Angmer Erlang was a Danish telecommunication engineer who developed the formula to assess how many switches/lines are required to be sure of meeting a particular service level.
Even this looks complicated! We have described a process that can be followed by any practice using simple tables drawn up on paper. For those that wish to be more sophisticated in their modelling, there are a number of modelling and calculation tools available. For those that have good Excel skills there is a free add-in available here.
When should it be used and when might care be needed?
The formula can be used to calculate a service level that can be achieved with a given number of ‘agents’ to answer the phone, or to calculate the number of agents needed to meet a particular level of demand.
Caution should be exercised if calls that come in are of very widely varying lengths (for example, if a considerable number are completed in less than two minutes and an equivalent number take over 15 minutes). In these cases more sophisticated modelling may be required.
Fortunately, incoming calls to a surgery typically average around 2 minutes or a little less and very few extend for longer than 8 minutes. So the Erlang formula is suitable for the purpose.
Services using the formula should be aware that although the mathematics is sound, the smaller the practice the greater the chance that demand varies significantly from day to day or hour to hour. This is caused only by random variation in relatively small numbers. For this reason, it may be necessary to allow for a larger number of calls than average, if a given service level is to be reliably achieved.
