Date: Wed, 20 Jul 1994 10:13:05 -0700 From: braden@ISI.EDU (Bob Braden) Message-Id: <199407201713.AA20911@zephyr.isi.edu> To: end2end-interest@ISI.EDU, hkim@gradient.cis.upenn.edu Subject: Re: Is there a log? Actually, ISI does keep a log, but it is not publicly available at present. We could make it available, if there is interest. However, you would not find the msgs you want there. Attached are the Van Jacobson Classic messages on fast recovery/retransmit, from my private cache. This should give you something to digest... Bob Braden _______________________________________________________________ From @A.ISI.EDU:tcp-ip-RELAY@SRI-NIC.ARPA Fri Feb 12 02:52:00 1988 To: tcp-ip@sri-nic.arpa Subject: Dynamic Congestion Avoidance / Control (long message) Date: Thu, 11 Feb 88 22:17:04 PST From: Van Jacobson <van@lbl-csam.arpa> Status: RO Content-Length: 33790 X-Lines: 688 A dozen people forwarded Phil Karn's question about TCP congestion control to me, usually with pithy subject lines like "how much longer till you publish something?". I do have three RFCs and two papers in various stages of preparation, but innate laziness combined with this semester's unexpectedly large teaching load means it will probably be late spring before anything gets finished. In the interim, here's a sort-of overview of our congestion control work. I should point out these algorithms are joint work with Mike Karels of UC Berkeley (I guess my name got stuck on things because I make the presentations while Mike is off fighting the battles on EGP or routing or domains or ...). I should also mention that there's not a whole lot that's original. In particular, the two most important algorithms are quite close to (prior) work done by DEC's Raj Jain. This was by accident in one case and deliberate in the other. This stuff has been discussed on the ietf and end2end lists (Phil participated in some of those discussions and was, in fact, one of the early beta testers for our new tcp -- I have this nagging suspicion I was set up). I've appended a couple of those mail messages. Mike and I have put a number (six, actually) of new algorithms into the 4bsd tcp. Our own measurements and the reports of our beta testers suggest that the result is quite good at dealing with current, congested conditions on the Internet. The various algorithms were developed and presented at different times over the past year and it may not be clear to anyone but the developers how, or if, the pieces relate. Most of the changes spring from one observation: The flow on a TCP connection (or ISO TP-4 or XNS SPP connection) should, by the design of the protocol, obey a `conservation of packets' principle. And, if this principle were obeyed, congestion collapse would become the exception rather than the rule. Thus congestion control turns into finding places where conservation is violated and fixing them. By `conservation of packets' I mean the following: If you look at the connection "in equilibrium", i.e., running stably with a full window of data in transit, you notice that the flow is what a physicist would call "conservative": A new packet isn't put into the network until an old packet leaves. Two scientific disciplines that deal with flow, hydrodynamics and thermodynamics, predict that systems with this conservation property should be extremely robust in the face of congestion. Observation of the Arpanet or NSFNet suggests that they were not particularly robust in the face of congestion. From whence comes the discrepancy? [Someone asked me for a simple explanation of why a conservative flow system should be stable under load. I've been trying to come up with one, thus far without success -- absolutely nothing in hydrodynamics admits to simple explanations. The shortest explanation is that the inhomogenous forcing terms in the Fokker-Planck equation vanish and the remaining terms are highly damped. But I don't suppose this means much to anyone (it doesn't mean much to me). My intuition is that conservation means there's never an `energy difference' between the outside world and the system that the system could use to `pump up' an instability to a state of collapse. Thus the only mechanism the system can use for self-destruction is to re-arrange its internal energy and create a difference large enough to break something. But entropy (or diffusion) always trys to erase large internal energy differences so collapse via these mechanisms is improbable. Possible, but improbable, at least until the load gets so outrageous that collective, non-ergodic effects start to dominate the overall behavior.] Packet conservation can fail three ways: 1) the connection doesn't get to equilibrium, or 2) a sender injects a packet before an old packet has exited, or 3) the equilibrium can't be reached because of resource limits along the path. (1) has to be from a connection starting or restarting after a packet loss. Another way to look at the conservation property is to say that the sender uses acks as a "clock" to strobe new packets into the network. Since the receiver can generate acks no faster than data packets can get through the network, the protocol is "self clocking" (an ack can't go in until a packet comes out, a packet can't go in until an ack comes out). Self clocking systems automatically adjust to bandwidth and delay variations and have a wide dynamic range (an important issue when you realize that TCP spans everything from 800 Mbit/sec Cray channels to 1200 bit/sec packet radio links). But the same thing that makes a self-clocked system stable when it's running makes it hard to get started -- to get data flowing you want acks to clock packets out but to get acks you have to have data flowing. To get the `clock' started, we came up with an algorithm called slow-start that gradually increases the amount of data flowing. Although we flatter ourselves that the design of this algorithm is quite subtle, the implementation is trivial -- 3 lines of code and one new state variable in the sender: 1) whenever you're starting or restarting after a loss, set your "congestion window" to 1 packet. 2) when you get an ack for new data, increase the congestion window by one packet. 3) when you send, send the minimum of the receiver's advertised window and the congestion window. (This is quite similar to Raj Jain's CUTE algorithm described in IEEE Transactions on Communications, Oct, '86, although we didn't know about CUTE at the time we were developing slowstart). Actually, the slow-start window increase isn't all that gradual: The window opening takes time proportional to log2(W) where W is the window size in packets. This opens the window fast enough to have a negligible effect on performance, even on links that require a very large window. And the algorithm guarantees that a connection will source data at a rate at most twice the maximum possible on the path. (Without slow-start, by contrast, when 10Mb ethernet hosts talk over the 56Kb Arpanet via IP gateways, the gateways see a window's worth of packets (8-16) delivered at 200 times the path bandwidth.) Once you can reliably start data flowing, problems (2) and (3) have to be addressed. Assuming that the protocol implementation is correct, (2) must represent a failure of sender's retransmit timer. A good round trip time estimator (the core of the retransmit timer) is the single most important feature of any protocol implementation that expects to survive heavy load. And it almost always gets botched. One mistake seems to be not estimating the variance of the rtt. >From queuing theory we know that rtt and rtt variation increase very quickly with load. Measuring the load by rho (the ratio of average arrival rate to average departure rate), the rtt goes up like 1/(1-rho) and the variation in rtt goes like 1/(1-rho)^2. To make this concrete, if the network is running at 75% of capacity (as the Arpanet was in last April's collapse), you should expect rtt to vary by a factor of 16 around its mean value. The RFC793 parameter "beta" accounts for rtt variation. The suggested value of "2" can adapt to loads of at most 30%. Above this point, a connection will respond to load increases by retransmitting packets that have only been delayed in transit. This makes the network do useless work (wasting bandwidth on duplicates of packets that have been or will be delivered) at a time when it's known to be having trouble with useful work. I.e., this is the network equivalent of pouring gasoline on a fire. We came up a cheap method for estimating variation (see first of attached msgs) and the resulting retransmit timer essentially eliminates spurious retransmissions. A pleasant side effect of estimating "beta" rather than using a fixed value is that low load as well as high load performance improves, particularly over high delay paths such as satellite links. Another timer mistake seems to be in the backoff after a retransmit: If we have to retransmit a packet more than once, how should the retransmits be spaced? It turns out there's only one scheme that's likely to work, exponential backoff, but proving this is a bit involved (one of the two papers alluded to in to opening goes through a proof). We might finesse a proof by noting that a network is, to a very good approximation, a linear system. (That is, it is composed of elements that behave like linear operators -- integrators, delays, gain stages, etc.). Linear system theory says that if a system is stable, the stability is exponential. This suggests that if we have a system that is unstable (a network subject to random load shocks and prone to congestive collapse), the way to stabilize it is to add some exponential damping (read: exponential timer backoff) to its primary excitation (read: senders, traffic sources). Once the timers are in good shape, you can state with some confidence that a timeout really means a lost packet and not a busted timer. At this point you can do something about (3). Packets can get lost for two reasons: they are damaged in transit or the network is congested and somewhere on the path there was insufficient buffer capacity. On most of the network paths we use, loss due to damage is rare (<<1%) so it is very probable that a packet loss is due to congestion in the network. Say we try to develop a `congestion avoidance' strategy like the one Raj Jain, et.al., propose in DEC TR506 and ISO 8473. It must have two components: The network must be able to signal the transport endpoints that congestion is occurring (or about to occur). And the endpoints must have a policy that decreases utilization if this signal is received and increases utilization if the signal isn't received. If packet loss is (almost) always due to congestion and if a timeout is (almost) always due to a lost packet, we have a good candidate for the `network is congested' signal. Particularly since this signal is delivered automatically by all existing networks, without special modification (as opposed to, say, ISO 8473 which requires a new bit in the packet headers and a mod to *all* existing gateways to set this bit). [As a (lengthy) aside: Using `lost packets' to communicate information seems to bother people. The second of the two papers mentioned above is devoted to analytic and simulation investigations of our algorithm under various network conditions. I'll briefly mention some of the objections we've heard and, I think, addressed. There have been claims that signaling congestion via dropping packets will adversely affect total throughput (it's easily proved that the opposite is true) or that this signal will be `too slow' compared to alternatives (The fundamental frequency of the system is set by its average round trip time. From control theory and Nyquist's theorem, any control strategy that attempts to respond in less than two round trip times will be unstable. A packet loss is detected in at most two rtt, the minimum stable response time). There have also been claims that this scheme will result in unfair or sub-optimal resource allocation (this is untrue if equivalent implementations of ISO and our schemes are compared) or that mistaking damage for congestion will unnecessarily throttle the endpoints on some paths with a high intrinsic loss rate (this is mostly untrue -- the scheme we propose is analytically tractable so we've worked out its behavior under random loss. It turns out that window flow control schemes just don't handle high loss rates well and throughput of a vanilla TCP under high, random loss is abysmal. Adding our congestion control scheme makes things slightly worse but the practical difference is negligible. As an example (that we have calculated and Jon Crowcroft at UCL has measured), it takes 40 256-byte packets to fill the Satnet pipe. Satnet currently shows a random, 1% average packet loss. The maximum throughput a vanilla tcp could achieve at this loss rate is 56% of the 40kbs channel bandwidth. The maximum throughput our TCP can achieve at this loss rate is 49% of the channel bandwidth. In theory, the use of dynamic congestion control should allow one to achieve much better throughput under high loss than is possible with normal TCP -- performance comparable to, say, NETBLT over the same lossy link. The reason is that regular TCP tries to communicate two different things with one number (the window field in the packet): the amount of buffer the receiver has available and the delay-bandwidth product of the pipe. Our congestion control scheme separates these two numbers. The sender estimates the pipe size so the receiver window need only describe the receiver's buffer size. As long as the receiver advertises a sufficiently large buffer, (twice the delay- bandwidth product) a 1% loss rate would translate into a 1% throughput effect, not a factor-of-two effect. Of course, we have yet to put this theory to test.] The other part of a congestion avoidance strategy, the endnode action, is almost identical in Jain's DEC/ISO scheme and our TCP. This is not an accident (we copied Jain's scheme after hearing his presentation at the Boston IETF & realizing that the scheme was, in a sense, universal): The endnode strategy follows directly from a first-order time-series model of the network. Say we measure network `load' by average queue length over fixed intervals of some appropriate length (something near the rtt). If L(i) is the load at interval i, a network not subject to congestion can be modeled by saying L(i) changes slowly compared to the sampling time. I.e., L(i) = N (the average queue length doesn't change over time). If the network is subject to congestion, this zero'th order model breaks down. The average queue length becomes the sum of two terms, the N above that accounts for the average arrival rate of new traffic and a new term that accounts for the left-over traffic from the last time interval: L(i) = N + a L(i-1) (As pragmatists, we extend the original model just enough to explain the new behavior. What we're doing here is taking the first two terms in a taylor series expansion of L(t) when we find that just the first term is inadequate. There is reason to believe one would eventually need a three term, second order model, but not until the Internet has grown to several times its current size.) When the network is congested, the `a' term must be large and the load (queues) will start increasing exponentially. The only way to stabilize the system is if the traffic sources throttle back at least as fast as the queues are growing. Since the way a source controls load in a window-based protocol is to adjust the size of the window, W, we end up with the sender policy On congestion: W(i) = d W(i-1) (d < 1) I.e., a multiplicative decrease of the window size. (This will turn into an exponential decrease over time if the congestion persists.) If there's no congestion, the `a' term must be near zero and the network load is about constant. You have to try to increase the bandwidth you're using to find out the current limit (e.g., you could have been sharing the path with someone else and converged to a window that gives you each half the available bandwidth. If he shuts down, 50% of the bandwidth will get wasted unless you make some effort to increase your window size.) What should the increase policy be? The first thought is to use a symmetric, multiplicative increase, possibly with a longer time constant. E.g., W(i) = b W(i-1), 1 < b <= 1/d. This is a mistake. The result will oscillate wildly and, on the average, deliver poor throughput. The reason why is tedious to explain. It has to do with that fact that it is easy to drive the net into saturation but hard for the net to recover (what Kleinrock, vol.2, calls the "rush-hour effect"). Thus overestimating the available bandwidth is costly. But an exponential, almost regardless of its time constant, increases so quickly that large overestimates are inevitable. Without justification, I'll simply state that the best increase policy is to make small, constant changes to the window size (if you've had a control theory course, you've seen the justification): On no congestion: W(i) = W(i-1) + u (u << the path delay- bandwidth product) I.e., an additive increase policy. This is exactly the policy that Jain, et.al., suggest in DEC TR-506 and exactly the policy we've implemented in TCP. The only difference in our implementations is the choice of constants for `d' and `u'. We picked .5 and 1 for reasons that are partially explained in the second of the attached messages. A more complete analysis is in the second in-progress paper (and may be discussed at the upcoming IETF meeting). All of the preceding has probably made it sound as if the dynamic congestion algorithm is hairy but it's not. Like slow-start, it turns out to be three lines of code and one new connection state variable (the combined slow-start/congestion control algorithm is described in the second of the attached msgs). That covers about everything that's been done to date. It's about 1/3 of what we think clearly needs to be done. The next big step is to do the gateway `congestion detection' algorithms so that a signal is sent to the endnodes as early as possible (but not so early that the gateway ends up starved for traffic). The way we anticipate doing these algorithms, gateway `self protection' from a mis-behaving host will fall-out for free (that host will simply have most of its packets dropped as the gateway trys to tell it that it's using more than its fair share). Thus, like the endnode algorithm, the gateway algorithm will improve things even if no endnode is modified to do dynamic congestion avoidance. And nodes that do implement congestion avoidance will get their fair share of bandwidth and a minimum number of packet drops. Since congestion grows exponentially, detecting it early is important. (If it's detected early, small adjustments to the senders' windows will cure it. Otherwise massive adjustments will be necessary to give the net enough spare capacity to pump out the backlog.) But, given the bursty nature of traffic, reliable detection is a non-trivial problem. There is a scheme proposed in DEC TR-506 but we think it might have convergence problems under high load and/or significant second-order dynamics in the traffic. We are thinking of using some of our earlier work on ARMAX models for rtt/queue length prediction as the basis of the detection. Preliminary results suggest that this approach works well at high load, is immune to second-order effects in the traffic and is cheap enough to compute that it wouldn't slow down thousand-packet-per-second gateways. In addition to the gateway algorithms, we want to apply the endnode algorithms to connectionless traffic (e.g., domain server queries, RPC requests). We have the rate-based equivalent of the TCP window algorithm worked out (there should be a message describing it on the tcp list sometime in the near future). Sun Microsystems has been very interested, and supportive, during the development of the TCP congestion control (I believe Sun OS 4.0 will ship with our new TCP) and Sun has offered to cooperate in developing the RPC dynamic congestion control algorithms, using NFS as a test-bed (since NFS is known to have congestion problems). The far future holds some work on controlling second-order, non- ergodic effects, adaptively determining the rate constants in the control algorithm, and some other things that are too vague to mention. - Van ---------------------------- To: markl@PTT.LCS.MIT.EDU Subject: Re: interpacket arrival variance and mean In-reply-to: Your message of Mon, 08 Jun 87 12:31:33 EDT. Date: Mon, 15 Jun 87 06:08:01 PDT From: Van JacobsonMark - I'm working on long paper about transport protocol timers (models, estimation, implementations, common implementation mistakes, etc.). This has me all primed on the subject so attached is a long-winded explanation and example C code for estimating the mean and variance of a series of measurements. Though I know your application isn't tcp, I'm going to use a new tcp retransmit timer algorithm as an example. The algorithm illustrates the method and, based on 3 months of experiment, is much better than the algorithm in rfc793 (though it isn't as good as the algorithm I talked about at IETF and am currently debugging). Theory ------ You're probably familiar with the rfc793 algorithm for estimating the mean round trip time. This is the simplest example of a class of estimators called "recursive prediction error" or "stochastic gradient" algorithms. In the past 20 years these algorithms have revolutionized estimation and control theory so it's probably worth while to look at the rfc793 estimator in some detail. Given a new measurement, Meas, of the rtt, tcp updates an estimate of the average rtt, Avg, by Avg <- (1 - g) Avg + g Meas where g is a "gain" (0 < g < 1) that should be related to the signal- to-noise ratio (or, equivalently, variance) of Meas. This makes a bit more sense (and computes faster) if we rearrange and collect terms multiplied by g to get Avg <- Avg + g (Meas - Avg) We can think of "Avg" as a prediction of the next measurement. So "Meas - Avg" is the error in that prediction and the expression above says we make a new prediction based on the old prediction plus some fraction of the prediction error. The prediction error is the sum of two components: (1) error due to "noise" in the measurement (i.e., random, unpredictable effects like fluctuations in competing traffic) and (2) error due to a bad choice of "Avg". Calling the random error RE and the predictor error PE, Avg <- Avg + g RE + g PE The "g PE" term gives Avg a kick in the right direction while the "g RE" term gives it a kick in a random direction. Over a number of samples, the random kicks cancel each other out so this algorithm tends to converge to the correct average. But g represents a compromise: We want a large g to get mileage out of the PE term but a small g to minimize the damage from the RE term. Since the PE terms move Avg toward the real average no matter what value we use for g, it's almost always better to use a gain that's too small rather than one that's too large. Typical gain choices are .1 - .2 (though it's always a good idea to take long look at your raw data before picking a gain). It's probably obvious that Avg will oscillate randomly around the true average and the standard deviation of Avg will be something like g sdev(Meas). Also that Avg converges to the true average exponentially with time constant 1/g. So making g smaller gives a stabler Avg at the expense of taking a much longer time to get to the true average. [My paper makes the preceding hand-waving a bit more rigorous but I assume no one cares about rigor. If you do care, check out almost any text on digital filtering or estimation theory.] If we want some measure of the variation in Meas, say to compute a good value for the tcp retransmit timer, there are lots of choices. Statisticians love variance because it has some nice mathematical properties. But variance requires squaring (Meas - Avg) so an estimator for it will contain two multiplies and a large chance of integer overflow. Also, most of the applications I can think of want variation in the same units as Avg and Meas, so we'll be forced to take the square root of the variance to use it (i.e., probably at least a divide, multiply and two adds). A variation measure that's easy to compute, and has a nice, intuitive justification, is the mean prediction error or mean deviation. This is just the average of abs(Meas - Avg). Intuitively, this is an estimate of how badly we've blown our recent predictions (which seems like just the thing we'd want to set up a retransmit timer). Statistically, standard deviation (= sqrt variance) goes like sqrt(sum((Meas - Avg)^2)) while mean deviation goes like sum(sqrt((Meas - Avg)^2)). Thus, by the triangle inequality, mean deviation should be a more "conservative" estimate of variation. If you really want standard deviation for some obscure reason, there's usually a simple relation between mdev and sdev. Eg., if the prediction errors are normally distributed, mdev = sqrt(pi/2) sdev. For most common distributions the factor to go from sdev to mdev is near one (sqrt(pi/2) ~= 1.25). Ie., mdev is a good approximation of sdev (and is much easier to compute). Practice -------- So let's do estimators for Avg and mean deviation, Mdev. Both estimators compute means so we get two instances of the rfc793 algorithm: Err = abs (Meas - Avg) Avg <- Avg + g (Meas - Avg) Mdev <- Mdev + g (Err - Mdev) If we want to do the above fast, it should probably be done in integer arithmetic. But the expressions contain fractions (g < 1) so we'll have to do some scaling to keep everything integer. If we chose g so that 1/g is an integer, the scaling is easy. A particularly good choice for g is a reciprocal power of 2 (ie., g = 1/2^n for some n). Multiplying through by 1/g gives 2^n Avg <- 2^n Avg + (Meas - Avg) 2^n Mdev <- 2^n Mdev + (Err - Mdev) To minimize round-off error, we probably want to keep the scaled versions of Avg and Mdev rather than the unscaled versions. If we pick g = .125 = 1/8 (close to the .1 that rfc793 suggests) and express all the above in C: Meas -= (Avg >> 3); Avg += Meas; if (Meas < 0) Meas = -Meas; Meas -= (Mdev >> 3); Mdev += Meas; I've been using a variant of this to compute the retransmit timer for my tcp. It's clearly faster than the two floating point multiplies that 4.3bsd uses and gives you twice as much information. Since the variation is estimated dynamically rather than using the wired-in beta of rfc793, the retransmit performance is also much better: faster retransmissions on low variance links and fewer spurious retransmissions on high variance links. It's not necessary to use the same gain for Avg and Mdev. Empirically, it looks like a retransmit timer estimate works better if there's more gain (bigger g) in the Mdev estimator. This forces the timer to go up quickly in response to changes in the rtt. (Although it may not be obvious, the absolute value in the calculation of Mdev introduces an asymmetry in the timer: Because Mdev has the same sign as an increase and the opposite sign of a decrease, more gain in Mdev makes the timer go up fast and come down slow, "automatically" giving the behavior Dave Mills suggests in rfc889.) Using a gain of .25 on the deviation and computing the retransmit timer, rto, as Avg + 2 Mdev, my tcp timer code looks like: Meas -= (Avg >> 3); Avg += Meas; if (Meas < 0) Meas = -Meas; Meas -= (Mdev >> 2); Mdev += Meas; rto = (Avg >> 3) + (Mdev >> 1); Hope this helps. - Van --------------------------------- To: jain%erlang.DEC@decwrl.dec.com (Raj Jain, LKG1-2/A19, DTN: 226-7642) Cc: ietf@gateway.mitre.org Subject: Re: Your congestion scheme In-Reply-To: Your message of 03 Nov 87 12:51:00 GMT. Date: Mon, 16 Nov 87 06:03:29 PST From: Van Jacobson Raj, Thanks for the note. I hope you'll excuse my taking the liberty of cc'ing this reply to the ietf: At the last meeting there was a great deal of interest in your congestion control scheme and our adaptation of it. > I am curious to know what values of increase amount and decrease > factor did you use. In our previous study on congestion using > timeout (CUTE scheme, IEEE JSAC, Oct 1986), we had found that the > decrease factor should be small since packet losses are > expensive. In fact, we found that a decrease factor of zero > (decreasing to one) was the best. We use .5 for the decrease factor and 1 for the increase factor. We also use something very close to CUTE (Mike Karels and I were behind on our journal reading so we independently rediscovered the algorithm and called it slow-start). Since we use a lost packet as the "congestion experienced" indicator, the CUTE algorithm and the congestion avoidance algorithm (BTW, have you picked a name for it yet?) get run together, even though they are logically distinct. The sender keeps two state variables for congestion control: a congestion window, cwnd, and a threshhold size, ssthresh, to switch between the two algorithms. The sender's output routine sends the minimum of cwnd and the window advertised by the receiver. The rest of the congestion control sender code looks like: On a timeout, record half the current window size as "ssthresh" (this is the multiplicative decrease part of the congestion avoidance algorithm), then set the congestion window to 1 packet and call the output routine (this initiates slowstart/CUTE). When new data is acked, the sender does something like if (cwnd < ssthresh) // if we're still doing slowstart cwnd += 1 packet // open the window exponentially else cwnd += 1/cwnd // otherwise do the Congestion // Avoidance increment-by-1 Notice that our variation of CUTE opens the window exponentially in time, as opposed to the linear scheme in your JSAC article. We looked at a linear scheme but were concerned about the performance hit on links with a large bandwidth-delay product (ie., satellite links). An exponential builds up fast enough to accomodate any bandwidth-delay and our testing showed no more packet drops with exponential opening that with linear opening. (My model of what slowstart is doing -- starting an ack "clock" to meter out packets -- suggested that there should be no loss-rate difference between the two policies). The reason for the 1/2 decrease, as opposed to the 7/8 you use, was the following hand-waving: When a packet is dropped, you're either starting (or restarting after a drop) or steady-state sending. If you're starting, you know that half the current window size "worked", ie., that a window's worth of packets were exchanged with no drops (slowstart guarantees this). Thus on congestion you set the window to the largest size that you know works then slowly increase the size. If the connection is steady-state running and a packet is dropped, it's probably because a new connection started up and took some of your bandwidth. We usually run our nets with rho <= .5 so it's probable that there are now exactly two conversations sharing the bandwidth. Ie., that you should reduce your window by half because the bandwidth available to you has been reduced to half. And, if there are more than two conversations sharing the bandwidth, halving your window is conservative -- and being conservative at high traffic intensities is probably wise. Obviously, this large decrease term is accounting for the high cost of our "congestion experienced" indicator compared to yours -- a dropped packet vs. a bit in the ack. If the DEC bit were available, the preceding "logic" should be ignored. But I wanted tcp congestion avoidance that we could deploy immediately and incrementally, without adding code to the hundreds of Internet gateways. So using dropped packets seemed like the only choice. And, in system terms, the cost isn't that high: Currently packets are dropped only when a large queue has formed. If we had a bit to force senders to reduce their windows, we'd still be stuck with the queue since we'd still be running the bottleneck at 100% utilization so there's no excess bandwidth available to dissipate the queue. If we toss a packet, a sender will shut up for 2 rtt, exactly the time we need to empty the queue (in the ususal case). If that sender restarts with the correct window size the queue won't reform. Thus we've reduced the delay to minimum without the system losing any bottleneck bandwidth. The 1-packet increase has less justification that the .5 decrease. In fact, it's almost certainly too large. If the algorithm converges to a window size of w, you get O(w^2) packets between drops with an additive increase policy. We were shooting for an average drop rate of <1% and found that on the Arpanet (the worst case of the 4 networks we tested), windows converged to 8 - 12 packets. This yields 1 packet increments for a 1% average drop rate. But, since we've done nothing in the gateways, the window we converge to is the maximum the gateway can accept without dropping packets. I.e., in the terms you used, we are just to the left of the cliff rather than just to the right of the knee. If we now fix the gateways so they start dropping packets when the queue gets pushed past the knee, our increment will be much too agressive and we'll have to drop it by at least a factor of 4 (since all my measurements on an unloaded Arpanet or Milnet place their "pipe size" at 4-5 packets). Mike and I have talked about a second order control loop to adaptively determine the appropriate increment to use for a path (there doesn't seem to be much need to adjust the decrement). It looks trivial to implement such a loop (since changing the increment affects the frequency of oscillation but not the mean window size, the loop would affect rate of convergence but not convergence and (first-order) stability). But we think 2nd order stuff should wait until we've spent some time on the 1st order part of the algorithm for the gateways. I'm tired and probably no longer making sense. I think I'll head home and get some sleep. Hope to hear from you soon. Cheers. - Van >From van@helios.ee.lbl.gov Mon Apr 30 01:44:05 1990 To: end2end-interest@ISI.EDU Subject: modified TCP congestion avoidance algorithm Date: Mon, 30 Apr 90 01:40:59 PDT From: Van Jacobson Status: RO Content-Length: 12896 X-Lines: 297 This is a description of the modified TCP congestion avoidance algorithm that I promised at the teleconference. BTW, on re-reading, I noticed there were several errors in Lixia's note besides the problem I noted at the teleconference. I don't know whether that's because I mis-communicated the algorithm at dinner (as I recall, I'd had some wine) or because she's convinced that TCP is ultimately irrelevant :). Either way, you will probably be disappointed if you experiment with what's in that note. First, I should point out once again that there are two completely independent window adjustment algorithms running in the sender: Slow-start is run when the pipe is empty (i.e., when first starting or re-starting after a timeout). Its goal is to get the "ack clock" started so packets will be metered into the network at a reasonable rate. The other algorithm, congestion avoidance, is run any time *but* when (re-)starting and is responsible for estimating the (dynamically varying) pipesize. You will cause yourself, or me, no end of confusion if you lump these separate algorithms (as Lixia's message did). The modifications described here are only to the congestion avoidance algorithm, not to slow-start, and they are intended to apply to large bandwidth-delay product paths (though they don't do any harm on other paths). Remember that with regular TCP (or with slow-start/c-a TCP), throughput really starts to go to hell when the probability of packet loss is on the order of the bandwidth-delay product. E.g., you might expect a 1% packet loss rate to translate into a 1% lower throughput but for, say, a TCP connection with a 100 packet b-d p. (= window), it results in a 50-75% throughput loss. To make TCP effective on fat pipes, it would be nice if throughput degraded only as function of loss probability rather than as the product of the loss probabilty and the b-d p. (Assuming, of course, that we can do this without sacrificing congestion avoidance.) These mods do two things: (1) prevent the pipe from going empty after a loss (if the pipe doesn't go empty, you won't have to waste round-trip times re-filling it) and (2) correctly account for the amount of data actually in the pipe (since that's what congestion avoidance is supposed to be estimating and adapting to). For (1), remember that we use a packet loss as a signal that the pipe is overfull (congested) and that packet loss can be detected one of two different ways: (a) via a retransmit timeout or (b) when some small number (3-4) of consecutive duplicate acks has been received (the "fast retransmit" algorithm). In case (a), the pipe is guaranteed to be empty so we must slow-start. In case (b), if the duplicate ack threshhold is small compared to the bandwidth-delay product, we will detect the loss with the pipe almost full. I.e., given a threshhold of 3 packets and an LBL-MIT bandwidth-delay of around 24KB or 16 packets (assuming 1500 byte MTUs), the pipe is 75% full when fast-retransmit detects a loss (actually, until gateways start doing some sort of congestion control, the pipe is overfull when the loss is detected so *at least* 75% of the packets needed for ack clocking are in transit when fast-retransmit happens). Since the pipe is full, there's no need to slow-start after a fast-retransmit. For (2), consider what a duplicate ack means: either the network duplicated a packet (i.e., the NSFNet braindead IBM token ring adapters) or the receiver got an out-of-order packet. The usual cause of out-of-order packets at the receiver is a missing packet. I.e., if there are W packets in transit and one is dropped, the receiver will get W-1 out-of-order and (4.3-tahoe TCP will) generate W-1 duplicate acks. If the `consecutive duplicates' threshhold is set high enough, we can reasonably assume that duplicate acks mean dropped packets. But there's more information in the ack: The receiver can only generate one in response to a packet arrival. I.e., a duplicate ack means that a packet has left the network (it is now cached at the receiver). If the sender is limitted by the congestion window, a packet can now be sent. (The congestion window is a count of how many packets will fit in the pipe. The ack says a packet has left the pipe so a new one can be added to take its place.) To put this another way, say the current congestion window is C (i.e, C packets will fit in the pipe) and D duplicate acks have been received. Then only C-D packets are actually in the pipe and the sender wants to use a window of C+D packets to fill the pipe to its estimated capacity (C+D sent - D received = C in pipe). So, conceptually, the slow-start/cong.avoid/fast-rexmit changes are: - The sender's input routine is changed to set `cwnd' to `ssthresh' when the dup ack threshhold is reached. [It used to set cwnd to mss to force a slow-start.] Everything else stays the same. - The sender's output routine is changed to use an effective window of min(snd_wnd, cwnd + dupacks*mss) [the change is the addition of the `dupacks*mss' term.] `Dupacks' is zero until the rexmit threshhold is reached and zero except when receiving a sequence of duplicate acks. The actual implementation is slightly different than the above because I wanted to avoid the multiply in the output routine (multiplies are expensive on some risc machines). A diff of the old and new fastrexmit code is attached (your line numbers will vary). Note that we still do congestion avoidance (i.e., the window is reduced by 50% when we detect the packet loss). But, as long as the receiver's offered window is large enough (it needs to be at most twice the bandwidth-delay product), we continue sending packets (at exactly half the rate we were sending before the loss) even after the loss is detected so the pipe stays full at exactly the level we want and a slow-start isn't necessary. Some algebra might make this last clear: Say U is the sequence number of the first un-acked packet and we are using a window size of W when packet U is dropped. Packets [U..U+W) are in transit. When the loss is detected, we send packet U and pull the window back to W/2. But in the round-trip time it takes the U retransmit to fill the receiver's hole and an ack to get back, W-1 dup acks will arrive (one for each packet in transit). The window is effectively inflated by one packet for each of these acks so packets [U..U+W/2+W-1) are sent. But we don't re-send packets unless we know they've been lost so the amount actually sent between the loss detection and the recovery ack is U+W/2+W-1 - U+W = W/2-1 which is exactly the amount congestion avoidance allows us to send (if we add in the rexmit of U). The recovery ack is for packet U+W so when the effective window is pulled back from W/2+W-1 to W/2 (which happens because the recovery ack is `new' and sets dupack to zero), we are allowed to send up to packet U+W+W/2 which is exactly the first packet we haven't yet sent. (I.e., there is no sudden burst of packets as the `hole' is filled.) Also, when sending packets between the loss detection and the recovery ack, we do nothing for the first W/2 dup acks (because they only allow us to send packets we've already sent) and the bottleneck gateway is given W/2 packet times to clean out its backlog. Thus when we start sending our W/2-1 new packets, the bottleneck queue is as empty as it can be. [I don't know if you can get the flavor of what happens from this description -- it's hard to see without a picture. But I was delighted by how beautifully it worked -- it was like watching the innards of an engine when all the separate motions of crank, pistons and valves suddenly fit together and everything appears in exactly the right place at just the right time.] Also note that this algorithm interoperates with old tcp's: Most pre-tahoe tcp's don't generate the dup acks on out-of-order packets. If we don't get the dup acks, fast retransmit never fires and the window is never inflated so everything happens in the old way (via timeouts). Everything works just as it did without the new algorithm (and just as slow). If you want to simulate this, the intended environment is: - large bandwidth-delay product (say 20 or more packets) - receiver advertising window of two b-d p (or, equivalently, advertised window of the unloaded b-d p but two or more connections simultaneously sharing the path). - average loss rate (from congestion or other source) less than one lost packet per round-trip-time per active connection. (The algorithm works at higher loss rate but the TCP selective ack option has to be implemented otherwise the pipe will go empty waiting to fill the second hole and throughput will once again degrade at the product of the loss rate and b-d p. With selective ack, throughput is insensitive to b-d p at any loss rate.) And, of course, we should always remember that good engineering practise suggests a b-d p worth of buffer at each bottleneck -- less buffer and your simulation will exhibit the interesting pathologies of a poorly engineered network but will probably tell you little about the workings of the algorithm (unless the algorithm misbehaves badly under these conditions but my simulations and measurements say that it doesn't). In these days of $100/megabyte memory, I dearly hope that this particular example of bad engineering is of historical interest only. - Van ----------------- *** /tmp/,RCSt1a26717 Mon Apr 30 01:35:17 1990 --- tcp_input.c Mon Apr 30 01:33:30 1990 *************** *** 834,850 **** * Kludge snd_nxt & the congestion * window so we send only this one ! * packet. If this packet fills the ! * only hole in the receiver's seq. ! * space, the next real ack will fully ! * open our window. This means we ! * have to do the usual slow-start to ! * not overwhelm an intermediate gateway ! * with a burst of packets. Leave ! * here with the congestion window set ! * to allow 2 packets on the next real ! * ack and the exp-to-linear thresh ! * set for half the current window ! * size (since we know we're losing at ! * the current window size). */ if (tp->t_timer[TCPT_REXMT] == 0 || --- 834,850 ---- * Kludge snd_nxt & the congestion * window so we send only this one ! * packet. ! * ! * We know we're losing at the current ! * window size so do congestion avoidance ! * (set ssthresh to half the current window ! * and pull our congestion window back to ! * the new ssthresh). ! * ! * Dup acks mean that packets have left the ! * network (they're now cached at the receiver) ! * so bump cwnd by the amount in the receiver ! * to keep a constant cwnd packets in the ! * network. */ if (tp->t_timer[TCPT_REXMT] == 0 || *************** *** 853,864 **** else if (++tp->t_dupacks == tcprexmtthresh) { tcp_seq onxt = tp->snd_nxt; ! u_int win = ! MIN(tp->snd_wnd, tp->snd_cwnd) / 2 / ! tp->t_maxseg; if (win < 2) win = 2; tp->snd_ssthresh = win * tp->t_maxseg; - tp->t_timer[TCPT_REXMT] = 0; tp->t_rtt = 0; --- 853,864 ---- else if (++tp->t_dupacks == tcprexmtthresh) { tcp_seq onxt = tp->snd_nxt; ! u_int win = MIN(tp->snd_wnd, ! tp->snd_cwnd); + win /= tp->t_maxseg; + win >>= 1; if (win < 2) win = 2; tp->snd_ssthresh = win * tp->t_maxseg; tp->t_timer[TCPT_REXMT] = 0; tp->t_rtt = 0; *************** *** 866,873 **** tp->snd_cwnd = tp->t_maxseg; (void) tcp_output(tp); ! if (SEQ_GT(onxt, tp->snd_nxt)) tp->snd_nxt = onxt; goto drop; } } else --- 866,879 ---- tp->snd_cwnd = tp->t_maxseg; (void) tcp_output(tp); ! tp->snd_cwnd = tp->snd_ssthresh + ! tp->t_maxseg * ! tp->t_dupacks; if (SEQ_GT(onxt, tp->snd_nxt)) tp->snd_nxt = onxt; goto drop; + } else if (tp->t_dupacks > tcprexmtthresh) { + tp->snd_cwnd += tp->t_maxseg; + (void) tcp_output(tp); + goto drop; } } else *************** *** 874,877 **** --- 880,890 ---- tp->t_dupacks = 0; break; + } + if (tp->t_dupacks) { + /* + * the congestion window was inflated to account for + * the other side's cached packets - retract it. + */ + tp->snd_cwnd = tp->snd_ssthresh; } tp->t_dupacks = 0; *** /tmp/,RCSt1a26725 Mon Apr 30 01:35:23 1990 --- tcp_timer.c Mon Apr 30 00:36:29 1990 *************** *** 223,226 **** --- 223,227 ---- tp->snd_cwnd = tp->t_maxseg; tp->snd_ssthresh = win * tp->t_maxseg; + tp->t_dupacks = 0; } (void) tcp_output(tp); >From van@helios.ee.lbl.gov Mon Apr 30 10:37:36 1990 To: end2end-interest@ISI.EDU Subject: modified TCP congestion avoidance algorithm (correction) Date: Mon, 30 Apr 90 10:36:12 PDT From: Van Jacobson Status: RO Content-Length: 838 X-Lines: 27 I shouldn't make last minute 'fixes'. The code I sent out last night had a small error: *** t.c Mon Apr 30 10:28:52 1990 --- tcp_input.c Mon Apr 30 10:30:41 1990 *************** *** 885,893 **** * the congestion window was inflated to account for * the other side's cached packets - retract it. */ ! tp->snd_cwnd = tp->snd_ssthresh; } - tp->t_dupacks = 0; if (SEQ_GT(ti->ti_ack, tp->snd_max)) { tcpstat.tcps_rcvacktoomuch++; goto dropafterack; --- 885,894 ---- * the congestion window was inflated to account for * the other side's cached packets - retract it. */ ! if (tp->snd_cwnd > tp->snd_ssthresh) ! tp->snd_cwnd = tp->snd_ssthresh; ! tp->t_dupacks = 0; } if (SEQ_GT(ti->ti_ack, tp->snd_max)) { tcpstat.tcps_rcvacktoomuch++; goto dropafterack;