You pick up your iPhone while waiting in line at a coffee shop. You google a not-so-famous actor, get linked to a Wikipedia entry listing his recent movies and popular YouTube clips of several of them. You check out user reviews on Amazon and pick one, download that movie on BitTorrent or stream that in Netflix. But suddenly the WiFi logo on your phone is gone and you're on 3G. Video quality starts to degrade, but you don't know if it's the server getting crowded or the Internet is congested somewhere. In any case, it costs you $10 per Gigabyte, and you decide to stop watching the movie, and instead multitask between sending tweets and calling your friend on Skype, while songs stream from iCloud to your phone. You're happy with the call quality, but get a little irritated when you see there're no new followers on Twitter. You may wonder how they all kind of work, and why sometimes they don't. Take a look at the list of 20 questions below. Each question is selected not just for its relevance to our daily lives, but also for the core concepts in the field of networking illustrated by its answers. This course is about formulating and answering these 20 questions. All the features of this course are available for free. It does not offer a certificate upon completion.
Fairness Functions and Properties
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En provenance du cours de Princeton University
Networks: Friends, Money, and Bytes
65 notes
À partir de la leçon
Is It Fair that My Neighbor’s iPad Downloads Faster?
In this final lecture of the course, we will study a subject that we touched upon many times previously and forms an essential part of both social choice theory and technology network design: quantifying fairness of resource allocation.
Rencontrer les enseignants
Mung ChiangProfessor
Electrical Engineering
Christopher BrintonLecturer
Electrical Engineering
The first example is on LTE air interface,
okay? Let's actually go through the detail of calculating the speed.
Well, first of all, let's just look at the connection between the end-user
device over the air to the eNobe, okay?
And let's only look at the physical layer first,
okay? So, there's no application to speak of.
Well, what is the formula of this speed here?
Roughly speaking, it goes like this. We want to look at the number of bits
transmitted, right? And then, divide by the time.
So, the number of bits transmitted over time. And there is a standard unit of
time called a sub frame of data, one unit of time, and that is one millisecond in
the standardization. Let's just count how many bits can be
sent over that one millisecond then, okay? Well, we need to know the number of
symbols per frequency block. Then, we multiply that by the number of
frequency blocks. Then, we multiply by the number of bits
per symbol. Then, we multiply by any extra gains,
such as the coding, or MIM, MIMO or multiple antenna gain,
okay? So, the formula looks something like this.
We look at the number of symbols per carrier, okay?
Different how rich of descriptive power there is
per carrier. Meaning, per small block of the frequency
that you're using, okay? Minus the control overhead that you need
for example for channel estimation, to know how good the channel is before
deciding what kind of modulation you can use,
okay? Then, you multiply that difference by the
number of carriers per frequency block. As mentioned in advanced material part of
last lecture and a quick summary here, is that the frequency block is divided into
a few blocks, okay? a number of blocks. And each block is then further divided
into different carriers, [SOUND] okay? So, signals are modulated onto different
carriers and then we got many blocks of these carriers for LTE.
So, you multiply this difference by the number of carriers you have for frequency
block, then you subtract out other overhead,
okay? Then, you multiply by the number of bits that you can transmit per symbol.
If you got a good channel, you can carry more bits per symbol through a so called
higher order modulation. Again, the detail doesn't concern us
because this is not a signal processing for communication course.
Then, we multiply the number of frequency blocks you have, all together.
And then, you multiply by the additional gains such as coding gain and MIMO
antenna gain. Now, in the ideal case, we get the
following kind of numbers, okay?
So, symbols per carrier is usually say, fourteen in the ideal case for LTE.
And the control overhead per carrier is let's say one,
[SOUND] okay? And then, we multiply by the number of carriers per frequency
block. Usually, there are twelve carriers,
okay? So, multiply by twelve, and each one has a frequency block of 180
kilohertz. And then, there's a channel estimation
overhead, okay? And this amount of overhead is used
to sense something called pilot symbols to estimate how good the channel is, and
is ideally around, ten symbols, okay? For a four by four antenna system.
And then, you look at the number of bits per symbol
that you can run. Ideally, this would be say six.
Meaning that you have two to the six which is 64, so-called 64 qam modulation,
okay? That's when the channel is very good, you can afford a higher auto
modulation as to be heard correctly at a receiver.
So, you can carry six bits for every symbol.
And then, you multiply the number of frequency blocks you have, which is
altogether a 100 frequency blocks, okay?
Together with some garband, you all together are consuming 20 megahertz then,
which is the channel with typically an LTE system.
Then, you multiply by the coding rate, [SOUND] okay? Which is basically a number
between zero and one. Between zero and one.
More efficient your error correction coding is meaning you'd only need to add
a little bit of redundancy in order to prepare for the channel distortion of
your bits then closer to one you are, for example 0.9, okay?
Now, these days, we've got very advanced error correction coding methodologies
developed in the past decade or so, that can get you very close to one but you
still can get exactly to one. Say, for the kind of a good system that
we are talking about, it get to a 0.9, okay? And then, there is the gain for
using multiple antennas. Theoretically, if you use say, four by
four MIMO system. Meaning, there are four antennas and the
transmitter for other receiver. Then, you can have four spatially
separate channels. So, you get a factor of four on the
spacing. Alright.
So, if you add these up, okay? Then, you get the following number,
315360 bits, okay? For every one millisecond.
So that implies you divide it by one millisecond, you get basically 315
megabit per second. And that's the kind of number you hear in
the physical layer speed for a 4G, okay? LTE.
Which is a huge number, if you think about it, okay?
Our home, broadband wireline access networks
usually getting something like 25 to 50 megabit per second,
okay? Wi-Fi, even if you use that 11N, a fancy
version of Wi-Fi. So, we talked about last time, you are
getting something like 100 megabit per second.
So, this is talking about a wide area wireless network.
And you can get 300, more than 300 megabit per second, okay?
This is huge, okay? In fact, if you can truly get this, you
can run ultra HD video, which requires 100 megabyte per second or so.
You can run many, many channels of HD over the air on your cell phone, LTE
cellphone, okay?
If you can truly get applications layer useful through put at over 300 megabyte
per second, okay? But in practice, what we get is the
following. Still restricting ourselves only to the
physical layer, and only to the link between the end-user device and eNobe,
okay? Not talking about any other overhand, not
talking about any other non-ideal network conditions yet.
Just this very simple case where you should get very big
number. Let's look at the practical number.
Usually, we actually get something more like twelve symbols per carrier, and the
overhead per carrier is like two symbols, okay?
You multiply it by twelve carriers per frequency.
The overhead in things like channel estimation tend to be bigger than ten.
Say, 20 symbols and practice for a mime or four by four channel.
And then, you multiply by the number bits per symbol which instead of
two to the six is often two to the four. That is sixteen plan because the channel
is not good enough or because too much interference,
non-ideal interface condition that forces you to talk slower with a lower auto
modulation. So, you multiply by four instead of six
bits per symbol, okay?
Then, you don't actually have 100 frequency blocks because you use so
called two way communication based on half duplex,
okay? Half of that goes to the one direction,
the other half goes to the other direction.
If you use time division multiplex, sometimes you get 60% of the frequency
blocks for down-link, 40% for up-link. Let's say, we're talking about down-link
from eNobe to you, okay?
That would be 60, right?
So, it's not 100. And then, you multiply by the coding
gain. And for the channel that we're dealing
with, we may only be able to get say 70% efficiency.
Then, you multiply by the MIMO multiple antenna gain.
You may have a four by four system, okay? Four transmit antenna, four receive
antenna. But they may be placed so close to each
other, and the air in between them may be such
that you don't have four independent channels.
You actually only have two independent channels.
So, you got a factor of two instead of four.
You carry out the calculation and you see a number that is [SOUND] 28,000 bits for
each millisecond. So, you divide by one millisecond, that
implies you get 28 megabit per second [SOUND] rather than 315 megabit per
second. Now, 28 megabit per second is still very
fast. If you can still actually get 28. in your application layer throughput,
useful throughput, that is great,
okay? That is faster than most Wi-Fi we are
used to. So, can you get to 28 megabit per second
for application layer useful throughput? Well, probably not.
Okay? We have not add much beyond the physical
and then lave the Mac layer. This is already 8% of ideal number.
Let's add a few more. For example, more interference among
users at peak hours. Upper layer, layers,
layers three, four, five protocol over has headers, control signals protocol
semantics, okay? You add back haul network congestion,
okay? And that would reduce it further,
okay? In fact, we haven't even added layer two fully, okay?
Layer two for LTE, we mentioned there are three sub-layers,
PDCP, RLE, MAC.
They all have their own overhead just in the header, okay?
So, you've got from 315 megabit per second, down to 28 or so just by physical
layer. And then after layer two, all the header,
you know, down to 25, okay?
And after further overhead in terms of header and semantics and the control
signal, and after further back on network
non-ideal situations, you can easily get another factor of two to five reduction.
That means, you know, finally are getting down to something like five to ten
megabit per second that you can experience say, in downloading a bigger
PowerPoint email attachment. Not 300 and fifteen, but five to ten.
And you see that this is like 3% of the advertised speed,
okay? Now actually, if you can get to ten megabyte per second, that's not bad at
all. You can run a pretty good experience of
video, okay?
You can do many other applications on your phone.
So, LTE compared to 3G is still great, okay?
You just have to compare apple with apple, orange with orange,
okay? You can either compare LTE's physical
layer ideal condition just between device and eNobe with the same kind of number
with 3G. Or you can compare the useful throughput
application layer for LTE with that for 3G,
okay? As long as you do a fair comparison, you
can see that 4G LTE is indeed much faster than 3G.
No doubt about that. What is tricky however, is that you can't
just take these kind of numbers and say, oh, I'm going to get 300 megabit per
second. it's going to be so fast in downloading
everything and I can watch ultra HD movie on my iPhone 5 or something,
okay? You have to say realistically by the time
you experience in the application layer end to end in a normal time of the day,
you're going to get down more like ten megabit per second.
Which is still pretty good for like a normal video.
But not HD, and way, way less than something like ultra HD.
Well, that's just for the air interface detail example.
Let's go through a couple of other examples in the back hall,
just on the TCP side.
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