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This paper purpose is to investigate exponential behavior conditions for theinfinite 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 Poissonarrivals busy period length distribution moments computation. In infiniteservers queue with Poisson arrivals practical applications, in economic,management, and business areas, the management of the effective number ofservers is essential since the physical presence of infinite servers is notviable and so it is necessary to create that condition through an adequatemanagement of the number of servers during the busy period.

In the Search for the Infinite Servers Queue with Poisson Arrivals Busy Period Distribution Exponential Behavior