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 = 11

It is very important to calculate the capacity properly, because overloading Verba recording servers can lead to packet loss and voice or picture dropouts in sound/video files.

You 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

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