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## Erlang and Grade of Service

This page describes Erlang and Grade of Service basics in a telephone network and mention example calculation of Erlang and Grade of Service.

### Erlang

Erlang is the unit of telephone call traffic. It is defined as average number of calls in progress at some time. Erlang equation is mentioned below.

Erlang traffic measurements are carried out by wireless network designers to understand the voice traffic patterns in the network. This will help them derive how many lines will be needed between telephone system and PSTN central office(CO) or between the two cellular/wireless networks.

Erlang A = C*h/T
Where, C is average no. of call arrived during time interval T
h is the average call holding time.

In North America CCS(Call Seconds per hour) is used in place of Erlang.
1 Erlang = 36 CCS.

### Erlang Traffic models

Following section mentions difference between Erlang B, Extended Erlang B and Erlang C.
• Erlang B: It is used to derive number of lines needed when traffic in erlangs during busy hour is known. This traffic model is mostly used. It assumes that blocked calls are cleared immediately.
• Extended Erlang B: It considers that percentage of calls which encounters blocking need to be represented to the system immediately. It is similar to Erlang B.
• Erlang C: This traffic model assumes that all the blocked calls need to be stayed until they are handled by the system. This traffic model is application for the call center design where in, calls is not answered immediately will enter into the queue.

Grade of Service(GoS) is the measure of traffic congestion in telephone network. Congestion in the network results in lost call scenario.
Hence Traffic carried = traffic offered - traffic lost

For the lost call system, Grade of Service, say B is defined as follows. Grade of Service Equation is mentioned below.
B = Traffic lost/ Traffic offered

### EXAMPLE of Erlang and Grade of Service

Let us say for a telephone network Erlang is A and Grade of Service is B , then traffic lost is AB and traffic carried is A(1-B).

Let us do some calculations with the data given below.
1400 calls were offered in busy hour with some trunk lines. Out of these 7 calls were lost. Average call duration was about 4 minutes.

In the above scenario, busy hour means T is about 60 minutes
Traffic offered = A=Ch/T = 1400 x 4 /60 = about 93.3 Erlang
Traffic carried = 1393 x 4 /60 = about 92.86 Erlang
Traffic lost = 7 x 4 /60 = 0.46 Erlang
Grade of Service = 7/1400 = 0.005
Congestion period = 0.005 x 3600 = 18 seconds

### Erlang-GoS Calculator

Refer Erlang and GoS page for calculator.