Calculating recording channel capacity

Erlang B formula

An Erlang is a unit of telecommunications traffic measurement.  Strictly speaking, one Erlang represents the continuous use of one voice path.  In practice, it is used to describe the total traffic volume of one hour.

For example, if a group of users made 30 calls in one hour, and each call had an average call duration of 5 minutes, then the number of Erlangs this represents is worked out as follows:

Minutes of traffic in the hour = number of calls x duration

Minutes of traffic in the hour = 30 x 5

Minutes of traffic in the hour = 150

Hours of traffic in the hour = 150 / 60

Hours of traffic in the hour = 2.5

Traffic figure = 2.5 Erlangs

Erlang traffic measurements are made in order to help telecommunications network designers understand traffic patterns within their voice networks.  Erlang traffic measurements or estimates can be used to work out how many lines are required between a telephone system and a central office (PSTN exchange lines), or between multiple network locations.

If you measure network traffic load during the busiest hour, this period represents the maximum traffic load that your network must support. The result gives you a traffic load measurement commonly referred to as the Busy Hour Traffic (BHT) .

The Erlang B model is used when blocked calls are rerouted, that never come back to the original trunk group. This model assumes a random call arrival pattern. The caller makes only one attempt; if the call is blocked, then the call is rerouted. The Erlang B model is commonly used for first-attempt trunk groups where you don t need take into consideration the retry rate, because callers are rerouted, or you expect to see very little blockage.

The following formula is used to derive the Erlang B traffic model:

Where:

  • B(c,a) is the probability of blocking the call.
  • c is the number of circuits.
  • a is the traffic load.

Using the Erlang B formula to estimate capacity

The Erlang B formula can help you calculate the channel capacity required for the Verba system (required recording channels):

  • B(c,a) equals 0, because it is not permissible to block any call in the recorder.
  • a is a number in Erlangs, which represents the call traffic load during the busiest hour in the system (BHT) that have to be recorded. Use the calculation example above to define your BHT.
  • c is the number of required recording channels for the Verba system.

Example:

Busy Hour Traffic = 2.5 Erlangs

Probability of blocking the call = 0

Required recording channels = 11You can use the following table to calculate the number of recording channels for a Recording Server server (required recording channel numbers for predefined BHTs):

BHT

[Erlang]

c

BHT

[Erlang]

c

BHT

[Erlang]

c

BHT

[Erlang]

c

BHT

[Erlang]

c

1.00

7

21.00

40

41.00

66

61.00

91

81.00

114

2.00

10

22.00

41

42.00

67

62.00

92

82.00

116

3.00

12

23.00

43

43.00

69

63.00

93

83.00

117

4.00

14

24.00

44

44.00

70

64.00

94

84.00

118

5.00

16

25.00

45

45.00

71

65.00

95

85.00

119

6.00

18

26.00

47

46.00

72

66.00

97

86.00

120

7.00

19

27.00

48

47.00

74

67.00

98

87.00

121

8.00

21

28.00

49

48.00

75

68.00

99

88.00

123

9.00

23

29.00

51

49.00

76

69.00

100

89.00

124

10.00

24

30.00

52

50.00

77

70.00

101

90.00

125

11.00

26

31.00

53

51.00

78

71.00

103

91.00

126

12.00

27

32.00

55

52.00

80

72.00

104

92.00

127

13.00

29

33.00

56

53.00

81

73.00

105

93.00

128

14.00

30

34.00

57

54.00

82

74.00

106

94.00

130

15.00

32

35.00

58

55.00

83

75.00

107

95.00

131

16.00

33

36.00

60

56.00

85

76.00

108

96.00

132

17.00

34

37.00

61

57.00

86

77.00

110

97.00

133

18.00

36

38.00

62

58.00

87

78.00

111

98.00

134

19.00

37

39.00

64

59.00

88

79.00

112

99.00

135

20.00

39

40.00

65

60.00

89

80.00

113

100.00

137

There is a very useful Erlang B, Extended Erlang B and Erlang C calculator at the following URL: http://www.erlang.com/calculator/index.htm