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Pages 227-249

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From page 227... ... ~ am going to be talking about statistical models for Internet packet traffic. The models contribute in adding to the basic understanding of Tnternet packet traffic, which was very much in need of understanding, and also provide a mechanism for open-Ioop generation of packet traffic for engineering studies. Read the entire page →
From page 228... ... to oth" ~ ends when: one or more connection~losing control packets are se~ Now, to carry out this transfer, the two computers establish a connection. That is the word that is used. Read the entire page →
From page 229... ... tints' iligi`~! link sheds, I''rxe c..~-~i~lit eden: kiv'~r link speeds, fewer c~onnechon,; Let's take a look at an example here. Read the entire page →
From page 230... ... There are fewer connections using the links at any given time, just less traffic generally. As we move into the core and hit the service providers, the link speeds are going up, the usage of the links goes way up. Read the entire page →
From page 231... ... Now, if we want to understand Internet traffic, one extremely useful and effective measurement scenario is to attach a device to a link. So, we want to understand the packet traffic on a link. Read the entire page →
From page 232... ... The highest packet rate of collection is this 2.5 gigabit per second link, which is the link of a service provider out on the West Coast. The rate there is 80,000 packets per second. Read the entire page →
From page 233... ... l',�~' ~�at,: inter-arrival times (see) o;-;reGI~r; b'}o ;~numuer2' e c, measure at~magnitude of multiplexing snubber) Read the entire page →
From page 234... ... It goes up to about a second. So, we are going through nearly six orders of magnitude in these end arrival times. Read the entire page →
From page 235... ... So, we get end arrival times that seem to come in little bursts here, and there are sort of striations that you can see. So, just from this time plot, you see that there must be time relationships, time correlation. Read the entire page →
From page 236... ... For the byte counts, a similar process, except that, instead of just counting the number of packets during the interval, you add up the sizes of all the packets arriving during that interval. So, packet counts and byte counts, they are all long-range dependent, sizes and arrivals by packet counts. Read the entire page →
From page 237... ... theory. arm empirical study � wkb Enough aggregation' a go ussian time series ~ a cats reduction method � widespread wavelet remodeling ~ fractional Brownian motion a popular model Arrivals and Sized the marked point process * Read the entire page →
From page 238... ... Here is a Weibull quartile plot of the ens! arrival times of one particular low-Ioad trace. Read the entire page →
From page 239... ... You have to be forgiving, of course, because when you have an arbitrarily large amount of data, of course, nothing ever fits. So, Weibull in fact, turns out to be an excellent approximation of the distribution of the end arrival times. Read the entire page →
From page 240... ... Now we start to see a little bit of deviation down here at the low end of the distribution, not enough, though, to jeopardize modeling these things by Weibull. By the way, there is a minimum end arrival time. Read the entire page →
From page 241... ... be the cumulative (listribution function of the nominal, with mean zero and variance one. So, what we clid was, we said, all right, we got a good handle on the marginal distribution and now we are going to transform the time series. Read the entire page →
From page 242... ... Everything works if ~ am taken to a Gaussian time series. Then, of course, everything is perfectly legitimate. Read the entire page →
From page 243... ... _ - ~.~3~ ~$-:~R,,,~.%~:s, ~~* .~ ~ (~.~It is a linear combination of two time series, one of them white noise, a, and one of them a very simple, long-range depen(lent series, mixed according to this parameter D Read the entire page →
From page 244... ... used only Or fitting find not fat generation \> (J,y,, and '9~`,~' and Hi- read as a function of the <#>.nnection Ad, ~ ~ianeratio'1 of: packet marked point process trend In by Specking r~ arid ,':>~, So, you need a little bit of extra stuff in there to account for the observed Read the entire page →
From page 245... ... What we found was that the shape parameter of the Weibul1 and those two 0 's for the end arrivals and the sizes, change with the connection load. What we decided to do is to sort of fit the behavior. Read the entire page →
From page 246... ... The models fit, provided the number of active connections is about the same as a number of, say, eight. Read the entire page →
From page 247... ... So, we will see. There is going to be a special issue of papers in Statistical Science on Internet traffic, and Read the entire page →
From page 248... ... The question is, how high can we get before that happens, and that is what the simulation tells you, and that is what nobody knew, by the way. Service providers just didn't know how to -- ~ am sorry, ~ am taking too long for this question. Read the entire page →
From page 249... ... 249 AUDIENCE: [Question off microphone.] Read the entire page →

From page 227...

... ~ am going to be talking about statistical models for Internet packet traffic. The models contribute in adding to the basic understanding of Tnternet packet traffic, which was very much in need of understanding, and also provide a mechanism for open-Ioop generation of packet traffic for engineering studies.