  This paper purpose is to investigate exponential behavior conditions for the
infinite servers queue with Poisson arrivals busy period length distribution.
It is presented a general theoretical result that is the basis of this work.
The complementary analysis rely on the infinite servers queue with Poisson
arrivals busy period length distribution moments computation. In infinite
servers queue with Poisson arrivals practical applications, in economic,
management, and business areas, the management of the effective number of
servers is essential since the physical presence of infinite servers is not
viable and so it is necessary to create that condition through an adequate
management of the number of servers during the busy period.
