Erlang PBX Calculator
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How many telephone lines do I need?

Traffic units and busy probability

Average call duration (minutes):
Number of calls in peak hour: Busy probability:
Number of lines available:

First of all, "Erlang" (as defined by the Ericsson Computer Science Laboratory) is a traffic unit, describing the total traffic volume of one hour. For instance, if you get 30 calls in one hour and each has an average duration of 5 minutes, the traffic figure will be (30 * 5) / 60 = 2.5 Erlang. It is obvious that you will need at least three lines to handle this traffic. But even then, due to the random nature of calls and the probability of chance, you will still have a significant rate of callers who do not get through and hear a busy signal instead.

There are three common equations used for different situations. This one is called Erlang B with B = busy rate, A = traffic volume in Erlang, and N = number of available channels. Erlang B is the most commonly used traffic model, designed to evaluate how many lines are required for a specified traffic volume. The model assumes that all blocked calls are immediately cleared. Here is a Javascript-based calculator using the Erlang B equation. Simply enter the average call duration you expect, the number of calls in the peak hour, and the number of lines you have. Note that one ISDN T0/S0 line has two channels, so enter 2 if you have one basic-rate ISDN interface (BRI).

The calculated "busy" probability is quite reliable as long as it is below 20 % (and no professional would accept a significantly higher rate in planning a PBX or audiotext platform, for example). It is interesting to see that an increased number of channels drastically improves the accessibility of a system.

There are a few things that must be kept in mind when using the Erlang equation. It assumes a randomly distributed traffic from a more or less unlimited number of potential callers. (The other extreme would be, for instance, if you have two lines and only two possible callers: These two people would never hear a busy signal.) A random distribution may not be always realistic since people tend to redial immediately when they hear a busy signal -- especially when using a modem instead of a telephone. In this case, the actual busy rate will be higher than the one calculated by the Erlang equation.

If you already have a number of lines and measure the traffic volume being handled by them, then you do not really know the possible traffic because some callers will be rejected due to busy lines. In this case, the calculation should be re-iterated. For instance, if you see 100 calls in the peak hour and the calculator says that the busy probability is 10 %, then increase the number of calls by these 10 % and enter 110 to recalculate the result. Talk to your local phone line provider about YOUR details.

Erlang PBX Calculator

This is an important business concept for telephone communications. View the source.

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