a packet from the queue has been transmitted. This technique is known as "tail drop", since the packet that arrived most recently (i.e., the one on the tail of the queue) is dropped when the queue is full. This method has served the Internet well for years, but it has two important drawbacks. 1. Lock-Out In some situations tail drop allows a single connection or a few flows to monopolize queue space, preventing other connections from getting room in the queue. This "lock-out" phenomenon is often the result of synchronization or other timing effects.
2. Full Queues The tail drop discipline allows queues to maintain a full (or, almost full) status for long periods of time, since tail drop signals congestion (via a packet drop) only when the queue has become full. It is important to reduce the steady-state queue size, and this is perhaps queue management's most important goal. The naive assumption might be that there is a simple tradeoff between delay and throughput, and that the recommendation that queues be maintained in a "non-full" state essentially translates to a recommendation that low end-to-end delay is more important than high throughput. However, this does not take into account the critical role that packet bursts play in Internet performance. Even though TCP constrains a flow's window size, packets often arrive at routers in bursts [Leland94]. If the queue is full or almost full, an arriving burst will cause multiple packets to be dropped. This can result in a global synchronization of flows throttling back, followed by a sustained period of lowered link utilization, reducing overall throughput. The point of buffering in the network is to absorb data bursts and to transmit them during the (hopefully) ensuing bursts of silence. This is essential to permit the transmission of bursty data. It should be clear why we would like to have normally- small queues in routers: we want to have queue capacity to absorb the bursts. The counter-intuitive result is that maintaining normally-small queues can result in higher throughput as well as lower end-to-end delay. In short, queue limits should not reflect the steady state queues we want maintained in the network; instead, they should reflect the size of bursts we need to absorb. Besides tail drop, two alternative queue disciplines that can be applied when the queue becomes full are "random drop on full" or "drop front on full". Under the random drop on full discipline, a router drops a randomly selected packet from the queue (which can be an expensive operation, since it naively requires an O(N) walk through the packet queue) when the queue is full and a new packet arrives. Under the "drop front on full" discipline [Lakshman96], the router drops the packet at the front of the queue when the queue is full and a new packet arrives. Both of these solve the lock-out problem, but neither solves the full-queues problem described above.
We know in general how to solve the full-queues problem for "responsive" flows, i.e., those flows that throttle back in response to congestion notification. In the current Internet, dropped packets serve as a critical mechanism of congestion notification to end nodes. The solution to the full-queues problem is for routers to drop packets before a queue becomes full, so that end nodes can respond to congestion before buffers overflow. We call such a proactive approach "active queue management". By dropping packets before buffers overflow, active queue management allows routers to control when and how many packets to drop. The next section introduces RED, an active queue management mechanism that solves both problems listed above (given responsive flows). In summary, an active queue management mechanism can provide the following advantages for responsive flows. 1. Reduce number of packets dropped in routers Packet bursts are an unavoidable aspect of packet networks [Willinger95]. If all the queue space in a router is already committed to "steady state" traffic or if the buffer space is inadequate, then the router will have no ability to buffer bursts. By keeping the average queue size small, active queue management will provide greater capacity to absorb naturally- occurring bursts without dropping packets. Furthermore, without active queue management, more packets will be dropped when a queue does overflow. This is undesirable for several reasons. First, with a shared queue and the tail drop discipline, an unnecessary global synchronization of flows cutting back can result in lowered average link utilization, and hence lowered network throughput. Second, TCP recovers with more difficulty from a burst of packet drops than from a single packet drop. Third, unnecessary packet drops represent a possible waste of bandwidth on the way to the drop point. We note that while RED can manage queue lengths and reduce end- to-end latency even in the absence of end-to-end congestion control, RED will be able to reduce packet dropping only in an environment that continues to be dominated by end-to-end congestion control. 2. Provide lower-delay interactive service By keeping the average queue size small, queue management will reduce the delays seen by flows. This is particularly important for interactive applications such as short Web transfers, Telnet traffic, or interactive audio-video sessions, whose subjective
(and objective) performance is better when the end-to-end delay is low. 3. Avoid lock-out behavior Active queue management can prevent lock-out behavior by ensuring that there will almost always be a buffer available for an incoming packet. For the same reason, active queue management can prevent a router bias against low bandwidth but highly bursty flows. It is clear that lock-out is undesirable because it constitutes a gross unfairness among groups of flows. However, we stop short of calling this benefit "increased fairness", because general fairness among flows requires per-flow state, which is not provided by queue management. For example, in a router using queue management but only FIFO scheduling, two TCP flows may receive very different bandwidths simply because they have different round-trip times [Floyd91], and a flow that does not use congestion control may receive more bandwidth than a flow that does. Per-flow state to achieve general fairness might be maintained by a per-flow scheduling algorithm such as Fair Queueing (FQ) [Demers90], or a class-based scheduling algorithm such as CBQ [Floyd95], for example. On the other hand, active queue management is needed even for routers that use per-flow scheduling algorithms such as FQ or class-based scheduling algorithms such as CBQ. This is because per-flow scheduling algorithms by themselves do nothing to control the overall queue size or the size of individual queues. Active queue management is needed to control the overall average queue sizes, so that arriving bursts can be accommodated without dropping packets. In addition, active queue management should be used to control the queue size for each individual flow or class, so that they do not experience unnecessarily high delays. Therefore, active queue management should be applied across the classes or flows as well as within each class or flow. In short, scheduling algorithms and queue management should be seen as complementary, not as replacements for each other. In particular, there have been implementations of queue management added to FQ, and work is in progress to add RED queue management to CBQ.
3. THE QUEUE MANAGEMENT ALGORITHM "RED" Random Early Detection, or RED, is an active queue management algorithm for routers that will provide the Internet performance advantages cited in the previous section [RED93]. In contrast to traditional queue management algorithms, which drop packets only when the buffer is full, the RED algorithm drops arriving packets probabilistically. The probability of drop increases as the estimated average queue size grows. Note that RED responds to a time-averaged queue length, not an instantaneous one. Thus, if the queue has been mostly empty in the "recent past", RED won't tend to drop packets (unless the queue overflows, of course!). On the other hand, if the queue has recently been relatively full, indicating persistent congestion, newly arriving packets are more likely to be dropped. The RED algorithm itself consists of two main parts: estimation of the average queue size and the decision of whether or not to drop an incoming packet. (a) Estimation of Average Queue Size RED estimates the average queue size, either in the forwarding path using a simple exponentially weighted moving average (such as presented in Appendix A of [Jacobson88]), or in the background (i.e., not in the forwarding path) using a similar mechanism. Note: The queue size can be measured either in units of packets or of bytes. This issue is discussed briefly in [RED93] in the "Future Work" section. Note: when the average queue size is computed in the forwarding path, there is a special case when a packet arrives and the queue is empty. In this case, the computation of the average queue size must take into account how much time has passed since the queue went empty. This is discussed further in [RED93]. (b) Packet Drop Decision In the second portion of the algorithm, RED decides whether or not to drop an incoming packet. It is RED's particular algorithm for dropping that results in performance improvement for responsive flows. Two RED parameters, minth (minimum threshold) and maxth (maximum threshold), figure prominently in
this decision process. Minth specifies the average queue size *below which* no packets will be dropped, while maxth specifies the average queue size *above which* all packets will be dropped. As the average queue size varies from minth to maxth, packets will be dropped with a probability that varies linearly from 0 to maxp. Note: a simplistic method of implementing this would be to calculate a new random number at each packet arrival, then compare that number with the above probability which varies from 0 to maxp. A more efficient implementation, described in [RED93], computes a random number *once* for each dropped packet. Note: the decision whether or not to drop an incoming packet can be made in "packet mode", ignoring packet sizes, or in "byte mode", taking into account the size of the incoming packet. The performance implications of the choice between packet mode or byte mode is discussed further in [Floyd97]. RED effectively controls the average queue size while still accommodating bursts of packets without loss. RED's use of randomness breaks up synchronized processes that lead to lock-out phenomena. There have been several implementations of RED in routers, and papers have been published reporting on experience with these implementations ([Villamizar94], [Gaynor96]). Additional reports of implementation experience would be welcome, and will be posted on the RED web page [REDWWW]. All available empirical evidence shows that the deployment of active queue management mechanisms in the Internet would have substantial performance benefits. There are seemingly no disadvantages to using the RED algorithm, and numerous advantages. Consequently, we believe that the RED active queue management algorithm should be widely deployed. We should note that there are some extreme scenarios for which RED will not be a cure, although it won't hurt and may still help. An example of such a scenario would be a very large number of flows, each so tiny that its fair share would be less than a single packet per RTT.
4. MANAGING AGGRESSIVE FLOWS One of the keys to the success of the Internet has been the congestion avoidance mechanisms of TCP. Because TCP "backs off" during congestion, a large number of TCP connections can share a single, congested link in such a way that bandwidth is shared reasonably equitably among similarly situated flows. The equitable sharing of bandwidth among flows depends on the fact that all flows are running basically the same congestion avoidance algorithms, conformant with the current TCP specification [HostReq89]. We introduce the term "TCP-compatible" for a flow that behaves under congestion like a flow produced by a conformant TCP. A TCP- compatible flow is responsive to congestion notification, and in steady-state it uses no more bandwidth than a conformant TCP running under comparable conditions (drop rate, RTT, MTU, etc.) It is convenient to divide flows into three classes: (1) TCP- compatible flows, (2) unresponsive flows, i.e., flows that do not slow down when congestion occurs, and (3) flows that are responsive but are not TCP-compatible. The last two classes contain more aggressive flows that pose significant threats to Internet performance, as we will now discuss. o Non-Responsive Flows There is a growing set of UDP-based applications whose congestion avoidance algorithms are inadequate or nonexistent (i.e, the flow does not throttle back upon receipt of congestion notification). Such UDP applications include streaming applications like packet voice and video, and also multicast bulk data transport [SRM96]. If no action is taken, such unresponsive flows could lead to a new congestion collapse. In general, all UDP-based streaming applications should incorporate effective congestion avoidance mechanisms. For example, recent research has shown the possibility of incorporating congestion avoidance mechanisms such as Receiver- driven Layered Multicast (RLM) within UDP-based streaming applications such as packet video [McCanne96; Bolot94]. Further research and development on ways to accomplish congestion avoidance for streaming applications will be very important. However, it will also be important for the network to be able to protect itself against unresponsive flows, and mechanisms to accomplish this must be developed and deployed. Deployment of such mechanisms would provide incentive for every streaming application to become responsive by incorporating its own
congestion control. o Non-TCP-Compatible Transport Protocols The second threat is posed by transport protocol implementations that are responsive to congestion notification but, either deliberately or through faulty implementations, are not TCP- compatible. Such applications can grab an unfair share of the network bandwidth. For example, the popularity of the Internet has caused a proliferation in the number of TCP implementations. Some of these may fail to implement the TCP congestion avoidance mechanisms correctly because of poor implementation. Others may deliberately be implemented with congestion avoidance algorithms that are more aggressive in their use of bandwidth than other TCP implementations; this would allow a vendor to claim to have a "faster TCP". The logical consequence of such implementations would be a spiral of increasingly aggressive TCP implementations, leading back to the point where there is effectively no congestion avoidance and the Internet is chronically congested. Note that there is a well-known way to achieve more aggressive TCP performance without even changing TCP: open multiple connections to the same place, as has been done in some Web browsers. The projected increase in more aggressive flows of both these classes, as a fraction of total Internet traffic, clearly poses a threat to the future Internet. There is an urgent need for measurements of current conditions and for further research into the various ways of managing such flows. There are many difficult issues in identifying and isolating unresponsive or non-TCP-compatible flows at an acceptable router overhead cost. Finally, there is little measurement or simulation evidence available about the rate at which these threats are likely to be realized, or about the expected benefit of router algorithms for managing such flows. There is an issue about the appropriate granularity of a "flow". There are a few "natural" answers: 1) a TCP or UDP connection (source address/port, destination address/port); 2) a source/destination host pair; 3) a given source host or a given destination host. We would guess that the source/destination host pair gives the most appropriate granularity in many circumstances. However, it is possible that different vendors/providers could set different granularities for defining a flow (as a way of "distinguishing" themselves from one another), or that different granularities could
be chosen for different places in the network. It may be the case that the granularity is less important than the fact that we are dealing with more unresponsive flows at *some* granularity. The granularity of flows for congestion management is, at least in part, a policy question that needs to be addressed in the wider IETF community. 5. CONCLUSIONS AND RECOMMENDATIONS This discussion leads us to make the following recommendations to the IETF and to the Internet community as a whole. o RECOMMENDATION 1: Internet routers should implement some active queue management mechanism to manage queue lengths, reduce end-to-end latency, reduce packet dropping, and avoid lock-out phenomena within the Internet. The default mechanism for managing queue lengths to meet these goals in FIFO queues is Random Early Detection (RED) [RED93]. Unless a developer has reasons to provide another equivalent mechanism, we recommend that RED be used. o RECOMMENDATION 2: It is urgent to begin or continue research, engineering, and measurement efforts contributing to the design of mechanisms to deal with flows that are unresponsive to congestion notification or are responsive but more aggressive than TCP. Although there has already been some limited deployment of RED in the Internet, we may expect that widespread implementation and deployment of RED in accordance with Recommendation 1 will expose a number of engineering issues. For example, such issues may include: implementation questions for Gigabit routers, the use of RED in layer 2 switches, and the possible use of additional considerations, such as priority, in deciding which packets to drop. We again emphasize that the widespread implementation and deployment of RED would not, in and of itself, achieve the goals of Recommendation 2. Widespread implementation and deployment of RED will also enable the introduction of other new functionality into the Internet. One example of an enabled functionality would be the addition of explicit congestion notification [Ramakrishnan97] to the Internet architecture, as a mechanism for congestion notification in addition
to packet drops. A second example of new functionality would be implementation of queues with packets of different drop priorities; packets would be transmitted in the order in which they arrived, but during times of congestion packets of the lower drop priority would be preferentially dropped. 6. References [Bolot94] Bolot, J.-C., Turletti, T., and Wakeman, I., Scalable Feedback Control for Multicast Video Distribution in the Internet, ACM SIGCOMM '94, Sept. 1994. [Demers90] Demers, A., Keshav, S., and Shenker, S., Analysis and Simulation of a Fair Queueing Algorithm, Internetworking: Research and Experience, Vol. 1, 1990, pp. 3-26. [Floyd91] Floyd, S., Connections with Multiple Congested Gateways in Packet-Switched Networks Part 1: One-way Traffic. Computer Communications Review, Vol.21, No.5, October 1991, pp. 30-47. URL http://ftp.ee.lbl.gov/floyd/. [Floyd95] Floyd, S., and Jacobson, V., Link-sharing and Resource Management Models for Packet Networks. IEEE/ACM Transactions on Networking, Vol. 3 No. 4, pp. 365-386, August 1995. [Floyd97] Floyd, S., RED: Discussions of Byte and Packet Modes, March 1997 email, http://www-nrg.ee.lbl.gov/floyd/REDaveraging.txt. [Gaynor96] Gaynor, M., Proactive Packet Dropping Methods for TCP Gateways, October 1996, URL http://www.eecs.harvard.edu/~gaynor/ final.ps. [HostReq89] Braden, R., Ed., "Requirements for Internet Hosts -- Communication Layers", STD 3, RFC 1122, October 1989. [Jacobson88] V. Jacobson, Congestion Avoidance and Control, ACM SIGCOMM '88, August 1988. [Lakshman96] T. V. Lakshman, Arnie Neidhardt, Teunis Ott, The Drop From Front Strategy in TCP Over ATM and Its Interworking with Other Control Features, Infocom 96, MA28.1. [Leland94] W. Leland, M. Taqqu, W. Willinger, and D. Wilson, On the Self-Similar Nature of Ethernet Traffic (Extended Version), IEEE/ACM Transactions on Networking, 2(1), pp. 1-15, February 1994.
[McCanne96] McCanne, S., Jacobson, V., and M. Vetterli, Receiver- driven Layered Multicast, ACM SIGCOMM [Nagle84] Nagle, J., "Congestion Control in IP/TCP", RFC 896, January 1984. [Ramakrishnan97] Ramakrishnan, K. K., and S. Floyd, "A Proposal to add Explicit Congestion Notification (ECN) to IPv6 and to TCP", Work in Progress. [RED93] Floyd, S., and Jacobson, V., Random Early Detection gateways for Congestion Avoidance, IEEE/ACM Transactions on Networking, V.1 N.4, August 1993, pp. 397-413. Also available from http://ftp.ee.lbl.gov/floyd/red.html. [REDWWW] Floyd, S., The RED Web Page, 1997, URL http://ftp.ee.lbl.gov/floyd/red.html. [RFC 2001] Stevens, W., "TCP Slow Start, Congestion Avoidance, Fast Retransmit, and Fast Recovery Algorithms", RFC 2001, January 1997. [Shenker96] Shenker, S., Partridge, C., and R. Guerin, "Specification of Guaranteed Quality of Service", Work in Progress. [SRM96] Floyd. S., Jacobson, V., McCanne, S., Liu, C., and L. Zhang, A Reliable Multicast Framework for Light-weight Sessions and Application Level Framing. ACM SIGCOMM '96, pp 342-355. [Villamizar94] Villamizar, C., and Song, C., High Performance TCP in ANSNET. Computer Communications Review, V. 24 N. 5, October 1994, pp. 45-60. URL http://ftp.ans.net/pub/papers/tcp-performance.ps. [Willinger95] W. Willinger, M. S. Taqqu, R. Sherman, D. V. Wilson, Self-Similarity Through High-Variability: Statistical Analysis of Ethernet LAN Traffic at the Source Level, ACM SIGCOMM '95, pp. 100- 113, August 1995. [Wroclawski96] Wroclawski, J., "Specification of the Controlled-Load Network Element Service", Work in Progress.
Security Considerations While security is a very important issue, it is largely orthogonal to the performance issues discussed in this memo. We note, however, that denial-of-service attacks may create unresponsive traffic flows that are indistinguishable from flows from normal high-bandwidth isochronous applications, and the mechanism suggested in Recommendation 2 will be equally applicable to such attacks. Authors' Addresses Bob Braden USC Information Sciences Institute 4676 Admiralty Way Marina del Rey, CA 90292 Phone: 310-822-1511 EMail: Braden@ISI.EDU David D. Clark MIT Laboratory for Computer Science 545 Technology Sq. Cambridge, MA 02139 Phone: 617-253-6003 EMail: DDC@lcs.mit.edu Jon Crowcroft University College London Department of Computer Science Gower Street London, WC1E 6BT ENGLAND Phone: +44 171 380 7296 EMail: Jon.Crowcroft@cs.ucl.ac.uk Bruce Davie Cisco Systems, Inc. 250 Apollo Drive Chelmsford, MA 01824 Phone: EMail: firstname.lastname@example.org
Steve Deering Cisco Systems, Inc. 170 West Tasman Drive San Jose, CA 95134-1706 Phone: 408-527-8213 EMail: email@example.com Deborah Estrin USC Information Sciences Institute 4676 Admiralty Way Marina del Rey, CA 90292 Phone: 310-822-1511 EMail: Estrin@usc.edu Sally Floyd Lawrence Berkeley National Laboratory, MS 50B-2239, One Cyclotron Road, Berkeley CA 94720 Phone: 510-486-7518 EMail: Floyd@ee.lbl.gov Van Jacobson Lawrence Berkeley National Laboratory, MS 46A, One Cyclotron Road, Berkeley CA 94720 Phone: 510-486-7519 EMail: Van@ee.lbl.gov Greg Minshall Fiberlane Communications 1399 Charleston Road Mountain View, CA 94043 Phone: +1 650 237 3164 EMail: Minshall@fiberlane.com
Craig Partridge BBN Technologies 10 Moulton St. Cambridge MA 02138 Phone: 510-558-8675 EMail: firstname.lastname@example.org Larry Peterson Department of Computer Science University of Arizona Tucson, AZ 85721 Phone: 520-621-4231 EMail: LLP@cs.arizona.edu K. K. Ramakrishnan AT&T Labs. Research Rm. A155 180 Park Avenue Florham Park, N.J. 07932 Phone: 973-360-8766 EMail: KKRama@research.att.com Scott Shenker Xerox PARC 3333 Coyote Hill Road Palo Alto, CA 94304 Phone: 415-812-4840 EMail: Shenker@parc.xerox.com John Wroclawski MIT Laboratory for Computer Science 545 Technology Sq. Cambridge, MA 02139 Phone: 617-253-7885 EMail: JTW@lcs.mit.edu Lixia Zhang UCLA 4531G Boelter Hall Los Angeles, CA 90024 Phone: 310-825-2695 EMail: Lixia@cs.ucla.edu
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