We compute moments of the length of the busy period ofMX=G=1=n systems starting with an arbitrary
number of customers in the system using a recursive algorithm that is based on the fact that the length of a busy
period initiated by multiple customers in a system of some xed capacity can be expressed in terms of the lengths
of busy periods of systems with smaller or equal capacities and initiated by a single customer. The computational
complexity of the algorithm proposed in the paper is derived and numerical examples provided.