What is GoS and how does it apply to DMR?

Wikipedia describes GoS quite well I think: "Grade of Service is the probability of a call in a circuit group being blocked or delayed for more than a specified interval, expressed as a vulgar fraction or decimal fraction. This is always with reference to the busy hour when the traffic intensity is the greatest. Grade of service may be viewed independently from the perspective of incoming versus outgoing calls, and is not necessarily equal in each direction or between different source-destination pairs."

In simplier terms (that the rest of us can understand), it is the statistical likelihood that you will press the PTT and either get a busy tone or get put into the queue.

To illustrate GoS, I like to use the weather report: in last night's weather report, you will have seen mention being made of the chance of rain - lets say this was 50%. Today comes and it's sunny from sunrise to sunset. Did the climatologist get it wrong? No, but yes it didn't rain today. However, if you took 100 days last year where there was a 50% chance of rain, you'd probably find that on approximately 50 of those days, it rained.

So if you sat one day and made a call of a certain duration on your radio system 100 times and twice, the system was busy, you could say that the GoS was 2%. Of course the GoS will vary throughout the day and will be lowest when nobody is at work or they are sleeping.

To calculate the GoS, we have to use a set of formulas developed by Agner Krarup Erlang (pictured above) who was a Danish mathematician and engineer who worked for KT A/S (the telephone network operator in Copenhagen) in the early 1900's. He was asked to help them work out how many trunk lines would be needed to serve a certain number of  subscribers.

As a result of Erlang's work, we have two formulas we use in radio communications: Erlang B for conventional systems and Erlang C for trunked systems. Erlang B assumes that a call will fail if all the trunks (lines, channels) are occupied. Erlang C assumes that a call will be queued (ring or put on hold) for a certain amount of time before being granted. Some prefer to use Engset instead of Erlang C.

These formulas can be found on Wikipedia. However, Motorola has produced the MOTOTRBO System Design Tool, available to all Motorola Partners, which allows you to calculate the number of channels (slots) required to achieve a particular GoS. This tool is also able to perform a number of other calculations relevant to MOTOTRBO systems.

If you have your own tool, MOTOTRBO conventional and (Single/Multisite) Capacity Plus will follow Erlang B (call fails when no slots are free) and Capacity Max will follow Erlang C (call is queued when all slots are busy). 

On Capacity Max, call priority and call pre-emption will skew the numbers and Erlang C will be accurate when all calls are groups have the same priority and no preemption is used.