For those who might be interested in Little's law there is a nice paper by John Little on the occasion of the 50th anniversary of the result.
https://www.informs.org/Blogs/Operations-Research-Forum/Little-s-Law-as-Viewed-on-its-50th-Anniversary https://www.informs.org/content/download/255808/2414681/file/little_paper.pdf Nice read. Luca P.S. Who has not a copy of L. Kleinrock's books? I do have and am not ready to lend them! On Fri, Jul 9, 2021 at 11:01 AM Leonard Kleinrock <l...@cs.ucla.edu> wrote: > David, > > I totally appreciate your attention to when and when not analytical > modeling works. Let me clarify a few things from your note. > > First, Little's law (also known as Little’s lemma or, as I use in my book, > Little’s result) does not assume Poisson arrivals - it is good for *any* > arrival process and any service process and is an equality between time > averages. It states that the time average of the number in a system (for a > sample path *w)* is equal to the average arrival rate to the system > multiplied by the time-averaged time in the system for that sample path. > This is often written as NTimeAvg =λ·TTimeAvg . Moreover, if the > system is also ergodic, then the time average equals the ensemble average > and we often write it as N ̄ = λ T ̄ . In any case, this requires > neither Poisson arrivals nor exponential service times. > > Queueing theorists often do study the case of Poisson arrivals. True, it > makes the analysis easier, yet there is a better reason it is often used, > and that is because the sum of a large number of independent stationary > renewal processes approaches a Poisson process. So nature often gives us > Poisson arrivals. > > Best, > Len > > > > On Jul 8, 2021, at 12:38 PM, David P. Reed <dpr...@deepplum.com> wrote: > > I will tell you flat out that the arrival time distribution assumption > made by Little's Lemma that allows "estimation of queue depth" is totally > unreasonable on ANY Internet in practice. > > > The assumption is a Poisson Arrival Process. In reality, traffic arrivals > in real internet applications are extremely far from Poisson, and, of > course, using TCP windowing, become highly intercorrelated with crossing > traffic that shares the same queue. > > > So, as I've tried to tell many, many net-heads (people who ignore > applications layer behavior, like the people that think latency doesn't > matter to end users, only throughput), end-to-end packet arrival times on a > practical network are incredibly far from Poisson - and they are more like > fractal probability distributions, very irregular at all scales of time. > > > So, the idea that iperf can estimate queue depth by Little's Lemma by just > measuring saturation of capacity of a path is bogus.The less Poisson, the > worse the estimate gets, by a huge factor. > > > > > Where does the Poisson assumption come from? Well, like many theorems, it > is the simplest tractable closed form solution - it creates a simplified > view, by being a "single-parameter" distribution (the parameter is called > lambda for a Poisson distribution). And the analysis of a simple queue > with poisson arrival distribution and a static, fixed service time is the > first interesting Queueing Theory example in most textbooks. It is > suggestive of an interesting phenomenon, but it does NOT characterize any > real system. > > > It's the queueing theory equivalent of "First, we assume a spherical > cow...". in doing an example in a freshman physics class. > > > Unfortunately, most networking engineers understand neither queuing theory > nor application networking usage in interactive applications. Which makes > them arrogant. They assume all distributions are poisson! > > > > > On Tuesday, July 6, 2021 9:46am, "Ben Greear" <gree...@candelatech.com> > said: > > > Hello, > > > > I am interested to hear wish lists for network testing features. We make > test > > equipment, supporting lots > > of wifi stations and a distributed architecture, with built-in udp, tcp, > ipv6, > > http, ... protocols, > > and open to creating/improving some of our automated tests. > > > > I know Dave has some test scripts already, so I'm not necessarily > looking to > > reimplement that, > > but more fishing for other/new ideas. > > > > Thanks, > > Ben > > > > On 7/2/21 4:28 PM, Bob McMahon wrote: > > > I think we need the language of math here. It seems like the network > > power metric, introduced by Kleinrock and Jaffe in the late 70s, is > something > > useful. > > > Effective end/end queue depths per Little's law also seems useful. > Both are > > available in iperf 2 from a test perspective. Repurposing test > techniques to > > actual > > > traffic could be useful. Hence the question around what exact telemetry > > is useful to apps making socket write() and read() calls. > > > > > > Bob > > > > > > On Fri, Jul 2, 2021 at 10:07 AM Dave Taht <dave.t...@gmail.com > > <mailto:dave.t...@gmail.com <dave.t...@gmail.com>>> wrote: > > > > > > In terms of trying to find "Quality" I have tried to encourage folk to > > > both read "zen and the art of motorcycle maintenance"[0], and Deming's > > > work on "total quality management". > > > > > > My own slice at this network, computer and lifestyle "issue" is aiming > > > for "imperceptible latency" in all things. [1]. There's a lot of > > > fallout from that in terms of not just addressing queuing delay, but > > > caching, prefetching, and learning more about what a user really needs > > > (as opposed to wants) to know via intelligent agents. > > > > > > [0] If you want to get depressed, read Pirsig's successor to "zen...", > > > lila, which is in part about what happens when an engineer hits an > > > insoluble problem. > > > [1] https://www.internetsociety.org/events/latency2013/ > > <https://www.internetsociety.org/events/latency2013/> > > > > > > > > > > > > On Thu, Jul 1, 2021 at 6:16 PM David P. Reed <dpr...@deepplum.com > > <mailto:dpr...@deepplum.com <dpr...@deepplum.com>>> wrote: > > > > > > > > Well, nice that the folks doing the conference are willing to > > consider that quality of user experience has little to do with > signalling rate at > > the > > > physical layer or throughput of FTP transfers. > > > > > > > > > > > > > > > > But honestly, the fact that they call the problem "network quality" > > suggests that they REALLY, REALLY don't understand the Internet isn't > the hardware > > or > > > the routers or even the routing algorithms *to its users*. > > > > > > > > > > > > > > > > By ignoring the diversity of applications now and in the future, > > and the fact that we DON'T KNOW what will be coming up, this conference > will > > likely fall > > > into the usual trap that net-heads fall into - optimizing for some > > imaginary reality that doesn't exist, and in fact will probably never be > what > > users > > > actually will do given the chance. > > > > > > > > > > > > > > > > I saw this issue in 1976 in the group developing the original > > Internet protocols - a desire to put *into the network* special tricks > to optimize > > ASR33 > > > logins to remote computers from terminal concentrators (aka remote > > login), bulk file transfers between file systems on different > time-sharing > > systems, and > > > "sessions" (virtual circuits) that required logins. And then trying to > > exploit underlying "multicast" by building it into the IP layer, because > someone > > > thought that TV broadcast would be the dominant application. > > > > > > > > > > > > > > > > Frankly, to think of "quality" as something that can be "provided" > > by "the network" misses the entire point of "end-to-end argument in > system > > design". > > > Quality is not a property defined or created by The Network. If you > want > > to talk about Quality, you need to talk about users - all the users at > all times, > > > now and into the future, and that's something you can't do if you don't > > bother to include current and future users talking about what they might > expect > > to > > > experience that they don't experience. > > > > > > > > > > > > > > > > There was much fighting back in 1976 that basically involved > > "network experts" saying that the network was the place to "solve" such > issues as > > quality, > > > so applications could avoid having to solve such issues. > > > > > > > > > > > > > > > > What some of us managed to do was to argue that you can't "solve" > > such issues. All you can do is provide a framework that enables > different uses to > > > *cooperate* in some way. > > > > > > > > > > > > > > > > Which is why the Internet drops packets rather than queueing them, > > and why diffserv cannot work. > > > > > > > > (I know the latter is conftroversial, but at the moment, ALL of > > diffserv attempts to talk about end-to-end applicaiton specific metrics, > but > > never, ever > > > explains what the diffserv control points actually do w.r.t. what the > IP > > layer can actually control. So it is meaningless - another violation of > the > > > so-called end-to-end principle). > > > > > > > > > > > > > > > > Networks are about getting packets from here to there, multiplexing > > the underlying resources. That's it. Quality is a whole different thing. > Quality > > can > > > be improved by end-to-end approaches, if the underlying network > provides > > some kind of thing that actually creates a way for end-to-end > applications to > > > affect queueing and routing decisions, and more importantly getting > > "telemetry" from the network regarding what is actually going on with > the other > > > end-to-end users sharing the infrastructure. > > > > > > > > > > > > > > > > This conference won't talk about it this way. So don't waste your > > time. > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > > On Wednesday, June 30, 2021 8:12pm, "Dave Taht" > > <dave.t...@gmail.com <mailto:dave.t...@gmail.com <dave.t...@gmail.com>>> > said: > > > > > > > > > The program committee members are *amazing*. Perhaps, finally, > > we can > > > > > move the bar for the internet's quality metrics past endless, > > blind > > > > > repetitions of speedtest. > > > > > > > > > > For complete details, please see: > > > > > https://www.iab.org/activities/workshops/network-quality/ > > <https://www.iab.org/activities/workshops/network-quality/> > > > > > > > > > > Submissions Due: Monday 2nd August 2021, midnight AOE > > (Anywhere On Earth) > > > > > Invitations Issued by: Monday 16th August 2021 > > > > > > > > > > Workshop Date: This will be a virtual workshop, spread over > > three days: > > > > > > > > > > 1400-1800 UTC Tue 14th September 2021 > > > > > 1400-1800 UTC Wed 15th September 2021 > > > > > 1400-1800 UTC Thu 16th September 2021 > > > > > > > > > > Workshop co-chairs: Wes Hardaker, Evgeny Khorov, Omer Shapira > > > > > > > > > > The Program Committee members: > > > > > > > > > > Jari Arkko, Olivier Bonaventure, Vint Cerf, Stuart Cheshire, > > Sam > > > > > Crowford, Nick Feamster, Jim Gettys, Toke Hoiland-Jorgensen, > > Geoff > > > > > Huston, Cullen Jennings, Katarzyna Kosek-Szott, Mirja > > Kuehlewind, > > > > > Jason Livingood, Matt Mathias, Randall Meyer, Kathleen > > Nichols, > > > > > Christoph Paasch, Tommy Pauly, Greg White, Keith Winstein. > > > > > > > > > > Send Submissions to: network-quality-workshop...@iab.org > > <mailto:network-quality-workshop...@iab.org > <network-quality-workshop...@iab.org>>. > > > > > > > > > > Position papers from academia, industry, the open source > > community and > > > > > others that focus on measurements, experiences, observations > > and > > > > > advice for the future are welcome. Papers that reflect > > experience > > > > > based on deployed services are especially welcome. The > > organizers > > > > > understand that specific actions taken by operators are > > unlikely to be > > > > > discussed in detail, so papers discussing general categories > > of > > > > > actions and issues without naming specific technologies, > > products, or > > > > > other players in the ecosystem are expected. Papers should not > > focus > > > > > on specific protocol solutions. > > > > > > > > > > The workshop will be by invitation only. Those wishing to > > attend > > > > > should submit a position paper to the address above; it may > > take the > > > > > form of an Internet-Draft. > > > > > > > > > > All inputs submitted and considered relevant will be published > > on the > > > > > workshop website. The organisers will decide whom to invite > > based on > > > > > the submissions received. Sessions will be organized according > > to > > > > > content, and not every accepted submission or invited attendee > > will > > > > > have an opportunity to present as the intent is to foster > > discussion > > > > > and not simply to have a sequence of presentations. > > > > > > > > > > Position papers from those not planning to attend the virtual > > sessions > > > > > themselves are also encouraged. A workshop report will be > > published > > > > > afterwards. > > > > > > > > > > Overview: > > > > > > > > > > "We believe that one of the major factors behind this lack of > > progress > > > > > is the popular perception that throughput is the often sole > > measure of > > > > > the quality of Internet connectivity. With such narrow focus, > > people > > > > > don’t consider questions such as: > > > > > > > > > > What is the latency under typical working conditions? > > > > > How reliable is the connectivity across longer time periods? > > > > > Does the network allow the use of a broad range of protocols? > > > > > What services can be run by clients of the network? > > > > > What kind of IPv4, NAT or IPv6 connectivity is offered, and > > are there firewalls? > > > > > What security mechanisms are available for local services, > > such as DNS? > > > > > To what degree are the privacy, confidentiality, integrity > > and > > > > > authenticity of user communications guarded? > > > > > > > > > > Improving these aspects of network quality will likely depend > > on > > > > > measurement and exposing metrics to all involved parties, > > including to > > > > > end users in a meaningful way. Such measurements and exposure > > of the > > > > > right metrics will allow service providers and network > > operators to > > > > > focus on the aspects that impacts the users’ experience > > most and at > > > > > the same time empowers users to choose the Internet service > > that will > > > > > give them the best experience." > > > > > > > > > > > > > > > -- > > > > > Latest Podcast: > > > > > > > > https://www.linkedin.com/feed/update/urn:li:activity:6791014284936785920/ > > < > https://www.linkedin.com/feed/update/urn:li:activity:6791014284936785920/> > > > > > > > > > > Dave Täht CTO, TekLibre, LLC > > > > > _______________________________________________ > > > > > Cerowrt-devel mailing list > > > > > Cerowrt-devel@lists.bufferbloat.net > > <mailto:Cerowrt-devel@lists.bufferbloat.net > <Cerowrt-devel@lists.bufferbloat.net>> > > > > > https://lists.bufferbloat.net/listinfo/cerowrt-devel > > <https://lists.bufferbloat.net/listinfo/cerowrt-devel> > > > > > > > > > > > > > > > > > -- > > > Latest Podcast: > > > > https://www.linkedin.com/feed/update/urn:li:activity:6791014284936785920/ > > < > https://www.linkedin.com/feed/update/urn:li:activity:6791014284936785920/> > > > > > > Dave Täht CTO, TekLibre, LLC > > > _______________________________________________ > > > Make-wifi-fast mailing list > > > make-wifi-f...@lists.bufferbloat.net > > <mailto:make-wifi-f...@lists.bufferbloat.net > <make-wifi-f...@lists.bufferbloat.net>> > > > https://lists.bufferbloat.net/listinfo/make-wifi-fast > > <https://lists.bufferbloat.net/listinfo/make-wifi-fast> > > > > > > > > > This electronic communication and the information and any files > transmitted > > with it, or attached to it, are confidential and are intended solely for > the use > > of > > > the individual or entity to whom it is addressed and may contain > information > > that is confidential, legally privileged, protected by privacy laws, or > otherwise > > > restricted from disclosure to anyone else. If you are not the intended > > recipient or the person responsible for delivering the e-mail to the > intended > > recipient, > > > you are hereby notified that any use, copying, distributing, > dissemination, > > forwarding, printing, or copying of this e-mail is strictly prohibited. > If you > > > received this e-mail in error, please return the e-mail to the sender, > delete > > it from your computer, and destroy any printed copy of it. > > > > > > _______________________________________________ > > > Starlink mailing list > > > starl...@lists.bufferbloat.net > > > https://lists.bufferbloat.net/listinfo/starlink > > > > > > > > > -- > > Ben Greear <gree...@candelatech.com> > > Candela Technologies Inc http://www.candelatech.com > > > _______________________________________________ > Starlink mailing list > starl...@lists.bufferbloat.net > https://lists.bufferbloat.net/listinfo/starlink > > > _______________________________________________ > Make-wifi-fast mailing list > make-wifi-f...@lists.bufferbloat.net > https://lists.bufferbloat.net/listinfo/make-wifi-fast
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