Contents Telektronikk - Telenor

Table 1.
Values of the Loss, or Grade of Service, B. (Formula (1),
Section 1).
x αα y B
1 0.1 0.1 0.091
1 0.2 0.2 0.167
2 0.1 0.2 0.016
2 0.2 0.4 0.054
2 0.3 0.6 0.101
3 0.1 0.3 0.003
3 0.2 0.6 0.020
3 0.3 0.9 0.050
3 0.4 1.2 0.090
4 0.1 0.4 0.001
4 0.2 0.8 0.008
4 0.3 1.2 0.026
4 0.4 1.6 0.056
5 0.2 1.0 0.003
5 0.3 1.5 0.014
5 0.4 2.0 0.037
5 0.5 2.5 0.070
6 0.2 1.2 0.001
6 0.3 1.8 0.008
6 0.4 2.4 0.024
6 0.5 3.0 0.052
8 0.3 2.4 0.002
8 0.4 3.2 0.011
8 0.5 4.0 0.030
10 0.3 3 0.001
10 0.4 4 0.005
10 0.5 5 0.018
10 0.6 6 0.043
10 0.7 7 0.079
20 0.4 8 0.000
20 0.5 10 0.002
20 0.6 12 0.010
20 0.7 14 0.079
30 0.5 15 0.000
30 0.6 18 0.003
30 0.7 21 0.014
40 0.5 20 0.000
40 0.6 24 0.001
40 0.7 28 0.007
and, conversely, the transition from S2 to
S1 is:
S2 ⋅ 2 ⋅ dt,
which two quantities also are equal and
cancel each other.
Finally, we have
Sx-1 ⋅ y ⋅ dt
and
Sx ⋅ x ⋅ dt,
which also cancel
each other. The
result is that the
reciprocal changes
which take place
between the x +1
different states during the time dt, compensate
each other, so that the distribution
remains unaltered. We still have to
prove that neither will there be any alterations
in the distribution of the magnitude
of the remainders, i.e. that the
Table 2.
Values of the intensity of traffic, y, as a function of the number
of lines, x, for a loss of 1, 2, 3, 4 ‰.
x 1 ‰ 2 ‰ 3 ‰ 4 ‰
1 0.001 0.002 0.003 0.004
2 0.046 0.065 0.081 0.094
3 0.19 0.25 0.29 0.32
4 0.44 0.53 0.60 0.66
5 0.76 0.90 0.99 1.07
6 1.15 1.33 1.45 1.54
7 1.58 1.80 1.95 2.06
8 2.05 2.31 2.48 2.62
9 2.56 2.85 3.05 3.21
10 3.09 3.43 3.65 3.82
11 3.65 4.02 4.26 4.45
12 4.23 4.64 4.90 5.11
13 4.83 5.27 5.56 5.78
14 5.45 5.92 6.23 6.47
15 6.08 6.58 6.91 7.17
16 6.72 7.26 7.61 7.88
17 6.38 7.95 8.32 8.60
18 8.05 8.64 9.03 9.33
19 8.72 9.35 9.76 10.07
20 9.41 10.07 10.50 10.82
25 12.97 13.76 14.28 14.67
30 16.68 17.61 18.20 18.66
35 20.52 21.56 22.23 22.75
40 24.44 25.6 26.3 26.9
45 28.45 29.7 30.5 31.1
50 32.5 33.9 34.8 35.4
55 36.6 38.1 39.0 39.8
60 40.8 42.3 43.4 44.1
65 45.0 46.6 47.7 48.5
70 49.2 51.0 52.1 53.0
75 53.5 55.3 56.5 57.4
80 57.8 59.7 61.0 61.9
85 62.1 64.1 65.4 66.4
90 66.5 68.6 69.9 70.9
95 70.8 73.0 74.4 75.4
100 75.2 77.5 78.9 80.0
105 79.6 82.0 83.4 84.6
110 84.1 86.4 88.0 89.2
115 88.5 91.0 92.5 93.7
120 93.0 95.5 97.1 98.4
decrease and increase, also in this
respect, compensate each other.
5. Let us consider the cases in which the
number of current conversations is n, and
among these cases, more especially those
in which the magnitudes of the n remain-
43