Engset calculator

Below you find my Engset calculator. Just like the Erlang calculator it calculates the relation between blocking, traffic and number of lines. Any two of those determine the value of the third.

The added feature of the Engset model is that it does not assume an infinite user population, like the Erlang model does. One can specify (or compute) the number of users. Traffic can now be expressed in erlang or in erlang per user. The traffic value in the dimensionless quantity erlang signifies the number of lines that would be occupied on average if there were no blocking.

Specify any value by filling in the corresponding field. Calculate a specific value by clicking the button next to it.


Your boss wants to write in his brochure that your GSM system can support up to 50 users per radio cell, although he knows that in most cells there is only one frequency (with 8 time slots or "lines") available. These are the assumptions:


blocking probability




erlang per user

By clicking "calculate number of users" you can show that only 18.5 users can be supported.

You boss suggests to make the erlang per user = 0.1. You can show that this will only allow 34.0 users.

Your can tell that it is a good idea to keep the more realistic 0.1 erlang per user (1 busy time unit per 9 idle time units) but at the same time to double the number of lines. Now the permitted number of users is 92.4.

Fill in 100 in the field "number of users" and click "calculate blocking probability". This shows that by having two frequencies and accepting a blocking probability of 0.018... even 100 users can be supported per cell.

Frits Schoute.