Erlang and Grade of Service (GoS) Explained

This page provides an introduction to Erlang and Grade of Service (GoS) fundamentals within a telephone network. It includes an example calculation demonstrating how Erlang and GoS are determined.

Erlang

Erlang is the standard unit for measuring telephone call traffic intensity. It represents the average number of concurrent calls in progress at a given time. Wireless network designers rely on Erlang traffic measurements to gain insights into voice traffic patterns within the network. This information is crucial for determining the necessary number of lines required between a telephone system and a Public Switched Telephone Network (PSTN) central office (CO), or between two cellular/wireless networks.

The Erlang formula is as follows:

Erlang A = C * h / T

Where:

• A is the traffic intensity in Erlangs.
• C is the average number of call arrivals during the time interval T.
• h is the average call holding time (call duration).
• T is the time interval over which the measurements are taken

In North America, CCS (Call Seconds per hour) is sometimes used instead of Erlang. The conversion is:

1 Erlang = 36 CCS

Erlang Traffic Models

The following section highlights the differences between Erlang B, Extended Erlang B, and Erlang C models:

• Erlang B: This model is used to calculate the number of lines needed based on the traffic volume in Erlangs during the busy hour. It is the most commonly used traffic model. It operates under the assumption that blocked calls are cleared immediately from the system.
• Extended Erlang B: This model builds upon Erlang B by considering the percentage of blocked calls that are immediately represented to the system. It’s similar to Erlang B but with the added consideration of re-attempted calls.
• Erlang C: This model assumes that all blocked calls are held in a queue until they can be handled by the system. It is particularly applicable for call center design, where unanswered calls are placed in a queue for later handling.

GoS - Grade of Service

Grade of Service (GoS) is a metric used to evaluate traffic congestion within a telephone network. Network congestion leads to lost call scenarios.

Therefore:

Traffic carried = Traffic offered - Traffic lost

For systems that experience lost calls, the Grade of Service (B) is defined as:

B = Traffic lost / Traffic offered

Example Calculation of Erlang and Grade of Service

Let’s assume that for a telephone network, the Erlang traffic intensity is A, and the Grade of Service is B. Then, the traffic lost would be AB, and the traffic carried would be A(1-B).

Consider the following data:

• 1400 calls were offered during the busy hour using a set of trunk lines.
• 7 calls were lost.
• The average call duration was 4 minutes.

In this scenario, the busy hour (T) is 60 minutes.

• Traffic offered (A) = C * h / T = 1400 * 4 / 60 = approximately 93.3 Erlang
• Traffic carried = 1393 * 4 / 60 = approximately 92.86 Erlang
• Traffic lost = 7 * 4 / 60 = 0.46 Erlang
• Grade of Service (B) = 7 / 1400 = 0.005
• Congestion period = 0.005 * 3600 = 18 seconds