Sizing a trunk group

In this technical paper, we describe how to use the Erlang B traffic model to estimate the size of a trunk group in a telecommunications system. Our company provides professional software and free resources to speed up these calculations for you.

Erlang software tools needed

We provide free online Erlang traffic calculators to help with this analysis. A professional version for Windows is available for immediate download at 99 US Dollars and offers you increased speed, capacity and convenience. We also offer Erlang for Excel, an add-in that brings Erlang B functions into your own workbooks.

Designing voice networks

You cannot properly design a network without understanding the traffic patterns it will be expected to handle. To carry out a complete network design, you should construct a matrix of traffic figures between each site on that network. For each location, obtain traffic figures for calls to every other site. You can use this information to judge between which sites network links should be installed.

It is also common for traffic figures for calls carried over particular trunk groups to be retrieved from loggers. With existing networks, these figures are often used to calculate the optimum number of trunks for a group. Use this approach with caution because:

  • Call loggers can give a distorted view of the traffic on a link as they measure carried traffic rather than offered traffic. Changes to link capacities based on these figures can often be under-estimated because traffic models base their results on offered traffic. In other words, increasing the number of lines generates more traffic which needs more lines! Link traffic does not include those calls from callers forced to use the alternative routes because primary routes suffer from a weak grade of service.
  • Tweaking links avoids the central tenet of network design, which is to produce the most economical network layout. To design a network, try to give consideration to locations between which links should be introduced or removed rather than changing the size of existing links.

Dimensioning trunks with Erlang B

Of course, that is a rather idealised view. In the real world, links cannot be necessarily introduced and removed regularly, and the voice network layout may depend upon other factors such as data traffic carried over a network with voice and data integration.

So, a way of estimating the number of lines required for a known value of offered traffic is required. This is available in the form of the Erlang B traffic model, which calls for the following inputs:

  • Busy Hour Traffic
  • Blocking

Busy Hour Traffic (BHT)

This figure represents the quantity of traffic expressed in a unit called Erlangs. For the purposes of these calculations, 1 Erlang can be considered equivalent to 1 hour of calls. You will need to provide an estimate for this figure: the number of hours of traffic which is offered to a trunk group in its busiest hour. For example, if you know from your call logger that 350 calls are made on a trunk group, and the average call duration is 180 seconds, then the busy hour traffic will be:

BHT=Average call duration (s) * Calls per hour / 3600
BHT=180 * 350 / 3600
BHT=17.5 Erlangs


The blocking figure describes the calls that cannot be completed because insufficient lines have been provided. A figure of 0.01 means that 1% of calls would be blocked; this is a normal figure to use in traffic engineering. For some applications, a more relaxed target of 0.03 (3%) blocking is used.

Example calculation

Having established these two parameters, estimate the number of lines required using the Erlang B Traffic Model. You can use our online Erlang B calculator or our professional Erlang software to work through this example:

BHT=17.500 Erlangs

Pressing the Calculate button reveals that 27 lines will be required during the hour in question.

Reasons for caution

The Erlang B model makes certain assumptions about the nature of the call arrivals. Amongst them is the assumption that call arrivals are random (Poisson arrivals). Although this is reasonable in most applications, it can cause inaccurate results when there is a sudden peak of calls such as that generated by a radio or television advertisement. To anticipate this, you may prefer to over-engineer your solution.

It is important to note that the busy hour traffic figure should represent the busiest traffic load a trunk group will ever be offered. The trunk group being designed must be large enough to cater not just for today’s peak, but for every peak. Therefore, take care when calculating BHT.

2 Replies to “Sizing a trunk group”

  1. What if I wanted to calculate how many simultaneous calls received during non Busy hours. Do I use erlang B or extended B?

  2. That’s a tricky one to answer. You cannot really calculate the number of simultaneous calls received. You would normally measure the actual traffic and use that figure to work out how many lines you need. As for non-busy hours, again the traffic volume cannot be calculated because it depends on the source of the traffic and how it spreads throughout the day.

    In most cases, Erlang B will work fine – Extended Erlang B is only useful in the specific case where the are frequent retries because a significant proportion of calls are blocked.

  3. Just to clarify the meaning of “lines” needed here.
    Does it mean 1 channel of voice path needed like in traditional voice E1 trunk circuit, one line may be referring to 1 x E1 trunk with 30 channels of voice traffic.
    Hence, from your example above, you mentioned 17.5 Erlangs of traffic needs 27 lines during that hour. Does 27 lines mean 27 x E1 lines or 27 lines of voice channels in SIP trunk perspective ?

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