Disclaimer: I often use the M/M/1 queuing assumption for much of my work to keep the maths simple and believe that I am reasonably aware in which context it's a right or a wrong application :). Also, I don't intend to change the core topic of the thread, but since this has come up, I couldn't resist.
>> With 99% load M/M/1, 500 packets (750kB for 1500B MTU) of >> buffer is enough to make packet drop probability less than >> 1%. With 98% load, the probability is 0.0041%. To expand the above a bit so that there is no ambiguity. The above assumes that the router behaves like an M/M/1 queue. The expected number of packets in the systems can be given by [image: image.png] where [image: image.png] is the utilization. The probability that at least B packets are in the system is given by [image: image.png] where B is the number of packets in the system. for a link utilization of .98, the packet drop probability is .98**(500) = 0.000041%. for a link utilization of 99%, .99**500 = 0.00657%. >> When many TCPs are running, burst is averaged and traffic >> is poisson. M/M/1 queuing assumes that traffic is Poisson, and the Poisson assumption is 1) The number of sources is infinite 2) The traffic arrival pattern is random. I think the second assumption is where I often question whether the traffic arrival pattern is truly random. I have seen cases where traffic behaves more like self-similar. Most Poisson models rely on the Central limit theorem, which loosely states that the sample distribution will approach a normal distribution as we aggregate more from various distributions. The mean will smooth towards a value. Do you have any good pointers where the research has been done that today's internet traffic can be modeled accurately by Poisson? For as many papers supporting Poisson, I have seen as many papers saying it's not Poisson. https://www.icir.org/vern/papers/poisson.TON.pdf https://www.cs.wustl.edu/~jain/cse567-06/ftp/traffic_models2/#sec1.2 On Sun, 7 Aug 2022 at 04:18, Masataka Ohta <mo...@necom830.hpcl.titech.ac.jp> wrote: > Saku Ytti wrote: > > >> I'm afraid you imply too much buffer bloat only to cause > >> unnecessary and unpleasant delay. > >> > >> With 99% load M/M/1, 500 packets (750kB for 1500B MTU) of > >> buffer is enough to make packet drop probability less than > >> 1%. With 98% load, the probability is 0.0041%. > > > I feel like I'll live to regret asking. Which congestion control > > algorithm are you thinking of? > > I'm not assuming LAN environment, for which paced TCP may > be desirable (if bandwidth requirement is tight, which is > unlikely in LAN). > > > But Cubic and Reno will burst tcp window growth at sender rate, which > > may be much more than receiver rate, someone has to store that growth > > and pace it out at receiver rate, otherwise window won't grow, and > > receiver rate won't be achieved. > > When many TCPs are running, burst is averaged and traffic > is poisson. > > > So in an ideal scenario, no we don't need a lot of buffer, in > > practical situations today, yes we need quite a bit of buffer. > > That is an old theory known to be invalid (Ethernet switches with > small buffer is enough for IXes) and theoretically denied by: > > Sizing router buffers > https://dl.acm.org/doi/10.1145/1030194.1015499 > > after which paced TCP was developed for unimportant exceptional > cases of LAN. > > > Now add to this multiple logical interfaces, each having 4-8 queues, > > it adds up. > > Having so may queues requires sorting of queues to properly > prioritize them, which costs a lot of computation (and > performance loss) for no benefit and is a bad idea. > > > Also the shallow ingress buffers discussed in the thread are not delay > > buffers and the problem is complex because no device is marketable > > that can accept wire rate of minimum packet size, so what trade-offs > > do we carry, when we get bad traffic at wire rate at small packet > > size? We can't empty the ingress buffers fast enough, do we have > > physical memory for each port, do we share, how do we share? > > People who use irrationally small packets will suffer, which is > not a problem for the rest of us. > > Masataka Ohta > > >
