WEBVTT 00:00:00.000 --> 00:00:03.680 Welcome back to CSE 316 — Data Communication and Networking. 00:00:03.730 --> 00:00:09.390 This is the detailed video version of Session 6, and it closes Chapter 3. 00:00:09.440 --> 00:00:18.390 It runs about an hour and a half, in four sections, and as always it is meant to be watched the way you would use a textbook chapter — in pieces, with the pause button, and again before an exam. 00:00:21.700 --> 00:00:27.610 There is a checkpoint at the end of each section so you can tell whether to go on or go back. 00:00:27.660 --> 00:00:30.540 Here is the shape of it. 00:00:30.590 --> 00:00:33.420 First, we take the word 'bandwidth' apart. 00:00:33.470 --> 00:00:38.780 Then latency, which is a sum of exactly four parts - that we will discuss. 00:00:38.830 --> 00:00:43.670 Then the one genuinely new idea of the day: the bandwidth-delay product. 00:00:43.720 --> 00:00:47.630 And at the end, the answer to the question I am about to ask you. 00:00:47.680 --> 00:00:50.700 One administrative note before anything else. 00:00:50.750 --> 00:00:59.160 Weekly Online Quiz A2 is live on the course website and closes on Saturday at midnight — twenty minutes, one attempt. 00:00:59.210 --> 00:01:08.160 Classroom Quiz 1 is further out, in Week 5, in the first thirty minutes of Session 9 — thirty minutes, twenty marks, in class and on paper, covering everything from Session 1 up to that point. 00:01:12.770 --> 00:01:18.750 This video is part of your revision material for it. 00:01:18.800 --> 00:01:23.580 Before I define anything, here is the question this session answers. 00:01:23.630 --> 00:01:31.840 A satellite internet connection advertises 100 megabits per second — faster than most home broadband in this city. 00:01:31.890 --> 00:01:36.380 The rating is genuine; measured downloads really do come in fast. 00:01:36.430 --> 00:01:45.380 And yet video calls over that connection are famously miserable: long awkward pauses, two people constantly starting to talk at the same moment and stopping again. 00:01:47.160 --> 00:01:48.380 Why? 00:01:48.430 --> 00:01:52.270 Pause the video and commit to a reason — one sentence, written down. 00:01:52.320 --> 00:02:01.270 Section four settles it with one calculation — distance over speed, for the satellite's orbit. The answer is one of the four numbers this session defines, and it is not the hundred megabits. 00:02:09.810 --> 00:02:13.380 The point of today is not the satellite. 00:02:13.430 --> 00:02:22.150 The point is that everyone — civilians, journalists, salesmen — describes a network with one word: fast, or slow. 00:02:22.200 --> 00:02:24.190 Engineers are not allowed to. 00:02:24.240 --> 00:02:33.190 By the end of this session you will grade any link with four separate numbers, and you will know which of the four your application actually cares about. 00:02:33.240 --> 00:02:38.991 That is the whole session in one sentence. 00:02:39.041 --> 00:02:40.311 Section one. 00:02:40.361 --> 00:02:42.191 Bandwidth and throughput. 00:02:42.241 --> 00:02:51.191 Four numbers replace the word 'fast', and this section takes the first two — the one printed on the box, and the one you actually measure. 00:02:53.808 --> 00:03:02.098 Here is the map of the whole session — four words, precise from the start, because in ordinary speech all four get mashed into 'fast'. 00:03:02.148 --> 00:03:03.428 Bandwidth. 00:03:03.478 --> 00:03:08.268 What the link could carry — its potential. 00:03:08.318 --> 00:03:15.258 And the warning in that row: the word has two flavors, one measured in hertz and one in bits per second. 00:03:15.308 --> 00:03:24.118 Nyquist (Harry Nyquist) and Shannon (Claude Shannon), from the previous session, are the exchange rate between those two. 00:03:24.168 --> 00:03:26.278 We will separate the flavors properly in a moment. 00:03:26.328 --> 00:03:27.418 Throughput. 00:03:27.468 --> 00:03:32.588 What actually got through — the measured reality. 00:03:32.638 --> 00:03:37.658 Always less than the promise, and we will measure the gap on a real example. 00:03:37.708 --> 00:03:40.788 Latency, also called delay. 00:03:40.838 --> 00:03:47.728 How long the journey takes — from the first bit leaving the sender to the last bit arriving at the receiver. 00:03:47.778 --> 00:03:53.068 It is a sum of exactly four parts, and section two is entirely about them. 00:03:53.118 --> 00:03:54.498 And jitter. 00:03:54.548 --> 00:03:58.618 How much that delay wobbles from packet to packet. 00:03:58.668 --> 00:04:04.588 This is Session 1's old friend — you have already seen the eight packets and the frozen video. 00:04:04.638 --> 00:04:06.408 It gets one slide today. 00:04:06.458 --> 00:04:10.168 Every slide that follows sharpens one of these four rows. 00:04:10.218 --> 00:04:16.524 If at any point you feel lost, come back to this map. 00:04:16.574 --> 00:04:24.014 So, the first meaning of bandwidth — the one you already know, even if you did not know you knew it. 00:04:24.064 --> 00:04:33.014 In its original, analog sense, bandwidth is a range of frequencies: the width of the band a channel lets through, highest frequency minus lowest. 00:04:33.094 --> 00:04:38.874 A traditional telephone line passes roughly 300 hertz to 3,300 hertz, so its bandwidth is 3,000 hertz. 00:04:38.924 --> 00:04:44.884 That is a property of the medium and the electronics attached to it, and it is measured in hertz. 00:04:44.934 --> 00:04:48.234 And you have met this meaning already. 00:04:48.284 --> 00:04:57.234 Every time this course said 'the bandwidth of a composite signal', or asked how much bandwidth a channel must offer to pass a signal undamaged — that was this meaning. 00:04:59.524 --> 00:05:00.894 Purely analog. 00:05:00.944 --> 00:05:04.654 Nothing about bits in it at all. 00:05:04.704 --> 00:05:13.064 In networking, the very same word is used for a second, different quantity — a link's data rate, in bits per second. 00:05:13.114 --> 00:05:17.864 The two are related, and the next slide gives you the exchange rate between them. 00:05:17.914 --> 00:05:19.754 But they are not the same number. 00:05:19.804 --> 00:05:26.264 They are not even the same kind of number — one is a width in frequency, the other is a rate of data. 00:05:26.314 --> 00:05:35.264 An exam answer that mixes hertz with bits per second is wrong before the arithmetic even starts. 00:05:35.669 --> 00:05:38.229 The second meaning — the digital one. 00:05:38.279 --> 00:05:44.009 In everyday networking, bandwidth means the number of bits per second a link can carry. 00:05:44.059 --> 00:05:52.949 It is the number on the box: 100 megabits per second Ethernet, a 54 megabit Wi-Fi rate, a one gigabit fiber plan. 00:05:52.999 --> 00:05:56.909 A speed rating for data, not a range of frequencies. 00:05:56.959 --> 00:06:02.709 And the two meanings are not strangers — you already own the bridge between them. 00:06:02.759 --> 00:06:10.179 Give Nyquist or Shannon a bandwidth in hertz, and they hand you back the maximum data rate in bits per second. 00:06:10.229 --> 00:06:13.349 That is exactly what the previous session was for. 00:06:13.399 --> 00:06:21.169 Hertz is the analog potential of the channel; bits per second is what that potential is worth once you send data over it. 00:06:21.219 --> 00:06:26.789 One word, two currencies, and last session's theorems are the exchange rate. 00:06:26.839 --> 00:06:30.009 So which meaning does this session use? 00:06:30.059 --> 00:06:39.009 From here on — in this session, and in practice whenever a network engineer says 'bandwidth' without qualification — the word means bits per second: the rated capacity of a link. 00:06:41.999 --> 00:06:45.909 If hertz are ever meant, the units will say so explicitly. 00:06:45.959 --> 00:06:51.619 Keep that convention and you will never be caught. 00:06:51.669 --> 00:06:56.539 Now the first real distinction of the day: the promise against the reality. 00:06:56.589 --> 00:07:04.249 A link may have bandwidth B, but what you can actually push through it is some T — and T is less than B, always. 00:07:04.299 --> 00:07:06.729 Bandwidth is potential. 00:07:06.779 --> 00:07:10.669 It is the rating on the box — what the link is rated to carry. 00:07:10.719 --> 00:07:16.439 A 1 megabit link is a 1 megabit link at three in the morning with nobody using it. 00:07:16.489 --> 00:07:20.839 The rating does not change with traffic, with load, with the weather. 00:07:20.889 --> 00:07:23.279 It describes the link itself. 00:07:23.329 --> 00:07:25.859 Throughput is actual. 00:07:25.909 --> 00:07:29.099 It is what you measure getting through, here and now. 00:07:29.149 --> 00:07:35.489 The end devices, the protocol overhead, other people's traffic — everything takes its share. 00:07:35.539 --> 00:07:40.199 Throughput describes not the link but the whole system, at this moment. 00:07:40.249 --> 00:07:46.079 Measure it again in an hour and you may get a different number; the bandwidth will not have moved. 00:07:46.129 --> 00:07:49.079 Here is the picture to quote back to me. 00:07:49.129 --> 00:07:52.579 A sixty-lane highway carrying five cars a minute. 00:07:52.629 --> 00:07:56.089 Nobody looks at that and calls it a five-lane highway. 00:07:56.139 --> 00:08:01.009 The lanes are the bandwidth; the cars are the throughput. 00:08:01.059 --> 00:08:09.589 And in the same spirit: a 1 megabit link whose end devices can only process 200 kilobits per second carries 200 kilobits per second. 00:08:09.639 --> 00:08:18.211 The link never got slower — the rating is about the link, the measurement is about the system. 00:08:18.261 --> 00:08:26.181 Let us measure a real network — this is Forouzan's own example, 3.44, and I will do every step. 00:08:26.231 --> 00:08:29.511 A network has bandwidth 10 megabits per second. 00:08:29.561 --> 00:08:34.561 It can pass, on average, 12,000 frames per minute, each frame carrying 10,000 bits. 00:08:34.611 --> 00:08:36.601 What is the throughput? 00:08:36.651 --> 00:08:43.491 Step one — how many bits actually got through, and in what time? 00:08:43.541 --> 00:08:49.051 Twelve thousand frames times ten thousand bits is one hundred and twenty million bits. 00:08:49.101 --> 00:08:50.491 Per minute. 00:08:50.541 --> 00:08:54.261 Step two, and this is where the marks die. 00:08:54.311 --> 00:08:58.571 Throughput is measured per second, and our count is per minute. 00:08:58.621 --> 00:09:00.481 So divide by sixty. 00:09:00.531 --> 00:09:09.481 Do not skip past this line: this is the most common error on this example — a correct multiplication, and then one hundred and twenty megabits per second written down as the answer, sixty times too large. 00:09:13.871 --> 00:09:19.771 One hundred and twenty million divided by sixty is two million bits per second. 00:09:19.821 --> 00:09:22.931 The throughput is 2 megabits per second. 00:09:22.981 --> 00:09:25.661 Now stand back and look at it. 00:09:25.711 --> 00:09:28.621 A 10 megabit network, delivering 2. 00:09:28.671 --> 00:09:30.481 One fifth of the promise. 00:09:30.531 --> 00:09:36.761 Neither number is wrong — the link really is rated at ten, and the system really delivers two. 00:09:36.811 --> 00:09:41.861 The gap between them is not an error; the gap is where the engineering lives. 00:09:41.911 --> 00:09:49.296 And the next slide itemizes exactly where those missing megabits went. 00:09:49.346 --> 00:09:51.156 Eight megabits are missing. 00:09:51.206 --> 00:09:56.796 Let us name the thieves — there are three of them, and none is mysterious. 00:09:56.846 --> 00:09:59.806 First: the end devices. 00:09:59.856 --> 00:10:07.606 The link is rated at 10 megabits per second, but the machines at each end generate and absorb frames at their own pace. 00:10:07.656 --> 00:10:13.936 If the sender only produces 12,000 frames a minute, the wire spends most of its time idle, waiting. 00:10:13.986 --> 00:10:17.986 A link cannot carry what nobody gives it. 00:10:18.036 --> 00:10:21.156 Second: protocol overhead. 00:10:21.206 --> 00:10:23.786 Not every bit on the wire is your data. 00:10:23.836 --> 00:10:31.566 Headers, acknowledgments, retransmissions — the agreements we studied in Session 1 cost bits to operate. 00:10:31.616 --> 00:10:40.566 Sessions 21 and 22 put numbers on the acknowledgments and the retransmissions; Session 8 puts a number on the header. For now: the machinery takes a cut. 00:10:43.606 --> 00:10:46.266 Third: other traffic. 00:10:46.316 --> 00:10:49.986 That measurement was taken on a shared, working network. 00:10:50.036 --> 00:10:56.076 Other people's frames are in the same pipe, taking their share of the same ten megabits. 00:10:56.126 --> 00:11:00.106 And now a warning; put it in red in your notes. 00:11:00.156 --> 00:11:03.446 Throughput is not 'how fast the bits move'. 00:11:03.496 --> 00:11:12.446 Bits do not travel faster on a 10 megabit link than on a 1 megabit link — each individual bit crosses the wire at the same propagation speed either way. 00:11:14.446 --> 00:11:19.686 What a higher-bandwidth link does is push MORE bits onto the wire every second. 00:11:19.736 --> 00:11:24.346 The bits themselves are no quicker; there are simply more of them in flight. 00:11:24.396 --> 00:11:33.346 'How many per second' and 'how fast each one travels' are two different questions — and the second one is exactly where section two begins. 00:11:36.138 --> 00:11:37.458 First checkpoint. 00:11:37.508 --> 00:11:42.218 Pause the video and answer these three on paper, without scrolling back. 00:11:42.268 --> 00:11:43.478 One. 00:11:43.528 --> 00:11:48.788 A 100 megabit link carries a measured 40 megabits per second. 00:11:48.838 --> 00:11:54.638 Which number is the bandwidth, which is the throughput — and which of the two can change at three in the morning? 00:11:54.688 --> 00:11:55.828 Two. 00:11:55.878 --> 00:11:59.248 A network passes 6,000 frames per minute, each of 5,000 bits. 00:11:59.298 --> 00:12:00.438 What is the throughput? 00:12:00.488 --> 00:12:02.118 Three. 00:12:02.168 --> 00:12:11.118 True or false: on a 1 gigabit link, each bit travels across the wire faster than on a 1 megabit link. 00:12:13.598 --> 00:12:17.638 Pause now. 00:12:17.688 --> 00:12:19.128 Answers. 00:12:19.178 --> 00:12:25.538 The first: 100 megabits is the bandwidth — the rating; 40 megabits is the throughput — the measurement. 00:12:25.588 --> 00:12:30.598 Only the throughput can change at three in the morning. 00:12:30.648 --> 00:12:32.418 The rating never moves. 00:12:32.468 --> 00:12:37.698 The second: six thousand times five thousand is thirty million bits per minute. 00:12:37.748 --> 00:12:43.908 Divide by sixty: five hundred thousand bits per second — 500 kilobits per second. 00:12:43.958 --> 00:12:48.588 If you forgot the sixty, mark it in red and remember where the marks die. 00:12:48.638 --> 00:12:50.748 And the third: false. 00:12:50.798 --> 00:12:57.408 A fatter link pushes more bits on per second; each bit still travels at the same propagation speed. 00:12:57.458 --> 00:13:06.408 If you hesitated on this one, re-watch the last slide before going on — section two is built on it. 00:13:07.179 --> 00:13:08.469 Section two. 00:13:08.519 --> 00:13:12.719 Latency — the second axis, and four thieves of time. 00:13:12.769 --> 00:13:17.959 How long does the whole journey take, from the first bit sent to the last bit arrived? 00:13:18.009 --> 00:13:25.593 The answer is a sum of exactly four parts — always the same four. 00:13:25.833 --> 00:13:28.873 First, the definition, stated carefully. 00:13:28.923 --> 00:13:37.873 Latency — or delay, the words are interchangeable — is how long the ENTIRE message takes: from the moment the first bit leaves the source to the moment the last bit arrives at the destination. 00:13:41.983 --> 00:13:45.373 Two things about that sentence. 00:13:45.423 --> 00:13:50.403 First, why 'entire' matters: nothing is usable until the last bit lands. 00:13:50.453 --> 00:13:54.783 Half an image is not an image; a frame that is missing its tail is discarded whole. 00:13:54.833 --> 00:13:58.323 The clock stops at the last bit, not the first. 00:13:58.373 --> 00:14:05.193 And second, what latency is not: it is not another word for 'low bandwidth'. 00:14:05.243 --> 00:14:13.743 A link can be enormous and slow at the same time — and in section four I will show you a spectacular example of exactly that. 00:14:13.793 --> 00:14:18.453 Latency is its own axis, and it is measured in seconds. 00:14:18.503 --> 00:14:27.453 And here is the anatomy, which you should now read out loud: latency equals propagation time, plus transmission time, plus queuing time, plus processing delay. 00:14:30.603 --> 00:14:32.783 Four thefts, added together. 00:14:32.833 --> 00:14:41.240 The next slide names each thief; after that we compute the two that can be computed. 00:14:41.290 --> 00:14:43.870 The four components, one at a time. 00:14:43.920 --> 00:14:45.760 Propagation time. 00:14:45.810 --> 00:14:50.840 The physical journey — distance divided by propagation speed. 00:14:50.890 --> 00:14:59.840 This is pure physics: the signal has to cross the space between the two devices, and you pay this once per bit-journey no matter what you send. 00:15:00.160 --> 00:15:01.940 Transmission time. 00:15:01.990 --> 00:15:08.690 The time it takes to push the whole message onto the wire — message size divided by bandwidth. 00:15:08.740 --> 00:15:12.670 A big message, or a thin pipe, and this one grows. 00:15:12.720 --> 00:15:14.270 Queuing time. 00:15:14.320 --> 00:15:18.960 Waiting inside routers while other people's packets go first. 00:15:19.010 --> 00:15:27.960 This one depends on load — it is near zero on an empty network and can dominate everything at peak hour — which makes it the hardest of the four to predict. 00:15:29.110 --> 00:15:31.480 And processing delay. 00:15:31.530 --> 00:15:37.390 Each device along the path examines the packet, decides where it goes, and forwards it. 00:15:37.440 --> 00:15:44.720 That thinking takes time — usually a small time, but never zero, and it is paid again at every hop. 00:15:44.770 --> 00:15:48.910 Today we compute the first two exactly, with formulas. 00:15:48.960 --> 00:15:57.910 Queuing returns in Session 8, when we study how routers behave under load; processing stays a small honest tax that you name but rarely calculate. 00:16:01.717 --> 00:16:03.847 Thief one, in detail. 00:16:03.897 --> 00:16:08.617 Propagation time: distance divided by propagation speed. 00:16:08.667 --> 00:16:10.887 What does it depend on? 00:16:10.937 --> 00:16:16.847 Where the receiver is — the distance — and what the signal is traveling through — the speed. 00:16:16.897 --> 00:16:20.537 Move the receiver farther away and this number grows. 00:16:20.587 --> 00:16:22.747 That is all it responds to. 00:16:22.797 --> 00:16:28.207 And now look hard at what is NOT in the formula: the size of the message. 00:16:28.257 --> 00:16:34.257 One bit or one terabyte — each bit's journey time across the distance is identical. 00:16:34.307 --> 00:16:38.197 A bigger file never, ever lengthens propagation time. 00:16:38.247 --> 00:16:44.327 Examiners test this every year: message size is not in the propagation formula. 00:16:44.377 --> 00:16:46.757 Big files do not travel slower. 00:16:46.807 --> 00:16:48.757 There are just more bits. 00:16:48.807 --> 00:16:55.367 One honest word about the speed itself, because we should state our assumptions rather than smuggle them. 00:16:55.417 --> 00:17:00.477 Light in a vacuum travels at 3 times 10 to the 8 meters per second. 00:17:00.527 --> 00:17:03.457 In cable and fiber the signal is slower. 00:17:03.507 --> 00:17:12.457 Forouzan's examples assume 2.4 times 10 to the 8 meters per second — about eighty percent of light speed — and real optical fiber is closer to 2 times 10 to the 8, roughly two-thirds of c, because light genuinely slows down inside glass. 00:17:20.627 --> 00:17:29.577 In this session we use the book's 2.4 times 10 to the 8, so that our answers match the book's answers — and we state the assumption every single time we use it. 00:17:31.237 --> 00:17:37.010 So should you, in every exam solution. 00:17:37.060 --> 00:17:38.270 Thief two. 00:17:38.320 --> 00:17:42.400 Transmission time: message size divided by bandwidth. 00:17:42.450 --> 00:17:44.410 Picture what this actually is. 00:17:44.460 --> 00:17:52.960 The sender cannot place a whole file onto the wire in one motion — it feeds the bits on one at a time, at the link's rated speed. 00:17:53.010 --> 00:17:56.760 Transmission time is how long that feeding takes. 00:17:56.810 --> 00:17:59.140 So what does it depend on? 00:17:59.190 --> 00:18:06.050 How much you send — the size in bits — and how fat the pipe is — the bandwidth in bits per second. 00:18:06.100 --> 00:18:10.670 A 1 kilobyte and a 1 gigabyte message differ a million-fold here. 00:18:10.720 --> 00:18:18.070 And a tenfold fatter pipe cuts the time tenfold: this is the number that bandwidth upgrades actually improve. 00:18:18.120 --> 00:18:20.800 And what is NOT in this formula? 00:18:20.850 --> 00:18:21.940 Distance. 00:18:21.990 --> 00:18:29.080 Pushing a gigabyte onto the wire takes exactly the same time whether the receiver is in this room or in Chile. 00:18:29.130 --> 00:18:33.330 Distance belongs to propagation, and only to propagation. 00:18:33.380 --> 00:18:37.970 The two formulas own their own variables, and they do not share. 00:18:38.020 --> 00:18:43.120 Now the trap, and it is the most expensive trap in this chapter. 00:18:43.170 --> 00:18:47.510 File sizes come to you in BYTES — megabytes, kilobytes. 00:18:47.560 --> 00:18:49.930 Bandwidth is in BITS per second. 00:18:49.980 --> 00:18:53.080 Multiply bytes by eight before you divide. 00:18:53.130 --> 00:18:57.200 Five megabytes is forty million bits, not five million. 00:18:57.250 --> 00:19:06.200 Miss the eight and every subsequent number you write is wrong by a factor of eight — and this single conversion is the largest source of lost marks in the whole of section 3.6. 00:19:09.050 --> 00:19:10.400 Bytes times eight. 00:19:10.450 --> 00:19:15.096 Say it once out loud, now. 00:19:15.146 --> 00:19:17.216 Both formulas are on screen. 00:19:17.266 --> 00:19:22.436 Before the worked examples, I want the distinction to be reflex, not reasoning. 00:19:22.486 --> 00:19:31.436 Three quick questions — pause on each one, answer out loud, and only then let the answer appear. 00:19:32.796 --> 00:19:36.076 First: you double the file size. 00:19:36.126 --> 00:19:37.736 Which of the two grows? 00:19:37.786 --> 00:19:42.146 Pause and decide. 00:19:42.196 --> 00:19:45.116 Transmission time. 00:19:45.166 --> 00:19:51.856 Propagation never sees the size — the size is simply not in its formula. 00:19:51.906 --> 00:19:56.066 Second: the receiver moves from Dhaka to Sydney. 00:19:56.116 --> 00:19:57.366 Which grows? 00:19:57.416 --> 00:20:01.796 Pause and decide. 00:20:01.846 --> 00:20:03.296 Propagation time. 00:20:03.346 --> 00:20:06.656 Transmission never sees the distance. 00:20:06.706 --> 00:20:12.476 Third: you upgrade the link from 10 megabits to 1 gigabit per second. 00:20:12.526 --> 00:20:13.816 Which shrinks? 00:20:13.866 --> 00:20:18.596 Pause and decide. 00:20:18.646 --> 00:20:25.056 Transmission time — a hundredfold, because the bandwidth is in its denominator. 00:20:25.106 --> 00:20:34.056 And propagation does not move at all, which is a sentence worth sitting with: you just made the link a hundred times 'faster', and each bit's journey time did not improve by one nanosecond. 00:20:36.876 --> 00:20:39.576 If you got all three instantly, go on. 00:20:39.626 --> 00:20:48.576 If any of them took thought, run the slide once more — the worked examples assume this is reflex. 00:20:49.361 --> 00:20:51.481 Now we put real numbers in. 00:20:51.531 --> 00:21:00.141 Forouzan example 3.45: what is the propagation time if the distance between two points is 12,000 kilometers? 00:21:00.191 --> 00:21:06.741 Assume the propagation speed is 2.4 times 10 to the 8 meters per second in cable. 00:21:06.791 --> 00:21:11.851 Write the formula first, always — method marks are real. 00:21:11.901 --> 00:21:16.121 Propagation time equals distance divided by speed. 00:21:16.171 --> 00:21:20.091 Substitute — and convert as you substitute. 00:21:20.141 --> 00:21:25.091 Twelve thousand kilometers is twelve thousand times one thousand meters. 00:21:25.141 --> 00:21:30.261 Kilometers to meters first, because the speed is in meters per second. 00:21:30.311 --> 00:21:37.651 Mixed units are the quiet cousin of the bytes-times-eight trap: the formula only works when the units agree. 00:21:37.701 --> 00:21:46.241 So we have 1.2 times 10 to the 7 meters, divided by 2.4 times 10 to the 8 meters per second. 00:21:46.291 --> 00:21:54.321 Twelve over twenty-four is a half; ten to the seven over ten to the eight is one tenth. 00:21:54.371 --> 00:21:56.991 A half of one tenth: 0.05 seconds. 00:21:57.041 --> 00:21:58.941 Fifty milliseconds. 00:21:58.991 --> 00:22:05.821 A bit crosses an ocean-scale distance in fifty milliseconds — if the cable is direct. 00:22:05.871 --> 00:22:09.411 Keep this number; the next three slides use it. 00:22:09.461 --> 00:22:13.291 And for the gamers in the room: you have seen this number before. 00:22:13.341 --> 00:22:14.751 It is called ping. 00:22:14.801 --> 00:22:23.751 Half your ping to a European server is this exact calculation, plus the queues we cannot predict. 00:22:23.995 --> 00:22:31.005 Now the interesting question: of the two computable components, which one dominates? 00:22:31.055 --> 00:22:38.125 The answer is: it depends — and the next two examples are the two opposite regimes. 00:22:38.175 --> 00:22:38.985 Example 3.46. 00:22:39.035 --> 00:22:44.305 The same 12,000 kilometer path, the same 2.4 times 10 to the 8 speed. 00:22:44.355 --> 00:22:51.885 This time a 2.5 kilobyte message — an ordinary email — crosses it on a 1 gigabit per second network. 00:22:51.935 --> 00:22:53.465 Find both times. 00:22:53.515 --> 00:22:55.575 Propagation first. 00:22:55.625 --> 00:23:03.075 Same path, same speed — nothing in that formula changed, so it is still 50 milliseconds. 00:23:03.125 --> 00:23:12.075 Notice how little work that line took: propagation does not care in the slightest what we are sending. 00:23:13.425 --> 00:23:16.285 Transmission needs the size in bits. 00:23:16.335 --> 00:23:22.125 Two thousand five hundred bytes times eight: twenty thousand bits. 00:23:22.175 --> 00:23:25.565 The conversion, first, every time. 00:23:25.615 --> 00:23:31.365 Twenty thousand bits divided by 10 to the 9 bits per second: 0.00002 seconds. 00:23:31.415 --> 00:23:35.055 That is 0.020 milliseconds — twenty microseconds. 00:23:35.105 --> 00:23:36.835 Now compare. 00:23:36.885 --> 00:23:45.835 Fifty milliseconds of journey against two-hundredths of a millisecond of pushing: propagation outweighs transmission two and a half thousand to one. 00:23:47.075 --> 00:23:50.095 For short messages, distance is everything. 00:23:50.145 --> 00:23:55.615 And read the small print on that verdict: a faster link would change almost nothing here. 00:23:55.665 --> 00:24:03.025 If you upgraded this gigabit network tenfold, you would save eighteen microseconds on a fifty-millisecond total. 00:24:03.075 --> 00:24:07.411 Nobody would notice. 00:24:07.461 --> 00:24:13.001 Example 3.47 — the same question, in the opposite regime. 00:24:13.051 --> 00:24:16.501 The same 12,000 kilometer path once more. 00:24:16.551 --> 00:24:21.781 This time a 5 megabyte image crosses it on a 1 megabit per second network. 00:24:21.831 --> 00:24:23.731 Find both times. 00:24:23.781 --> 00:24:27.771 Propagation: still 50 milliseconds. 00:24:27.821 --> 00:24:30.421 Third example, third identical line. 00:24:30.471 --> 00:24:34.891 It has not moved once today, because the path has not moved. 00:24:34.941 --> 00:24:40.851 The size in bits: five million bytes times eight is forty million bits. 00:24:40.901 --> 00:24:46.751 Say the eight out loud every time — this is the exact line where it gets forgotten. 00:24:46.801 --> 00:24:53.161 Forty million bits divided by 10 to the 6 bits per second: forty seconds. 00:24:53.211 --> 00:24:55.621 Not milliseconds — seconds. 00:24:55.671 --> 00:25:01.001 Forty full seconds of feeding bits onto a thin pipe. 00:25:01.051 --> 00:25:01.961 Compare again. 00:25:02.011 --> 00:25:09.631 Forty seconds of pushing against 0.05 seconds of travel: transmission dominates eight hundred to one. 00:25:09.681 --> 00:25:18.631 For big messages on thin pipes, bandwidth is everything — and here a faster link is exactly what you want, because the journey time was never the problem. 00:25:22.690 --> 00:25:29.890 Put the two examples side by side, because together they make the point neither makes alone. 00:25:29.940 --> 00:25:34.200 Regime one: small message, long distance. 00:25:34.250 --> 00:25:41.550 The email — 50 milliseconds of travel against 0.020 of pushing, two and a half thousand to one. 00:25:41.600 --> 00:25:45.490 Propagation dominates, and more bandwidth barely helps. 00:25:45.540 --> 00:25:49.040 The only real fix is to shorten the distance. 00:25:49.090 --> 00:25:53.080 Regime two: big message, thin pipe. 00:25:53.130 --> 00:26:00.340 The image — forty seconds of pushing against a twentieth of a second of travel, eight hundred to one the other way. 00:26:00.390 --> 00:26:07.260 Transmission dominates, distance is almost irrelevant, and the fix genuinely is more bandwidth. 00:26:07.310 --> 00:26:08.510 Same path. 00:26:08.560 --> 00:26:09.860 Same physics. 00:26:09.910 --> 00:26:11.630 Opposite bottlenecks. 00:26:11.680 --> 00:26:20.630 Whether an upgrade helps you depends entirely on which regime you are in — which is why 'just buy a faster connection' is sometimes wisdom and sometimes a waste of money, and an engineer is the person who can tell which. 00:26:25.390 --> 00:26:28.630 And here is the industrial-scale proof. 00:26:28.680 --> 00:26:34.210 Netflix does not try to beat physics — no amount of money makes propagation faster. 00:26:34.260 --> 00:26:41.640 Instead it parks the film on a server in Dhaka, so the film streams to you from kilometers away instead of from California. 00:26:41.690 --> 00:26:44.410 It moves the distance, not the bits. 00:26:44.460 --> 00:26:50.880 Content delivery networks — an entire industry — are the propagation regime taken seriously. 00:26:50.930 --> 00:26:54.110 Open the delay explorer on the course page. 00:26:54.160 --> 00:27:00.760 Three sliders — distance, message size, bandwidth — and a live breakdown of the components. 00:27:00.810 --> 00:27:09.050 Set up the email case and watch propagation tower over everything; then drag the size up and watch transmission take over. 00:27:09.100 --> 00:27:14.970 Two minutes in this demo and the two regimes stop being slides and become intuition. 00:27:15.020 --> 00:27:23.009 Pause the video and play with it. 00:27:23.599 --> 00:27:28.919 Three worked examples told you that the same physics gives opposite answers. 00:27:28.969 --> 00:27:35.679 Here is that statement with three sliders on it. Watch one thing: which of the two bars is longer. 00:27:35.729 --> 00:27:39.509 Distance, bandwidth, message size. 00:27:39.559 --> 00:27:45.719 Those are the only three things you control, and everything on the right is computed from them. 00:27:45.769 --> 00:27:48.399 Same room, huge file. 00:27:48.449 --> 00:27:56.539 The distance is almost nothing, so propagation is almost nothing — and the orange transmission bar swallows the screen. 00:27:56.589 --> 00:28:00.909 A faster link fixes this. Moving the server does not. 00:28:00.959 --> 00:28:08.739 Now the opposite: fifteen thousand kilometres, one megabit, and a single keystroke. 00:28:08.789 --> 00:28:11.789 Propagation, sixty-two and a half milliseconds. 00:28:11.839 --> 00:28:14.239 Transmission, seven point eight. 00:28:14.289 --> 00:28:23.239 Total, seventy point three — and the verdict reads propagation-dominated, distance is the problem, eight times the transmission time. 00:28:23.409 --> 00:28:29.759 A faster link barely helps, because the bits are not queuing to get on; they are in flight. 00:28:29.809 --> 00:28:38.759 Fibre to Singapore, and a much fatter pipe: two thousand nine hundred kilometres, five hundred and forty-nine megabits, ninety-five kilobytes. 00:28:40.199 --> 00:28:49.149 Twelve point one nine milliseconds of propagation against one point three nine of transmission — still propagation-dominated, and now with six point six nine megabits sitting inside the pipe at any instant. 00:28:52.459 --> 00:28:58.479 That is the bandwidth-delay product, drawn as a volume rather than stated as a formula. 00:28:58.529 --> 00:29:04.799 And one last flip: two hundred and forty kilometres, ten gigabits, one gigabyte. 00:29:04.849 --> 00:29:07.989 Propagation, one millisecond. 00:29:08.039 --> 00:29:10.619 Transmission, eight hundred. 00:29:10.669 --> 00:29:18.559 Eight hundred times, the other way round — and the answer, this time, really is buy bandwidth. 00:29:18.609 --> 00:29:23.169 Same three sliders, four completely different engineering decisions. 00:29:23.219 --> 00:29:29.647 Which is why 'fast' is not a word this course lets you use. 00:29:29.697 --> 00:29:38.647 Before the checkpoint, the two components we cannot put on a calculator — because an honest engineer names all four, not just the two with tidy formulas. 00:29:39.607 --> 00:29:41.137 Queuing time. 00:29:41.187 --> 00:29:48.307 Inside every router on the path, your packet waits its turn while other people's packets go first. 00:29:48.357 --> 00:29:55.907 It is load-dependent — the same road at rush hour takes longer, and the same router at peak traffic holds your packet longer. 00:29:55.957 --> 00:30:00.297 Near zero at three in the morning; potentially dominant at peak. 00:30:00.347 --> 00:30:09.297 That is what makes it the hardest of the four to predict, and it is precisely the component that varies from packet to packet — remember that phrase when jitter returns in the next section. 00:30:11.457 --> 00:30:13.267 Processing delay. 00:30:13.317 --> 00:30:19.917 Each device on the path examines the header, checks for damage, and decides where to forward. 00:30:19.967 --> 00:30:28.617 Typically ten to fifty microseconds per device — small, but never zero, and it is paid again at every single hop. 00:30:28.667 --> 00:30:37.617 So here is the full, honest bill for our email: latency equals 50 milliseconds of propagation, plus 0.020 milliseconds of transmission, plus queuing, plus processing. 00:30:39.557 --> 00:30:48.507 On a quiet path processing is tens of microseconds per hop and queuing is under a millisecond; on a congested one, queuing can exceed everything else on the list combined. 00:30:54.527 --> 00:31:03.477 In an exam, state all four components even when you can only compute two — the examiner checks the list before the arithmetic, and 'latency equals propagation' is a marked-down answer even when the number happens to be right. 00:31:12.041 --> 00:31:13.601 Second checkpoint. 00:31:13.651 --> 00:31:17.831 Same rule — pause, paper, no scrolling back. 00:31:17.881 --> 00:31:19.091 One. 00:31:19.141 --> 00:31:24.751 A 1 gigabyte file and a 1 kilobyte file make the same journey. 00:31:24.801 --> 00:31:29.991 Which of the four components is identical for both — and which differs a million-fold? 00:31:30.041 --> 00:31:31.201 Two. 00:31:31.251 --> 00:31:37.901 6,000 kilometers of cable at 2.4 times 10 to the 8 meters per second — what is the propagation time? 00:31:37.951 --> 00:31:39.721 Three. 00:31:39.771 --> 00:31:47.811 A 2 megabyte file crosses an 8 megabit per second link — what is the transmission time? 00:31:47.861 --> 00:31:51.911 Pause now. 00:31:51.961 --> 00:31:53.401 Answers. 00:31:53.451 --> 00:32:01.181 The first: propagation is identical — distance over speed, and size is nowhere in that formula. 00:32:01.231 --> 00:32:07.061 Transmission differs a million-fold, because a gigabyte is a million kilobytes. 00:32:07.111 --> 00:32:15.161 The second: six million meters divided by 2.4 times 10 to the 8 is 0.025 seconds — 25 milliseconds. 00:32:15.211 --> 00:32:21.591 Half the book's 12,000 kilometer answer, for half the distance, which is a good sanity check. 00:32:21.641 --> 00:32:24.801 And the third: bytes times eight first. 00:32:24.851 --> 00:32:33.301 Two megabytes is sixteen million bits; sixteen million divided by eight million bits per second is 2 seconds. 00:32:33.351 --> 00:32:42.301 If you wrote a quarter of a second, you divided bytes by bits — go back to the unit trap. 00:32:43.635 --> 00:32:44.625 Section three. 00:32:44.675 --> 00:32:47.155 The pipe, and its volume. 00:32:47.205 --> 00:32:51.305 We have bandwidth in bits per second, and delay in seconds. 00:32:51.355 --> 00:33:00.305 Multiply them and something strange and useful happens: the seconds cancel, and you are left with plain bits — and those bits are somewhere physical, right now. 00:33:04.569 --> 00:33:10.469 This is Forouzan's picture, and I think it is the best one in section 3.6. 00:33:10.519 --> 00:33:15.139 Think of the link between sender and receiver as a pipe. 00:33:15.189 --> 00:33:20.419 Not as a metaphor for 'connection' — as an actual pipe with dimensions. 00:33:20.469 --> 00:33:26.059 Its cross-section is the bandwidth: how many bits per second can enter it. 00:33:26.109 --> 00:33:32.709 Its length is the delay: how many seconds a bit spends inside before it emerges at the far end. 00:33:32.759 --> 00:33:36.929 Two dimensions, two of the numbers we have already made precise. 00:33:36.979 --> 00:33:38.509 Now fill it. 00:33:38.559 --> 00:33:47.509 At any instant, the pipe contains bits — bits the sender has already transmitted, that the receiver has not yet received. 00:33:47.599 --> 00:33:55.179 They are not waiting somewhere; they are physically in transit, strung out along thousands of kilometers of glass. 00:33:55.229 --> 00:34:04.179 And the volume of the pipe — cross-section times length, bandwidth times delay — is exactly how many bits are in flight when the pipe is full: sent, committed, paid for, and not yet arrived. 00:34:06.839 --> 00:34:15.789 That quantity is called the bandwidth-delay product, and it is the one genuinely new idea of this session. 00:34:15.949 --> 00:34:24.084 A whole later chapter is built on this number, so let us immediately make it concrete. 00:34:24.134 --> 00:34:33.084 Take the two numbers we already own: a 10 megabit per second link, and the 50 millisecond delay from example 3.45. 00:34:34.394 --> 00:34:42.134 Multiply them, with the units written out: ten million bits per second, times 0.05 seconds. 00:34:42.184 --> 00:34:45.684 Watch the units before you watch the digits. 00:34:45.734 --> 00:34:49.854 Bits per second, times seconds — the seconds cancel. 00:34:49.904 --> 00:34:52.744 What remains is not a rate and not a time. 00:34:52.794 --> 00:34:54.294 It is plain bits. 00:34:54.344 --> 00:35:02.724 Whenever a product's units collapse into something simple like that, the result usually means something physical, and this one does. 00:35:02.774 --> 00:35:06.084 Ten million times 0.05: five hundred thousand bits. 00:35:06.134 --> 00:35:12.774 Half a million bits are inside the pipe when it is full. 00:35:12.824 --> 00:35:15.614 Now read that as an engineer. 00:35:15.664 --> 00:35:23.214 At every instant, half a million bits are airborne between you and that server — sent, but not yet arrived. 00:35:23.264 --> 00:35:32.214 If the sender pushes a small burst and then stops to wait for a reply, the pipe spends most of its time running empty, and capacity you paid for is wasted. 00:35:33.184 --> 00:35:42.134 To keep the link busy, the sender must keep the whole bandwidth-delay product outstanding — half a million bits committed, in flight, unacknowledged. 00:35:43.184 --> 00:35:50.232 That is not a stylistic choice; it is the geometry of the pipe. 00:35:50.282 --> 00:35:55.812 Your turn — the one drill of the session, and it is two multiplications. 00:35:55.862 --> 00:36:01.802 A fiber from Dhaka to Singapore has a one-way delay of 15 milliseconds. 00:36:01.852 --> 00:36:09.252 Question one: at 10 megabits per second, how many bits are in flight when the pipe is full? 00:36:09.302 --> 00:36:15.532 Question two: the ends are upgraded to 1 gigabit per second — same fiber, same 15 milliseconds. 00:36:15.582 --> 00:36:16.762 Now how many? 00:36:16.812 --> 00:36:21.442 Pause the video. 00:36:21.492 --> 00:36:24.552 Two minutes, pen and paper. 00:36:24.602 --> 00:36:30.612 The formula is one multiplication — the point is the comparison between your two answers. 00:36:30.662 --> 00:36:36.401 Do both before you let the next slide appear. 00:36:36.451 --> 00:36:37.971 Here it is. 00:36:38.021 --> 00:36:46.971 At 10 megabits: 10 to the 7 bits per second times 0.015 seconds — one hundred and fifty thousand bits in flight. 00:36:48.681 --> 00:36:53.711 At 1 gigabit: 10 to the 9 times 0.015 — fifteen MILLION bits in flight. 00:36:53.761 --> 00:37:00.341 From a hundred and fifty thousand to fifteen million — on the same fiber. 00:37:00.391 --> 00:37:07.501 Read the verdict carefully: the upgrade made nothing arrive sooner. 00:37:07.551 --> 00:37:16.501 The first bit still takes fifteen milliseconds, exactly as before, because propagation is distance over speed and neither moved. 00:37:16.591 --> 00:37:21.101 What the upgrade did is make the pipe a hundred times fatter. 00:37:21.151 --> 00:37:26.381 And that fatness is not free performance — it is a new obligation. 00:37:26.431 --> 00:37:35.381 To keep the gigabit link busy, the sender must now keep fifteen million bits outstanding instead of a hundred and fifty thousand — a hundred times more data committed and unacknowledged at every instant. 00:37:39.211 --> 00:37:42.681 Keeping a fat pipe full is a hundred times harder. 00:37:42.731 --> 00:37:50.663 So write this sentence down: more bandwidth is not automatically more performance. 00:37:50.713 --> 00:37:57.753 Let me make the obligation explicit, because this number is a hinge between this chapter and a later one. 00:37:57.803 --> 00:38:05.303 A sender that pushes a small burst and then stops to wait for a reply spends most of its time silent. 00:38:05.353 --> 00:38:12.693 The link's rating is unchanged — ten megabits, one gigabit, whatever you bought — and mostly unused. 00:38:12.743 --> 00:38:14.453 The pipe runs empty. 00:38:14.503 --> 00:38:17.663 You are paying for capacity you never fill. 00:38:17.713 --> 00:38:21.223 The cure is exactly the number we computed. 00:38:21.273 --> 00:38:30.223 The bandwidth-delay product is the number of bits a sender must keep outstanding — sent but not yet acknowledged — for the link to actually work at its rating. 00:38:30.813 --> 00:38:32.493 Not roughly that number. 00:38:32.543 --> 00:38:37.163 Exactly that number: that is what the volume of a pipe means. 00:38:37.213 --> 00:38:39.773 And here is the down payment. 00:38:39.823 --> 00:38:48.773 In Session 22 you will meet sliding-window protocols — the machinery by which real senders keep exactly the right amount of data in flight. 00:38:49.223 --> 00:38:53.723 The window size that keeps a link busy is its bandwidth-delay product. 00:38:53.773 --> 00:39:00.263 When you reach that chapter and wonder why its formulas look the way they do, this slide is the reason. 00:39:00.313 --> 00:39:08.452 Today you need the number and its meaning. Session 22 builds the machinery. 00:39:08.502 --> 00:39:13.442 The fourth number on the grade sheet, briefly — because you have already met it. 00:39:13.492 --> 00:39:18.902 In Session 1 I showed you eight packets making the same journey in the same total time, twice. 00:39:18.952 --> 00:39:27.902 Stream one: a packet every 30 milliseconds, steady as a metronome — 210 milliseconds in total. 00:39:31.422 --> 00:39:40.372 Stream two: thirty, thirty, thirty-nine, twenty-one, twenty-one, thirty-nine, thirty — the same 210 milliseconds in total, and therefore exactly the same average delay. 00:39:43.122 --> 00:39:49.972 That variation has a name: jitter — how much the latency wobbles from packet to packet. 00:39:50.022 --> 00:39:52.512 The second stream is not slower. 00:39:52.562 --> 00:39:59.352 It is uneven, and for video that unevenness means the picture freezes, then sprints to catch up. 00:39:59.402 --> 00:40:08.312 And that is why jitter is a performance metric in its own right: a file transfer never notices it, but a video call lives and dies by it. 00:40:08.362 --> 00:40:17.312 Same average delay, completely different experience — so the average alone cannot be the whole story, and jitter is the number that finishes it. 00:40:18.282 --> 00:40:24.792 One connection to make before we move on, now that you own the four components of latency. 00:40:24.842 --> 00:40:28.102 Where does the wobble come from? 00:40:28.152 --> 00:40:35.842 Mostly from queuing — the one component that changes packet to packet, as the queues inside each router grow and shrink around your traffic. 00:40:35.892 --> 00:40:43.212 Propagation is fixed by geography, transmission by size and rating; it is the queues that breathe. 00:40:43.262 --> 00:40:47.661 That is the whole slide. 00:40:47.711 --> 00:40:49.201 Third checkpoint. 00:40:49.251 --> 00:40:51.061 Pause and answer on paper. 00:40:51.111 --> 00:40:52.321 One. 00:40:52.371 --> 00:40:58.321 A link has bandwidth 100 megabits per second and a one-way delay of 20 milliseconds. 00:40:58.371 --> 00:41:01.031 How many bits fill the pipe? 00:41:01.081 --> 00:41:02.241 Two. 00:41:02.291 --> 00:41:07.191 The same link is upgraded to 1 gigabit on the same fiber. 00:41:07.241 --> 00:41:12.091 What happens to the first bit's arrival time, and what happens to the pipe's volume? 00:41:12.141 --> 00:41:13.321 Three. 00:41:13.371 --> 00:41:21.571 Two streams share the same 40 millisecond average delay; one is a perfect call, the other unusable. 00:41:21.621 --> 00:41:24.971 Which performance metric separates them? 00:41:25.021 --> 00:41:29.451 Pause now. 00:41:29.501 --> 00:41:30.401 Answers. 00:41:30.451 --> 00:41:34.941 The first: 10 to the 8 bits per second times 0.02 seconds — two million bits. 00:41:34.991 --> 00:41:43.761 The second: the first bit's arrival time does not change at all — propagation is distance over speed, and the fiber did not move. 00:41:43.811 --> 00:41:47.911 The volume grows tenfold, to twenty million bits. 00:41:47.961 --> 00:41:49.751 And the third: jitter. 00:41:49.801 --> 00:41:58.751 Same average, different variation — the average was never going to separate them. 00:41:59.717 --> 00:42:01.217 Section four. 00:42:01.267 --> 00:42:05.687 Back to the satellite from minute one — and this time we compute it. 00:42:05.737 --> 00:42:12.228 Then we grade one more machine, and it has wheels. 00:42:12.278 --> 00:42:14.888 Take out the guess you wrote down at the start. 00:42:14.938 --> 00:42:19.438 Before any arithmetic, look at the journey your packet actually makes. 00:42:19.488 --> 00:42:21.218 Your dish is on your roof. 00:42:21.268 --> 00:42:23.348 The satellite is in orbit. 00:42:23.398 --> 00:42:29.678 The ground station — the satellite company's link into the internet — is somewhere else on Earth. 00:42:29.728 --> 00:42:34.658 Leg one: your packet climbs from your dish to the satellite. 00:42:34.708 --> 00:42:38.028 Thirty-six thousand kilometers, straight up. 00:42:38.078 --> 00:42:43.178 Leg two: the satellite relays it down to the ground station. 00:42:43.228 --> 00:42:46.648 Thirty-six thousand kilometers, straight back down. 00:42:46.698 --> 00:42:53.168 Only then does your packet touch the ordinary internet and begin the terrestrial part of its journey. 00:42:53.218 --> 00:42:56.928 Why thirty-six thousand, of all numbers? 00:42:56.978 --> 00:43:05.038 Because this is a geostationary satellite: it must appear to hang motionless in the sky, so your dish never has to move. 00:43:05.088 --> 00:43:14.038 For that, its orbit must take exactly one day — and the only altitude where an orbit takes one day is about 35,786 kilometers above the equator. 00:43:17.338 --> 00:43:19.298 Call it thirty-six thousand. 00:43:19.348 --> 00:43:26.358 The altitude is not an engineering choice that a better company could improve; it is dictated by gravity. 00:43:26.408 --> 00:43:32.812 Every packet climbs all of it, and descends all of it. 00:43:32.862 --> 00:43:41.452 Now the arithmetic, and notice it is the same formula as example 3.45 — distance over speed, nothing new. 00:43:41.502 --> 00:43:42.912 One hop. 00:43:42.962 --> 00:43:50.552 Radio waves travel at essentially the speed of light: 3 times 10 to the 8 meters per second. 00:43:50.602 --> 00:43:54.152 Thirty-six thousand kilometers is 3.6 times 10 to the 7 meters. 00:43:54.202 --> 00:43:56.432 Divide: 0.12 seconds. 00:43:56.482 --> 00:44:01.932 One hundred and twenty milliseconds — for the climb alone. 00:44:01.982 --> 00:44:10.932 But your packet must go up AND down: two hops, two hundred and forty milliseconds, before it has even touched the internet. 00:44:13.212 --> 00:44:22.162 Every propagation number we computed today for cables across oceans was fifty milliseconds or less; this connection pays five times that just to reach the ground. 00:44:24.272 --> 00:44:27.222 And a conversation is round trip. 00:44:27.272 --> 00:44:36.222 The reply climbs and descends again: roughly four hundred and eighty milliseconds there-and-back — before a single queue, before any processing, before the terrestrial internet adds its own share. 00:44:42.192 --> 00:44:43.402 Now the verdict. 00:44:43.452 --> 00:44:52.402 From Session 1: one-way voice stays natural below about 150 milliseconds, and 400 milliseconds is the ceiling beyond which people start talking over each other. 00:44:54.462 --> 00:45:00.902 This link's round trip starts at 480 — over the ceiling before the network even gets busy. 00:45:00.952 --> 00:45:07.262 The call is doomed by geometry — by propagation delay — and no bandwidth upgrade can save it. 00:45:07.312 --> 00:45:10.042 So grade your guess. 00:45:10.092 --> 00:45:17.922 If you wrote 'the 100 megabits is fake', or 'satellites are slow at moving data' — no. 00:45:17.972 --> 00:45:22.242 The bandwidth was never a lie, and never the problem. 00:45:22.292 --> 00:45:31.242 Bandwidth says how many bits per second; latency says how long each journey takes; and a video call lives by the second number, which this link fails by physics. 00:45:31.912 --> 00:45:40.862 That, by the way, is exactly why the new satellite constellations fly at about 550 kilometers instead of 36,000: the same distance-over-speed arithmetic at 550 kilometers gives roughly two milliseconds a hop, and suddenly video calls work. 00:45:48.472 --> 00:45:53.945 Same physics, different geometry. 00:45:53.995 --> 00:45:58.985 One more machine to grade with your four numbers, and it is Forouzan's favorite. 00:45:59.035 --> 00:46:04.885 A truck leaves Dhaka this morning carrying one thousand hard drives, ten terabytes each. 00:46:04.935 --> 00:46:08.065 It reaches Chattogram in about six hours. 00:46:08.115 --> 00:46:10.745 Question: is that a high-bandwidth link? 00:46:10.795 --> 00:46:19.745 It moves data from one place to another, so it is a link — and links get graded on the four numbers like everybody else. 00:46:19.925 --> 00:46:20.405 The data. 00:46:20.455 --> 00:46:25.345 A thousand drives times ten terabytes is 10 to the 16 bytes. 00:46:25.395 --> 00:46:31.505 Bytes times eight — the rule follows us everywhere — is 8 times 10 to the 16 bits. 00:46:31.555 --> 00:46:33.465 Ten petabytes on wheels. 00:46:33.515 --> 00:46:34.885 The time. 00:46:34.935 --> 00:46:39.645 Six hours is twenty-one thousand six hundred seconds. 00:46:39.695 --> 00:46:44.975 Divide: 8 times 10 to the 16 over 21,600 — approximately 3.7 terabits per second. 00:46:45.025 --> 00:46:53.095 Against roughly 10 gigabits for a rentable link, that is about 370 times more. 00:46:53.145 --> 00:47:01.807 As a bit-mover, the truck beats anything you can rent. 00:47:01.857 --> 00:47:04.157 So is the truck a high-bandwidth link? 00:47:04.207 --> 00:47:07.847 Let us grade it on all four numbers, not one. 00:47:07.897 --> 00:47:13.057 As a bit-mover: 3.7 terabits per second of throughput. 00:47:13.107 --> 00:47:19.757 If your job is to move ten petabytes of backups from Dhaka to Chattogram, nothing you can rent comes close. 00:47:19.807 --> 00:47:23.927 Your nightly backup would love the truck. 00:47:23.977 --> 00:47:28.377 As a conversation: the latency is six hours. 00:47:28.427 --> 00:47:37.377 Twenty-one million, six hundred thousand milliseconds from first bit to last — and remember the definition: nothing at all has arrived until the truck does. 00:47:39.717 --> 00:47:46.607 Jitter: the variance of Dhaka road traffic, measured in hours. 00:47:46.657 --> 00:47:49.117 Try a video call over it. 00:47:49.167 --> 00:47:50.897 So — is it a high-bandwidth link? 00:47:50.947 --> 00:47:51.497 Yes. 00:47:51.547 --> 00:47:52.857 And a dreadful one. 00:47:52.907 --> 00:48:01.857 Both answers are right at the same time, because 'fast' was never one number — and that is the entire lesson of section 3.6. 00:48:02.107 --> 00:48:09.167 Sneakernet, by the way, is a real term in the literature, and this is Forouzan's own favorite example of it. 00:48:09.217 --> 00:48:18.167 One more for the road, since you now own the concept: the truck's own bandwidth-delay product is 3.7 terabits per second times 21,600 seconds — 8 times 10 to the 16 bits, the entire ten petabytes. 00:48:21.757 --> 00:48:24.767 Every bit is in flight for the whole journey. 00:48:24.817 --> 00:48:31.707 The truck is not attached to a pipe; the truck IS the pipe. 00:48:31.757 --> 00:48:34.247 The whole session in one table. 00:48:34.297 --> 00:48:36.727 Four numbers, four questions, four different customers. 00:48:36.777 --> 00:48:37.807 Bandwidth. 00:48:37.857 --> 00:48:41.547 What could the link carry? 00:48:41.597 --> 00:48:48.017 The number for the buyer — capacity planning, link shopping, reading the ISP's brochure with appropriate suspicion. 00:48:48.067 --> 00:48:49.307 Throughput. 00:48:49.357 --> 00:48:53.057 What actually got through? 00:48:53.107 --> 00:48:59.737 The number for the backup, the download, the bulk transfer — any job that cares about total bits moved. 00:48:59.787 --> 00:49:01.207 Latency. 00:49:01.257 --> 00:49:04.277 How long does one journey take? 00:49:04.327 --> 00:49:10.527 The number for the video call, the gamer, the trading system — any job where the moment matters. 00:49:10.577 --> 00:49:11.787 Jitter. 00:49:11.837 --> 00:49:14.087 Does the delay wobble? 00:49:14.137 --> 00:49:18.917 The number for live audio and video — smoothness, not speed. 00:49:18.967 --> 00:49:25.897 And the rule that ties the table together: ask which number your application lives and dies by. 00:49:25.947 --> 00:49:27.907 Grade the link on that number. 00:49:27.957 --> 00:49:30.927 Only then are you allowed to call it good or bad. 00:49:30.977 --> 00:49:37.807 The satellite failed the gamer and served the downloader; the truck fails the caller and delights the archivist. 00:49:37.857 --> 00:49:43.240 Neither link changed — the question did. 00:49:43.290 --> 00:49:48.630 Before the recap — the four mistakes I see every year, so you can make none of them. 00:49:48.680 --> 00:49:51.540 Classroom Quiz 1 is coming in Week 5. 00:49:51.590 --> 00:49:52.820 One. 00:49:52.870 --> 00:50:01.820 'The link is 1 megabit, so the throughput is 1 megabit.' No — bandwidth is the rating, throughput is the measurement, and T is less than B, always. 00:50:03.120 --> 00:50:08.150 They are different numbers answering different questions. 00:50:08.200 --> 00:50:09.350 Two. 00:50:09.400 --> 00:50:14.800 Dividing 5 megabytes by 1 megabit per second without converting. 00:50:14.850 --> 00:50:23.560 Bytes times eight first: 5 megabytes is forty million bits, and forty million over 10 to the 6 is forty seconds. 00:50:23.610 --> 00:50:29.730 This is the row to linger on — of the four, this is the one that costs the most marks. 00:50:29.780 --> 00:50:30.950 Three. 00:50:31.000 --> 00:50:35.940 'A bigger file means longer propagation time.' It does not. 00:50:35.990 --> 00:50:41.940 Propagation is distance over speed; the file's size touches only transmission time. 00:50:41.990 --> 00:50:43.210 Four. 00:50:43.260 --> 00:50:52.210 'Latency equals propagation, full stop.' Latency has four parts: propagation, plus transmission, plus queuing, plus processing. 00:50:54.450 --> 00:50:57.720 State all four, then compute the two you can. 00:50:57.770 --> 00:51:04.633 The list is worth marks even before the arithmetic starts. 00:51:04.683 --> 00:51:09.643 Let me close the content by naming exactly what you should now be able to do. 00:51:09.693 --> 00:51:18.643 Distinguish — bandwidth in hertz from bandwidth in bits per second, with Nyquist and Shannon as the exchange rate between them; and bandwidth from throughput, the promise from the measurement. 00:51:23.943 --> 00:51:32.833 Compute — a throughput from a real measurement, converting minutes to seconds and bytes to bits before anything else. 00:51:32.883 --> 00:51:41.833 Split — latency into its four components, and compute propagation and transmission exactly, each from its own formula with its own variables. 00:51:43.083 --> 00:51:52.033 Multiply — bandwidth by delay to get the bits in flight, and explain why a sender must keep exactly that many outstanding to keep the link busy. 00:51:53.603 --> 00:52:01.383 And judge — any link, from a fiber to a satellite to a truck, by the number your application lives by. 00:52:01.433 --> 00:52:03.433 Never by the word 'fast'. 00:52:03.483 --> 00:52:07.713 If any of those feel shaky, the section that covers it is still there. 00:52:07.763 --> 00:52:13.096 This is a video — use it as one. 00:52:13.366 --> 00:52:19.126 Five last questions — and notice they are exactly the shape of the questions the midterm asks. 00:52:19.176 --> 00:52:21.146 Pause and answer them on paper. 00:52:21.196 --> 00:52:22.396 One. 00:52:22.446 --> 00:52:27.056 A link passes 3,000 frames per minute, 4,000 bits each. 00:52:27.106 --> 00:52:29.636 What is the throughput? 00:52:29.686 --> 00:52:30.836 Two. 00:52:30.886 --> 00:52:39.576 24,000 kilometers of cable at 2.4 times 10 to the 8 meters per second — what is the propagation time? 00:52:39.626 --> 00:52:40.796 Three. 00:52:40.846 --> 00:52:48.466 A 1.25 megabyte file crosses a 10 megabit per second link — what is the transmission time? 00:52:48.516 --> 00:52:49.746 Four. 00:52:49.796 --> 00:52:57.876 Bandwidth 20 megabits per second, one-way delay 25 milliseconds — how many bits fill the pipe? 00:52:57.926 --> 00:52:59.196 Five. 00:52:59.246 --> 00:53:04.396 Name the four components of latency — and the two you computed today. 00:53:04.446 --> 00:53:08.506 Pause now. 00:53:08.556 --> 00:53:11.226 Take your time on these. 00:53:11.276 --> 00:53:20.226 One — three thousand times four thousand is twelve million bits per minute; divide by sixty: 200 kilobits per second. 00:53:20.626 --> 00:53:29.576 Two — 2.4 times 10 to the 7 meters over 2.4 times 10 to the 8: 0.1 seconds, one hundred milliseconds. 00:53:29.806 --> 00:53:38.206 Three — bytes times eight: ten million bits, over 10 to the 7 bits per second: exactly 1 second. 00:53:38.256 --> 00:53:43.156 Four — 2 times 10 to the 7 times 0.025: five hundred thousand bits. 00:53:43.206 --> 00:53:49.866 Five — propagation, transmission, queuing, processing; you computed the first two. 00:53:49.916 --> 00:53:58.866 Five out of five, with the units converted before the division every time, and you are ready for this week's online quiz. 00:54:02.588 --> 00:54:04.088 So take this with you. 00:54:04.138 --> 00:54:05.738 Never say 'fast'. 00:54:05.788 --> 00:54:14.738 Say throughput, or say latency — they are different kinds of fast, and everything you graded today, from the ocean cable to the satellite to the truck, was strong in one and weak in the other. 00:54:18.108 --> 00:54:26.558 Weekly Online Quiz A2 closes on Saturday at midnight — twenty minutes, one attempt — and today's four numbers are in it. 00:54:26.608 --> 00:54:35.558 Classroom Quiz 1 comes in Week 5, in the first thirty minutes of Session 9 — thirty minutes, twenty marks, on paper, calculator and pen, covering everything from Session 1 up to that point. 00:54:39.998 --> 00:54:43.748 The final-checks slide you just did is the shape of what is coming. 00:54:43.798 --> 00:54:47.388 Before the next session, read the opening of Chapter 9. 00:54:47.438 --> 00:54:56.388 We are done with wires: next we leave the physical layer behind and start grouping bits into frames — the data-link layer, where bits get names. 00:54:57.058 --> 00:55:02.638 See you in class, with your calculator.