Hmm, that's really interesting. Most interesting is that my understanding is that the control law was intended to deal with aggregates of mostly TCP-like traffic, and that an overload of unresponsive traffic wasn't much of a goal; this seems like vaguely reasonable behaviour, I suppose, given that pathological situation.
But I don't have a way to derive the control law from first principles at this time (I haven't been working on that for a long time now). On 25 September 2015 at 06:27, Bob Briscoe <[email protected]> wrote: > Toke, > > Having originally whinged that no-one ever responded to my original 2013 > posting, now it's my turn to be embarrassed for having missed your > interesting response for over 3 months. > > Cool that the analysis proves correct in practice - always nice. > > The question is still open whether this was the intention, and if so why > this particular control law was intended. > I would rather we started from a statement of what the control law ought > to do, then derive it. > > Andrew McGregor said he would have a go at this question some time ago... > Andrew? > > > Bob > > > > On 07/06/15 20:27, Toke Høiland-Jørgensen wrote: > > Hi Bob > > Apologies for reviving this ancient thread; been meaning to get around > to it sooner, but well... better late than never I suppose. > > (Web link to your original mail, in case Message-ID referencing > breaks:https://www.ietf.org/mail-archive/web/aqm/current/msg00376.html ). > > Having recently had a need to understand CoDel's behaviour in more > detail, your analysis popped out of wherever it's been hiding in the > back of my mind and presented itself as maybe a good place to start. :) > > So anyhow, I'm going to skip the initial assertions in your email and > focus on the analysis: > > > Here's my working (pls check it - I may have made mistakes) > _________________ > For brevity, I'll define some briefer variable names: > interval = I [s] > next_drop = D [s] > packet-rate = R [pkt/s] > count = n [pkt] > > >From the CoDel control law code: > D(n) = I / sqrt(n) > And the instantaneous drop probability is: > p(n) = 1/( R * D(n) ) > > Then the slope of the rise in drop probability with time is: > Delta p / Delta t = [p(n+1) - p(n)] / D(n) > = [1/D(n+1) - 1/D(n)] / [ R * D(n) ] > = sqrt(n) * [sqrt(n+1) - sqrt(n)] / [R*I*I] > = [ sqrt(n(n+1)) - n ] / R*I^2 > > I couldn't find anything wrong with the derivation. I'm not entirely > sure that I think it makes sense to speak about an "instantaneous drop > probability" for an algorithm that is not probabilistic in nature. > However, interpreting p(n) as "the fraction of packets dropped over the > interval from D(n) to D(n+1)" makes sense, I guess, and for this > analysis that works. > > > At count = 1, the numerator starts at sqrt(2)-1 = 0.414. > Amd as n increases, it rapidly tends to 1/2. > > So CoDel's rate of increase of drop probability with time is nearly constant > (it > is always between 0.414 and 0.5) and it rapidly approaches 0.5 after a few > drops, tending towards: > dp/dt = 1/(2*R*I^2) > > This constant increase clearly has very little to do with the square-root law > of > TCP Reno. > > In the above formula, drop probability increases inversely proportional to the > packet rate. For instance, with I = 100ms and 1500B packets > at 10Mb/s => R = 833 pkt/s => dp/dt = 6.0% /s > at 100Mb/s => R = 8333 pkt/s => dp/dt = 0.6% /s > > I also tried to test this. I configured CoDel (on a Linux 4.0 box) on > 1Mbps, 2Mbps and 10Mbps links with interval settings of 1 second and > 500ms, and a total packet limit of 100k packets. This was to make it > deliberately slower to react (so the change in drop probability is more > visible), and to make sure no packets are dropped from queue overflow. > > I then sent an unresponsive UDP stream over the link at 110% of the link > capacity (as passed to Iperf, so approximately), and collected the > output of `tc -s qdisc` every 0.2 seconds. > > The attached plot is of 'pkts dropped / (pkts sent + pkts dropped)' in a > 2-second sliding window over the duration of the test (the plot is also > available here:https://kau.toke.dk/ietf/codel-drop-rate/codel-drop-rate.svg ). > > I've included linear trend lines from the initial time to the point of > maximum drop probability, and as is apparent from the plot, got quite a > good fit (r>0.99 for all six data sets). The legend includes the slopes > of the linear fits for each of the data sets, which are not too far from > what your analysis predicts (and I'm guessing the difference can be > attributed to the difference in exact packet rates, but I haven't > checked). > > The Flent data files with the qdisc stats over time (readable by the > newest git version of Flent), as well as the Python script I used to > create the graph are available here: https://kau.toke.dk/ietf/codel-drop-rate/ > > So, in short: It seems that CoDel's "drop rate" does increase linearly > in the presence of a persistent queue, and that the rate of increase > depends on both the interval and the link rate. > > Now, I'll refrain from commenting on whether or not this is "bad", or > indeed if it is contrary to design. It was surprising to me at least, so > I thought I'd share my findings, in the hope that someone would either > find them useful or tell me how they're wrong (or both!). :) > > -Toke > > > > _______________________________________________ > aqm mailing [email protected]https://www.ietf.org/mailman/listinfo/aqm > > > -- > ________________________________________________________________ > Bob Briscoe http://bobbriscoe.net/ > > > _______________________________________________ > aqm mailing list > [email protected] > https://www.ietf.org/mailman/listinfo/aqm > > -- Andrew McGregor | SRE | [email protected] | +61 4 1071 2221
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