Little's Law mea culpa, but not invalidating my main point

Bob McMahon bob.mcmahon at broadcom.com
Fri Jul 9 16:24:23 EDT 2021 

A bit off topic per the control and queueing theory discussion; a four
second latency is going to fail our regression automation rigs. Way too
many WiFi users, particularly for games, require sub few hundreds of
milliseconds and sometimes even much lower. A TCP connect() getting behind
a 4 second buffer bloat queue is also a big fail for these test rigs.
Completely agree that average latency isn't what "users" complain about -
it typically requires a tail analysis.

Bob


On Fri, Jul 9, 2021 at 12:31 PM David P. Reed <dpreed at deepplum.com> wrote:

> Len - I admit I made a mistake in challenging Little's Law as being based
> on Poisson processes. It is more general. But it tells you an "average" in
> its base form, and latency averages are not useful for end user
> applications.
>
>
>
> However, Little's Law does assume something that is not actually valid
> about the kind of distributions seen in the network, and in fact, it is NOT
> true that networks converge on Poisson arrival times.
>
>
>
> The key issue is well-described in the sandard analysis of the M/M/1 queue
> (e.g. https://en.wikipedia.org/wiki/M/M/1_queue) , which is done only for
> Poisson processes, and is also limited to "stable" systems. But networks
> are never stable when fully loaded. They get unstable and those
> instabilities persist for a long time in the network. Instability is at
> core the underlying *requirement* of the Internet's usage.
>
>
>
> So specifically: real networks, even large ones, and certainly the
> Internet today, are not asymptotic limits of sums of stationary stochastic
> arrival processes. Each esternal terminal of any real network has a real
> user there, running a real application, and the network is a complex graph.
> This makes it completely unlike a single queue. Even the links within a
> network carry a relatively small number of application flows. There's no
> ability to apply the Law of Large Numbers to the distributions, because any
> particular path contains only a small number of serialized flows with
> hightly variable rates.
>
>
>
> Here's an example of what really happens in a real network (I've observed
> this in 5 different cities on ATT's cellular network, back when it was
> running Alcatel Lucent HSPA+ gear in those cities).
>
> But you can see this on any network where transient overload occurs,
> creating instability.
>
>
>
>
>
> At 7 AM, the data transmission of the network is roughty stable. That's
> because no links are overloaded within the network. Little's Law can tell
> you by observing the delay and throughput on any path that the average
> delay in the network is X.
>
>
>
> Continue sampling delay in the network as the day wears on. At about 10
> AM, ping delay starts to soar into the multiple second range. No packers
> are lost. The peak ping time is about 4000 milliseconds - 4 seconds in most
> of the networks. This is in downtown, no radio errors are reported, no link
> errors.
>
> So it is all queueing delay.
>
>
>
> Now what Little's law doesn't tell you much about average delay, because
> clearly *some* subpiece of the network is fully saturated. But what is
> interesting here is what is happening and where. You can't tell what is
> saturated, and in fact the entire network is quite unstable, because the
> peak is constantly varying and you don't know where the throughput is. All
> the packets are now arriving 4 seconds or so later.
>
>
>
> Why is the situaton not worse than 4 seconds? Well, there are multiple
> things going on:
>
>
>
> 1) TCP may be doing a lot of retransmissions (non-Poisson at all, not
> random either. The arrival process is entirely deterministic in each
> source, based on the retransmission timeout) or it may not be.
>
>
>
> 2) Users are pissed off, because they clicked on a web page, and got
> nothing back. They retry on their screen, or they try another site.
> Meanwhile, the underlying TCP connection remains there, pumping the network
> full of more packets on that old path, which is still backed up with
> packets that haven't been delivered that are sitting in queues. The real
> arrival process is not Poisson at all, its a deterministic, repeated
> retrsnsmission plus a new attempt to connect to a new site.
>
>
>
> 3) When the users get a web page back eventually, it is filled with names
> of other pieces needed to display that web page, which causes some number
> (often as many as 100) new pages to be fetched, ALL at the same time.
> Certainly not a stochastic process that will just obey the law of large
> numbers.
>
>
>
> All of these things are the result of initial instability, causing queues
> to build up.
>
>
>
> So what is the state of the system? is it stable? is it stochastic? Is it
> the sum of enough stochastic stable flows to average out to Poisson?
>
>
>
> The answer is clearly NO. Control theory (not queuing theory) suggests
> that this system is completely uncontrolled and unstable.
>
>
>
> So if the system is in this state, what does Little's Lemma tell us? What
> is the meaning of that hightly variable 4 second delay on ping packets, in
> terms of average utilizaton of the network?
>
>
>
> We don't even know what all the users really might need, if the system
> hadn't become unstable, because some users have given up, and others are
> trying even harder, and new users are arriving.
>
>
>
> What we do know, because ATT (at my suggestion) reconfigured their system
> after blaming Apple Computer company for "bugs" in the original iPhone in
> public, is that simply *dropping* packets sitting in queues more than a
> couple milliseconds MADE THE USERS HAPPY. Apparently the required capacity
> was there all along!
>
>
>
> So I conclude that the 4 second delay was the largest delay users could
> barely tolerate before deciding the network was DOWN and going away. And
> that the backup was the accumulation of useless packets sitting in queues
> because none of the end systems were receiving congestion signals (which
> for the Internet stack begins with packet dropping).
>
>
>
> I should say that most operators, and especially ATT in this case, do not
> measure end-to-end latency. Instead they use Little's Lemma to query
> routers for their current throughput in bits per second, and calculate
> latency as if Little's Lemma applied. This results in reports to management
> that literally say:
>
>
>
>   The network is not dropping packets, utilization is near 100% on many of
> our switches and routers.
>
>
>
> And management responds, Hooray! Because utilization of 100% of their
> hardware is their investors' metric of maximizing profits. The hardware
> they are operating is fully utilized. No waste! And users are happy because
> no packets have been dropped!
>
>
>
> Hmm... what's wrong with this picture? I can see why Donovan, CTO, would
> accuse Apple of lousy software that was ruining iPhone user experience!
> His network was operating without ANY problems.
>
> So it must be Apple!
>
>
>
> Well, no. The entire problem, as we saw when ATT just changed to shorten
> egress queues and drop packets when the egress queues overflowed, was that
> ATT's network was amplifying instability, not at the link level, but at the
> network level.
>
>
>
> And queueing theory can help with that, but *intro queueing theory* cannot.
>
>
>
> And a big part of that problem is the pervasive belief that, at the
> network boundary, *Poisson arrival* is a reasonable model for use in all
> cases.
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
>
> On Friday, July 9, 2021 6:05am, "Luca Muscariello" <muscariello at ieee.org>
> said:
>
> 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 <lk at 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 <dpreed at 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" <greearb at 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.taht at gmail.com
>> > <mailto:dave.taht at gmail.com <dave.taht at 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 <dpreed at deepplum.com
>> > <mailto:dpreed at deepplum.com <dpreed at 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.taht at gmail.com <mailto:dave.taht at gmail.com <dave.taht at 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-pc at iab.org
>> > <mailto:network-quality-workshop-pc at iab.org
>> <network-quality-workshop-pc at 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 at lists.bufferbloat.net
>> > <mailto:Cerowrt-devel at lists.bufferbloat.net
>> <Cerowrt-devel at 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-fast at lists.bufferbloat.net
>> > <mailto:Make-wifi-fast at lists.bufferbloat.net
>> <Make-wifi-fast at lists.bufferbloat.net>>
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>> > Ben Greear <greearb at candelatech.com>
>> > Candela Technologies Inc http://www.candelatech.com
>> >
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