Trunk Traffic Engineering

The number of PBX trunk circuits required to support expected inbound and outbound traffic loads is typically calculated using trunk traffic tables. The most popular trunk traffic table used for telephone system traffic engineering is based on the Erlang B queuing model. The Erlang B model assumes the following:

1. The number of traffic sources is large

2. The probability of blocking is small

3. Call attempts are random

4. Call holding times are exponential

5. Blocked calls are cleared from the system

The last assumption is very important because it says that there is no second call attempt if the first attempt receives a busy signal. The Poisson queuing model used for PBX station traffic engineering assumes that blocked call attempts are held in the system; that is, subsequent call attempts are made. Another popular telephone system queuing model is Erlang C, based on the assumption that blocked call attempts are held in a delay queue until a trunk is available. The Erlang C model is commonly used in ACD systems to calculate required agent positions used instead of a trunk circuit: inbound calls not immediately connected to an agent position are held in queue until an agent is available.

Another use of the Erlang C model is to calculate the required number of attendant positions to handle incoming trunk calls. Calls not presented to the attendant position are queued by the PBX system. Based on incoming traffic conditions, the average 250-station PBX system may require one, two, or three attendant positions to adequately answer and forward calls with acceptable queue delay times. As the PBX system size increases, the number of attendant positions is likely to increase, but the number of incremental attendant positions does not double when station size doubles because larger attendant position groups are more efficient than smaller groups based on traffic queuing theory conditions.

Erlang B is also a very useful queuing model for analyzing alternate routing on trunk groups within a PBX, where there are usually multiple available trunk circuits across multiple trunk groups. A call that is blocked at one trunk circuit can potentially overflow to another circuit or another trunk group. Erlang B is also used for analyzing traffic conditions across multiswitch networks, where there are many potential call routes per connection.

The Erlang B trunk traffic table consists of three data parameters: probability of blocking, number of trunk circuits, and Erlangs. An Erlang is a unit of measurement for trunk traffic. The maximum traffic load a trunk circuit can handle in 1 hour is equal to 1 Erlang. An Erlang is a dimensionless unit of measure. Knowing any two of the three data parameters allows table look-up of the third data parameter. For customers with existing PBX systems, it is easy to determine the current trunk traffic handling capacities per trunk group because the GoS is a given, as is the number of trunk circuits per trunk group.