The Erlang B model is used to represent a situation in which calls that arrive when all resources (for example, trunk channels) are busy, are blocked and subsequently denied service. The model further assumes that the calls follow Poisson arrival and departure processes (which is typical for actual calls in real configurations), and that blocked calls never retry.

There are four parameters associated with the Erlang B model:

• Offered load (Erlangs)

• Carried load, which is sometimes referred to as usage (Erlangs)

• Number of resources

• GoS (grade of service, which is the probability of blocking at the resources)

Normally, when working with anticipated traffic loads (for example, for a new configuration), we work with the offered load, the number of resources, and the GoS. On the other hand, when working with measured traffic loads (for example, found on traffic reports run on existing configurations), we work with the carried load (usage), the number of resources, and the GoS. In either case, given any two of the three relevant values, the Erlang B model produces the third value.

The Erlang C model is used to represent a situation in which calls that arrive when all resources (for example, trunk channels) are busy, are blocked and subsequently queued. Like the Erlang B model, the Erlang C model is predicated on the assumption that the calls follow Poisson arrival and departure processes. Furthermore, the Erlang C model assumes an infinite amount of space in the queue.

There are three parameters associated with the Erlang C model:

• Offered load, which equals the carried load in this model (Erlangs)

• Number of resources

• GoS (grade of service, which is the probability of blocking at the resources)

Given the values of any two of those three parameters, the Erlang C model produces the third value.

Note that the GoS is often expressed as P01 or P001. P01 represents at most 1 call out of every 100 being blocked at the resource of interest (that is, 1% blocking), and P001 represents at most 1 call out of every 1000 being blocked at the resource of interest (that is, 0.1% blocking).

Consider a situation in which a call that is blocked is constantly retried until it receives service, meaning that as soon as a busy signal is heard, the caller hangs up and immediately redials. This is the most extreme form of retrial, and it is almost as if each blocked call is simply placed in queue and receives service as soon as a resource frees up for it. In other words, the Erlang C model is a reasonable approximation for constant retrials.

So, since Erlang B represents no retrials and Erlang C approximates constant retrials, the average of the two models is a reasonable approximation for moderate retrials. In this document, the pure Erlang B model is used when ignoring the effect of retrials, and the average of the Erlang B and C models (that is, a mixed Erlang B/C model) is used when the effect of retrials is deemed to be relevant.

Although the Erlang C model deals with queueing effects, it is not a particularly reasonable model for inbound Call Centers unless the number of trunks is significantly higher than (for example, several orders of magnitude greater than) the number of agents. The M/M/c/k Finite Queue model, which is beyond the scope of this discussion, should be used instead. A pure Erlang C model is never used in this discussion.