# The Binomial distribution

The Binomial distribution is used for dimensioning trunk routes. The Binomial is used in lieu of the Erlang or Poisson distribution where there are a finite number of sources, such as dimensioning an outgoing trunk group for a small PABX. It is based on the following assumptions:

• There are an finite number of sources;
• Calls are served in random order;
• Blocked calls are held; and
• Holding times are exponentially distributed or constant.

The Binomial formula is used to predict the probability that a call will be blocked. The Binomial formula is:

where:
P=Binomial loss probability
N=Number of trunks in full availability group
S=Number of sources
a=Traffic offered to group in Erlangs per source

# The model calculator

Tables of Binomial values have been commonly published, but are inconvenient to use. This convenient calculator will find the number of trunks needed to deliver a specified service level given the traffic intensity.

# Traffic model using Binomial

Traffic intensity /source (Erlangs)

Number of sources

Fill in one only of the following:

Number of channels

The following buttons will pre-load and calculate example scenarios:

Dimension an outbound route for Grade of Service.

Find the % congestionbusy signals on an outbound route.

# Interpreting the results

The calculator will calculate either the unknown Grade Of Service or number of trunks required. If the calculation is of the number of trunks required, then it will also calculate the resulting Grade of Service for that number of trunks (which may be a little better than the objective).

# Examples description

## Example 1

I am planning a remote PABX connected by a tieline that will bes used for all inbound calls to that PABX which will have 15 active ends.

I estimate 30mE of inbound traffic per active end, and GOS should be better than 0.002.

How many trunks do I need in the tie line route?

Answer: to carry 0.45E (15*0.03), I need 4 trunks, and the actual grade of service should be 0.00064.

## Example 2

My Service Level Objective says that no less than 95% of the time my small PABX customers will get dial tone.

I have a two circuit outbound route, outbound traffic is 50mE per end and there are 12 ends.

Should the outbound route be sufficient to meet my Service Level Objective.

Answer: No, carrying 0.6E (12*0.05) on 2 trunks from 12 ends, the expected busy rate should be about 10.2%, so the success rate would be 89.8% which is below my objective. An additional trunk is required, which will bring the service level up to 98.48%.