In this post I go on with the exploratory analysis of the data as generated by the first TCP post serie. At the purpose, I load it back.
suppressPackageStartupMessages(library(ggplot2))
suppressPackageStartupMessages(library(Rmisc))
suppressPackageStartupMessages(library(knitr))
df <- read.csv("TCP_ea.csv", header=TRUE, stringsAsFactors = FALSE, sep=",")
dim(df)
## [1] 2501 10
kable(head(df,5))
| 0.00 |
2 |
0.2000000 |
0.0 |
0.0000000 |
0 |
10.000000 |
slowstart |
decrease |
high |
| 0.02 |
2 |
0.2066667 |
0.2 |
0.0000000 |
0 |
9.677419 |
slowstart |
increase |
high |
| 0.04 |
2 |
0.2000000 |
0.0 |
0.0015038 |
0 |
10.000000 |
slowstart |
decrease |
high |
| 0.06 |
2 |
0.2066667 |
0.2 |
0.0014925 |
0 |
9.677419 |
slowstart |
increase |
high |
| 0.08 |
2 |
0.2000000 |
0.0 |
0.0029851 |
0 |
10.000000 |
slowstart |
decrease |
high |
kable(tail(df,5))
| 2497 |
49.92 |
27.41972 |
0.9893418 |
23.68025 |
21.86931 |
0.0463816 |
27.71512 |
ca_steadystate |
decrease |
high |
| 2498 |
49.94 |
27.25502 |
0.9878185 |
23.63456 |
21.88293 |
0.0467328 |
27.59112 |
ca_steadystate |
decrease |
high |
| 2499 |
49.96 |
27.08724 |
0.9862126 |
23.58638 |
21.89610 |
0.0470732 |
27.46593 |
ca_steadystate |
decrease |
high |
| 2500 |
49.98 |
26.91647 |
0.9845232 |
23.53570 |
21.90881 |
0.0474025 |
27.33960 |
ca_steadystate |
decrease |
high |
| 2501 |
50.00 |
26.74279 |
0.9827496 |
23.48249 |
21.92104 |
0.0477203 |
27.21221 |
ca_steadystate |
decrease |
high |
To follow, summaries of the TCP variables \({W(t), R(t), q(t), x(q(t)), p(x(t)), S(t)}\) conditioned on TCP status value, {slow start, congestion avoidance transient state, congestion avoidance steady state}.
a <- aggregate(W~status, data=df, FUN=summary)
kable(data.frame(status=a$status, W=a$W))
| ca_steadystate |
10.77 |
17.18 |
22.920 |
22.120 |
27.47 |
30.86 |
| ca_transient |
10.59 |
18.02 |
23.270 |
22.600 |
27.59 |
30.97 |
| slowstart |
2.00 |
2.00 |
3.774 |
4.528 |
6.25 |
10.54 |
ggplot(data=df, aes(x=status, y=W)) + geom_boxplot(aes(fill=status))
a <- aggregate(R~status, data=df, FUN=summary)
kable(data.frame(status=a$status, R=a$R))
| ca_steadystate |
0.3949 |
0.5704 |
0.7477 |
0.7292 |
0.8967 |
1.0040 |
| ca_transient |
0.2592 |
0.5993 |
0.7725 |
0.7423 |
0.9089 |
1.0080 |
| slowstart |
0.2000 |
0.2000 |
0.2067 |
0.2109 |
0.2175 |
0.2512 |
ggplot(data=df, aes(x=status, y=R)) + geom_boxplot(aes(fill=status))
a <- aggregate(q~status, data=df, FUN=summary)
kable(data.frame(status=a$status, q=a$q))
| ca_steadystate |
5.848 |
11.11 |
16.43 |
15.8800 |
20.9000 |
24.130 |
| ca_transient |
1.775 |
11.98 |
17.18 |
16.2700 |
21.2700 |
24.240 |
| slowstart |
0.000 |
0.00 |
0.20 |
0.3257 |
0.5246 |
1.536 |
ggplot(data=df, aes(x=status, y=q)) + geom_boxplot(aes(fill=status))
a <- aggregate(x~status, data=df, FUN=summary)
kable(data.frame(status=a$status, x=a$x))
| ca_steadystate |
11.03000 |
12.340000 |
15.40000 |
15.79000 |
18.99000 |
22.04000 |
| ca_transient |
0.08942 |
7.205000 |
13.81000 |
12.91000 |
19.09000 |
22.10000 |
| slowstart |
0.00000 |
0.006562 |
0.01458 |
0.02079 |
0.02612 |
0.07846 |
ggplot(data=df, aes(x=status, y=x)) + geom_boxplot(aes(fill=status))
From the last two table above, the average queue length and its average EWMA are both less than the RED minimum threshold which is equal to 20.
a <- aggregate(p~status, data=df, FUN=summary)
kable(data.frame(status=a$status, p=a$p))
| ca_steadystate |
0 |
0 |
0 |
0.004996 |
0 |
0.05110 |
| ca_transient |
0 |
0 |
0 |
0.006827 |
0 |
0.05254 |
| slowstart |
0 |
0 |
0 |
0.000000 |
0 |
0.00000 |
ggplot(data=df, aes(x=status, y=p)) + geom_boxplot(aes(fill=status))
a <- aggregate(S~status, data=df, FUN=summary)
kable(data.frame(status=a$status, S=a$S))
| ca_steadystate |
20.110 |
31.00 |
31.17 |
30.30 |
31.47 |
31.96 |
| ca_transient |
20.110 |
31.03 |
31.22 |
30.73 |
31.58 |
40.86 |
| slowstart |
9.677 |
10.00 |
18.66 |
20.95 |
29.15 |
41.95 |
ggplot(data=df, aes(x=status, y=S)) + geom_boxplot(aes(fill=status))
From the last table above, the average TCP transmission rate keeps values close to the link capacity one. Moreover values dispersion of S is far less than the one of W, q and R.
To follow, summaries of TCP variables \({W(t), R(t), q(t), x(q(t)), p(x(t)), S(t)}\) conditioned on both status and TCP transmission rate slope {decrease, increase}.
a <- aggregate(W~(status+S_slope), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, W=a$W))
| ca_steadystate |
decrease |
13.59 |
19.950 |
24.390 |
23.850 |
28.050 |
30.860 |
| ca_transient |
decrease |
10.59 |
18.020 |
23.270 |
22.600 |
27.590 |
30.970 |
| slowstart |
decrease |
2.00 |
2.000 |
2.000 |
3.827 |
4.381 |
10.540 |
| ca_steadystate |
increase |
10.77 |
11.360 |
12.210 |
12.340 |
13.210 |
14.610 |
| slowstart |
increase |
2.00 |
2.444 |
4.068 |
4.739 |
6.711 |
9.963 |
a <- aggregate(R~(status+S_slope), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, R=a$R))
| ca_steadystate |
decrease |
0.4502 |
0.6512 |
0.7957 |
0.7773 |
0.9169 |
1.0040 |
| ca_transient |
decrease |
0.2592 |
0.5993 |
0.7725 |
0.7423 |
0.9089 |
1.0080 |
| slowstart |
decrease |
0.2000 |
0.2000 |
0.2000 |
0.2057 |
0.2000 |
0.2512 |
| ca_steadystate |
increase |
0.3949 |
0.4075 |
0.4298 |
0.4577 |
0.4771 |
0.6625 |
| slowstart |
increase |
0.2000 |
0.2054 |
0.2085 |
0.2124 |
0.2181 |
0.2440 |
a <- aggregate(q~(status+S_slope), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, q=a$q))
| ca_steadystate |
decrease |
7.506 |
13.540 |
17.870 |
17.3200 |
21.510 |
24.130 |
| ca_transient |
decrease |
1.775 |
11.980 |
17.180 |
16.2700 |
21.270 |
24.240 |
| slowstart |
decrease |
0.000 |
0.000 |
0.000 |
0.1707 |
0.000 |
1.536 |
| ca_steadystate |
increase |
5.848 |
6.226 |
6.893 |
7.7300 |
8.312 |
13.880 |
| slowstart |
increase |
0.000 |
0.163 |
0.254 |
0.3722 |
0.542 |
1.320 |
a <- aggregate(x~(status+S_slope), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, x=a$x))
| ca_steadystate |
decrease |
11.03000 |
12.010000 |
15.130000 |
15.66000 |
19.06000 |
22.04000 |
| ca_transient |
decrease |
0.08942 |
7.205000 |
13.810000 |
12.91000 |
19.09000 |
22.10000 |
| slowstart |
decrease |
0.00000 |
0.002985 |
0.005882 |
0.01671 |
0.01831 |
0.07846 |
| ca_steadystate |
increase |
12.71000 |
14.180000 |
16.280000 |
16.49000 |
18.77000 |
20.81000 |
| slowstart |
increase |
0.00000 |
0.008643 |
0.015950 |
0.02201 |
0.03093 |
0.06906 |
a <- aggregate(p~(status+S_slope), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, p=a$p))
| ca_steadystate |
decrease |
0 |
0 |
0 |
0.005630 |
0 |
0.05110 |
| ca_transient |
decrease |
0 |
0 |
0 |
0.006827 |
0 |
0.05254 |
| slowstart |
decrease |
0 |
0 |
0 |
0.000000 |
0 |
0.00000 |
| ca_steadystate |
increase |
0 |
0 |
0 |
0.001416 |
0 |
0.02166 |
| slowstart |
increase |
0 |
0 |
0 |
0.000000 |
0 |
0.00000 |
a <- aggregate(S~(status+S_slope), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, S=a$S))
| ca_steadystate |
decrease |
20.320 |
31.03 |
31.19 |
30.79 |
31.46 |
31.96 |
| ca_transient |
decrease |
20.110 |
31.03 |
31.22 |
30.73 |
31.58 |
40.86 |
| slowstart |
decrease |
10.000 |
10.00 |
10.00 |
17.94 |
21.90 |
41.95 |
| ca_steadystate |
increase |
20.110 |
22.92 |
29.42 |
27.51 |
31.65 |
31.96 |
| slowstart |
increase |
9.677 |
12.09 |
19.50 |
21.85 |
30.87 |
40.83 |
To follow, summaries of TCP variables \({W(t), R(t), q(t), x(q(t)), p(x(t)), S(t)}\) conditioned on status, slope and slope rate level {high, low}.
a <- aggregate(W~(status+S_slope+S_slope_rate), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, S_slope_rate = a$S_slope_rate, W=a$W))
| ca_steadystate |
decrease |
high |
13.87 |
21.310 |
27.740 |
25.510 |
30.120 |
30.860 |
| ca_transient |
decrease |
high |
10.59 |
12.910 |
17.290 |
19.450 |
26.730 |
30.970 |
| slowstart |
decrease |
high |
2.00 |
2.000 |
2.000 |
3.827 |
4.381 |
10.540 |
| ca_steadystate |
increase |
high |
10.77 |
11.240 |
11.870 |
11.990 |
12.690 |
13.760 |
| slowstart |
increase |
high |
2.00 |
2.444 |
4.068 |
4.739 |
6.711 |
9.963 |
| ca_steadystate |
decrease |
low |
13.59 |
19.870 |
24.080 |
23.630 |
27.670 |
30.830 |
| ca_transient |
decrease |
low |
13.32 |
19.600 |
23.980 |
23.490 |
27.680 |
30.950 |
| ca_steadystate |
increase |
low |
13.05 |
13.840 |
14.060 |
14.020 |
14.270 |
14.610 |
a <- aggregate(R~(status+S_slope+S_slope_rate), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, S_slope_rate = a$S_slope_rate, R=a$R))
| ca_steadystate |
decrease |
high |
0.6819 |
0.9015 |
0.9921 |
0.9396 |
1.0010 |
1.0040 |
| ca_transient |
decrease |
high |
0.2592 |
0.3963 |
0.8099 |
0.7081 |
0.9858 |
1.0080 |
| slowstart |
decrease |
high |
0.2000 |
0.2000 |
0.2000 |
0.2057 |
0.2000 |
0.2512 |
| ca_steadystate |
increase |
high |
0.3949 |
0.4054 |
0.4208 |
0.4567 |
0.4941 |
0.6496 |
| slowstart |
increase |
high |
0.2000 |
0.2054 |
0.2085 |
0.2124 |
0.2181 |
0.2440 |
| ca_steadystate |
decrease |
low |
0.4502 |
0.6315 |
0.7709 |
0.7564 |
0.8901 |
0.9955 |
| ca_transient |
decrease |
low |
0.4338 |
0.6236 |
0.7675 |
0.7520 |
0.8907 |
0.9992 |
| ca_steadystate |
increase |
low |
0.4270 |
0.4362 |
0.4429 |
0.4622 |
0.4496 |
0.6625 |
a <- aggregate(q~(status+S_slope+S_slope_rate), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, S_slope_rate = a$S_slope_rate, q=a$q))
| ca_steadystate |
decrease |
high |
14.460 |
21.050 |
23.760 |
22.1900 |
24.040 |
24.130 |
| ca_transient |
decrease |
high |
1.775 |
5.888 |
18.300 |
15.2400 |
23.580 |
24.240 |
| slowstart |
decrease |
high |
0.000 |
0.000 |
0.000 |
0.1707 |
0.000 |
1.536 |
| ca_steadystate |
increase |
high |
5.848 |
6.161 |
6.625 |
7.7020 |
8.823 |
13.490 |
| slowstart |
increase |
high |
0.000 |
0.163 |
0.254 |
0.3722 |
0.542 |
1.320 |
| ca_steadystate |
decrease |
low |
7.506 |
12.950 |
17.130 |
16.6900 |
20.700 |
23.860 |
| ca_transient |
decrease |
low |
7.013 |
12.710 |
17.030 |
16.5600 |
20.720 |
23.980 |
| ca_steadystate |
increase |
low |
6.810 |
7.086 |
7.287 |
7.8660 |
7.487 |
13.880 |
a <- aggregate(x~(status+S_slope+S_slope_rate), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, S_slope_rate = a$S_slope_rate, x=a$x))
| ca_steadystate |
decrease |
high |
20.95000 |
21.380000 |
21.680000 |
21.64000 |
21.91000 |
22.04000 |
| ca_transient |
decrease |
high |
0.08942 |
1.333000 |
21.380000 |
13.87000 |
21.90000 |
22.10000 |
| slowstart |
decrease |
high |
0.00000 |
0.002985 |
0.005882 |
0.01671 |
0.01831 |
0.07846 |
| ca_steadystate |
increase |
high |
13.52000 |
15.050000 |
16.980000 |
17.04000 |
19.02000 |
20.71000 |
| slowstart |
increase |
high |
0.00000 |
0.008643 |
0.015950 |
0.02201 |
0.03093 |
0.06906 |
| ca_steadystate |
decrease |
low |
11.03000 |
11.820000 |
14.240000 |
14.89000 |
17.72000 |
21.07000 |
| ca_transient |
decrease |
low |
2.17400 |
8.040000 |
13.170000 |
12.63000 |
17.47000 |
21.10000 |
| ca_steadystate |
increase |
low |
12.71000 |
12.910000 |
13.130000 |
13.83000 |
13.37000 |
20.81000 |
a <- aggregate(p~(status+S_slope+S_slope_rate), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, S_slope_rate = a$S_slope_rate, p=a$p))
| ca_steadystate |
decrease |
high |
0.02506 |
0.0345 |
0.04183 |
0.040800 |
0.04751 |
0.05110 |
| ca_transient |
decrease |
high |
0.00000 |
0.0000 |
0.03441 |
0.026770 |
0.04753 |
0.05254 |
| slowstart |
decrease |
high |
0.00000 |
0.0000 |
0.00000 |
0.000000 |
0.00000 |
0.00000 |
| ca_steadystate |
increase |
high |
0.00000 |
0.0000 |
0.00000 |
0.001299 |
0.00000 |
0.01901 |
| slowstart |
increase |
high |
0.00000 |
0.0000 |
0.00000 |
0.000000 |
0.00000 |
0.00000 |
| ca_steadystate |
decrease |
low |
0.00000 |
0.0000 |
0.00000 |
0.001106 |
0.00000 |
0.02631 |
| ca_transient |
decrease |
low |
0.00000 |
0.0000 |
0.00000 |
0.001138 |
0.00000 |
0.02701 |
| ca_steadystate |
increase |
low |
0.00000 |
0.0000 |
0.00000 |
0.001989 |
0.00000 |
0.02166 |
a <- aggregate(S~(status+S_slope+S_slope_rate), data=df, FUN=summary)
kable(data.frame(status=a$status, S_slope = a$S_slope, S_slope_rate = a$S_slope_rate, S=a$S))
| ca_steadystate |
decrease |
high |
20.340 |
23.64 |
27.96 |
26.83 |
30.00 |
30.97 |
| ca_transient |
decrease |
high |
20.120 |
24.20 |
29.81 |
28.71 |
32.57 |
40.86 |
| slowstart |
decrease |
high |
10.000 |
10.00 |
10.00 |
17.94 |
21.90 |
41.95 |
| ca_steadystate |
increase |
high |
20.120 |
22.33 |
27.97 |
26.84 |
31.05 |
31.88 |
| slowstart |
increase |
high |
9.677 |
12.09 |
19.50 |
21.85 |
30.87 |
40.83 |
| ca_steadystate |
decrease |
low |
20.320 |
31.08 |
31.24 |
31.30 |
31.50 |
31.96 |
| ca_transient |
decrease |
low |
20.110 |
31.08 |
31.25 |
31.30 |
31.52 |
32.20 |
| ca_steadystate |
increase |
low |
20.110 |
31.89 |
31.92 |
30.80 |
31.93 |
31.96 |
In the following post I will show phase diagrams able to shed some light on TCP performance goods and bads.
