How to use our online calculators or Windows products to work out how many lines are required in a trunk group.

Contents

• Purpose

• Designing networks
• Dimensioning trunks using Erlang B
• Reasons for caution

Purpose

This white paper discusses a method of optimising the number of lines in a trunk group based on the traffic carried by that trunk group. This is known as dimensioning a trunk group and can be used to work out how many lines are required into a call centre facility.

Designing networks

A network cannot be properly designed without understanding the traffic patterns which that network will carry. In order to carry out a complete network design, a matrix of traffic figures between every combination of site on that network should be gathered. For each site, a traffic figure should be obtained for calls to every other site, and this information can be used to calculate 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. Our opinion is that this practice is not a sound basis for network design for the following reasons:

• 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 who do not use the direct links because the grade of service is bad.
• Tweaking links as necessary avoids the central issue of network design which is to produce the most economical network layout. To design a network, consideration should be given to locations between which links should be introduced or removed rather than changing the size of existing links.

Dimensioning trunks using Erlang B

Of course, this is a rather idealistic view. In the real world, links cannot be 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 mode which requires the following inputs:

• Busy Hour Traffic
• Blocking

Busy Hour Traffic (B.H.T.)
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, which represents 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

Blocking
The blocking figure describes the calls which 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, 0.03 (3%) blocking is used.

Reasons for caution

The Erlang B models 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 quite reasonable in most applications, it can cause inaccurate results when there is a sudden peak of calls. This type of peak can be produced by a radio or television advertisement being shown and here drastic call peaks are expected, over-engineering of trunks and call center agents should always be carried out - always be on the safe side!

Our suggestion has been to obtain traffic figures from call loggers. Care must be taken when using this method. Extracting a figure for the traffic carried on a trunk group will often be sufficient, but it should be borne in mind that this figure would represent the traffic carried over a trunk group and not the traffic offered to a trunk group (that is, it would not include the traffic currently being blocked) - be careful!

Lastly, 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, extreme caution should be exercised when calculating BHT.

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