Editing Erlang (unit) (section)

== Erlang's analysis ==

The concepts and mathematics introduced by [[Agner Krarup Erlang]] have broad applicability beyond telephony.  They apply wherever users arrive more or less at random to receive exclusive service from any one of a group of service-providing elements without prior reservation, for example, where the service-providing elements are ticket-sales windows, toilets on an airplane, or motel rooms.  (Erlang's models do not apply where the service-providing elements are shared between several concurrent users or different amounts of service are consumed by different users, for instance, on circuits carrying data traffic.)

The goal of Erlang's traffic theory is to determine exactly how many service-providing elements should be provided in order to satisfy users, without wasteful over-provisioning.  To do this, a target is set for the [[grade of service]] (GoS) or [[quality of service]] (QoS).  For example, in a system where there is no queuing, the GoS may be that no more than 1 call in 100 is blocked (i.e., rejected) due to all circuits being in use (a GoS of 0.01), which becomes the target probability of call blocking, ''P''<sub>b</sub>, when using the Erlang B formula.

There are several resulting formulae, including [[Erlang (unit)#Erlang B formula|Erlang B]], [[Erlang (unit)#Erlang C formula|Erlang C]] and the related [[Engset formula]], based on different models of user behavior and system operation. These may each be derived by means of a special case of [[continuous-time Markov process]]es known as a [[birth–death process]]. The more recent [[Erlang (unit)#Extended Erlang B|Extended Erlang B]] method provides a further traffic solution that draws on Erlang's results.