Erlang based functions

Telco Network Cloud Manager - Performance provides a number of functions that can be used to analyze traffic data. These functions are based around:

• The Erlang B loss function, which models the behavior of contention for a non-queued limited resource.
• The Erlang C function, which models the behavior of contention of a queued limited resource.
• The Engset function, which models the behavior of contention by using the expected peak traffic, the number of sources (callers), and the number of circuits.

These functions allow the probability of blocking for the resource to be estimated, and thus the traffic that is offered to a resource and the capacity of an element to be calculated.

The grade of service calculation

The grade of service of a resource can be expressed as the probability of traffic that is being offered to the resource meeting a blocking condition. It is commonly used to assess network resources such as a circuit group or cell TCH. Grade of service is important both as a measure of the actual quality of service that is offered to subscribers, and also as a design parameter, the design grade of service. Grade of service is calculated from the perspective of the element that is providing the resource. What happens to the service request, the call, depends on the system in question:

In a loss system, the call is typically offered to an alternative trunk group or a different cell or sector. In a queued system, the call is queued and might later receive service from the element.

Therefore, care must be taken when the association between grade of service and subscriber-visible effects of congestion are made.

Offered traffic

The first step in calculating grade of service is to estimate the traffic that is offered to a resource. The offered traffic can be thought of as the traffic that would be carried if the resource had unlimited capacity. In general, the offered traffic cannot be measured directly because one of the following points is true:

• The number of bids for a resource is not known, such as an incoming circuit group.
• If the bids are known, only the traffic that might result from them can be estimated. For example, a measure of offered traffic might be obtained from bid and mean holding time data.

For a loss system, it is usual to estimate the offered traffic that uses the Erlang B function to calculate the lost traffic and thus the offered traffic. The algorithm uses an iterative approach to solve the equations.

For a queued system, the traffic that is offered is considered identical to the traffic carried. As the model assumes that an infinite queue is available, all traffic that is offered is ultimately carried, though perhaps after a significant delay. If the measurement period is long relative to the average holding time, this assumption is reasonable for the purposes of the model.

The toff function is provided for Erlang B that is passed the number of circuits and the measured carried traffic. The function returns the offered traffic. For example,

toff( 10, 4.3, "B" ) returns the offered traffic when 4.3 Erlangs is carried on 10 circuits.

Blocking probability

The grade of service, or blocking probability, is calculated that uses the gos function for Erlang B and C. This function is passed the number of available circuits and the offered traffic. For example,

gos({Neutral.TCH.defined_ch},{Neutral.TCH.offered_b},"B")

The function returns the grade of service that is expressed as a probability 0 - 1. For example, a value of 0.008 implies a blocking probability of 8 in 1000.

Capacity calculations

The theoretical maximum capacity of a resource is equal to the number of circuits available on the resource. For example, a circuit group of 60 circuits can potentially carry 60 Erlangs if all circuits are busy. However, it is clear that in such a situation the amount of blocking is high. Any traffic that is offered to the circuit group might have a probability of 1 of meeting a block condition.

Therefore, it is normal to define capacity in terms of that level of offered traffic that results in a grade of service equal to the design grade of service. It is known as the nominal capacity.

The nominal capacity of a resource is the traffic level at which the grade of service is equal to some predefined value. It is known as the critical traffic level.

Critical traffic

Typical values for the design grade of service are around 0.008.

The critical traffic level for a resource can be calculated with the crit function for Erlang B and C. This function is passed the number of available circuits and the design grade of service that is expressed as a probability.

For example, crit([Cell]![{Neutral.TCH.available_ch}] , .02, "B") returns the critical traffic, which might be carried based on a GOS of 0.2. If the number of circuits is negative, a value of 0 is used.

TC4 full availability

Using critical traffic to define capacity essentially defines a grade of service at a nominal load. Other measures of capacity also attempt to define levels of service at varying degrees of overload.

The TC4 traffic level is defined as that level of offered traffic that provides a grade of service of:

• 0.008 at nominal load
• 0.02 at 10% overload
• 0.05 at 20% overload

The TC4 capacity tends to be less than the critical traffic after approximately 30 circuits, as the second and third criteria start to limit the value as the number of circuits increase.

TC4(3, "B" )

Typically, this function is used for capacity of circuit groups, and not for elements with small numbers of circuits such as cells.