CHARACTERISTICS OF TCP CONNECTION ARRIVALS in Visual Studio .NET

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CHARACTERISTICS OF TCP CONNECTION ARRIVALS
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Fig. 15.11 Quality of t of application-speci c (HTTP) and time-dependent connection interarrival times for the external AT&T 18 November to 8 December 1995 dataset.
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four columns correspond to models tted over 12 hour time periods while the fth column corresponds to models tted over the whole dataset. It is rather interesting to note the huge variations in the value of the discrepancy for all models except the Weibull one. This is another indication that only the Weibull and none of the other models yields a satisfying t even over the different time periods.
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15.5 CHARACTERIZATION OF CONNECTION INTERARRIVAL TIMES
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(b) cdf values for source 1
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(c) cdf values for source 8
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Fig. 15.12 Fit of source- and application-speci c (HTTP) interarrival times over a one hour period of the external AT&T dataset from 16 to 31 March 1996. (a) The arrivals versus the source. (b) The empirical and the tted cumulative distributions of sources 1 and 8.
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Within the models for the 12 hour time period a clear periodicity is recognizable, a periodicity that has also been observed within other datasets. During the rst half of a day the Pareto and lognormal models give a better t than the exponential one, while the situation is reversed for the second half of the day. An explanation for this is that during night hours many fewer actions are initiated and, as such, the number of long interarrival times is larger, thus explaining why the heavy-tailed Pareto distribution yields a better t than the exponential distribution. The Weibull distribution yields an even better t than either the Pareto or the exponential one. We also consider the interarrival time distribution of all HTTP connections over all 1204 possible one hour time periods that contain suf cient observations. The Weibull models are statistically better than the Pareto models in 92.9% of the instances, better than the exponential models in 92.3% of the instances, and better than the lognormal in 94.5% of the instances. In only 0.7% of the instances is the Pareto model better than the Weibull one and in only 0.2% is the exponential model better than the Weibull model. (Even though the Weibull model contains the
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CHARACTERISTICS OF TCP CONNECTION ARRIVALS
^ Fig. 15.13 (a) Con dence intervals for l2 for the tted Weibull, lognormal, exponential, and Pareto model of TELNET interarrival times within each 12 hour time frame for the 29 30 June 1995 dataset. (b) Histogram of Weibull shape parameter c of the tted Weibull distributions for the HTTP application for one hour time periods for the external AT&T dataset from 16 to 30 March. (c) Histogram of Weibull shape parameter c of the tted Weibull distributions for the applications TELNET, X, FTP, HTTP, RFS, SMTP, and FINGER and two hour time periods for all CMU datasets.
exponential model, the exponential model can sometimes result in a better t than the Weibull model. This is possible since the parameter estimation for the Weibull model is more complex and can be less precise than for the exponential model.) Similar observations apply to the CMU datasets and other applications. Given that the Weibull model is superior for many applications and that its shape parameter c may vary quite substantially from one time period to the next, it is of interest to look at the distribution of the shape parameter c of the tted Weibull distributions. Figure 15.13(b) gives the histogram of Weibull shape parameter c for the tted Weibull distribution of the external AT&T dataset from 16 to 31 March 1996 and Fig. 15.13(c) does the same for the tted Weibull distributions for the applications TELNET, X, FTP, HTTP, RFS, SMTP, and FINGER over two hour time periods for all CMU datasets. That the number of Weibull models that have a shape parameter around one is small is another indication that the exponential model is inappropriate to model these interarrival times. That more than 50% of the shape parameters are less than 0.65 indicates the inherent burstiness of the request sequences.