The Erlang B formula is often used to calculate the blocking probability based on the average arrival rate, average service length and the number of servers. In hospitals it is important that patients are given the care that they need. This requires decision-making on the number of beds to use on each ward. Fully occupied wards mean that arriving patients cannot stay on their intended ward (they are blocked) and have to stay elsewhere with possibly less specific care. It is therefore that the Erlang B formula is often applied to dimension wards. Based on the average arrivals of new patients per day, the average length of stay and the number of beds, the Erlang B formula provides the chance that all beds are occupied. Hospitals should decide on the acceptable ‘blocking’ probability, but the occupancy level of the wards are also important. More beds result in lower blocking probabilities and lower occupancy levels at the same time. Both are important indicators for ward dimensioning.
However, the blocking probability as calculated by the Erlang B formula holds only for the situation in which patients arrive according to a Poisson process, meaning that the interarrival times should be exponentially distributed. If that is not the case, the use of the Erlang B formula to determine the number of necessary beds is discouraged. As an alternative, simulation offers the possibility to calculate the blocking probability for other type of arrival processes. The Simbox provides the most common distributions that can be used for modeling the arrival process. For arrival processes other than a Poisson process, simulation is really necessary in order to dimension wards in the right way.