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

@inproceedings{Ferreira2021InTS,
title={In the Search for the Infinite Servers Queue with Poisson Arrivals Busy Period Distribution Exponential Behavior},
author={Manuel Alberto M. Ferreira and Jos'e Ant'onio Filipe},
year={2021}
}
• Published 29 September 2021
• Mathematics
This paper purpose is to investigate exponential behavior conditions for the M|G|∞ queue busy period length distribution. It is presented a general theoretical result that is the basis of this work. The complementary analysis rely on the M|G|∞ queue busy period length distribution moments computation. In M|G|∞ queue 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…
1 Citations

## Tables from this paper

LAPLACE transform effectiveness in the M/G/oo queue busy period probabilistic study
The Laplace transform is a widely used tool in the study of probability distributions, often allowing for a probability density functions and distribution functions simpler determination and being a

## References

SHOWING 1-10 OF 11 REFERENCES
THE TIES BETWEEN THE MG∞ QUEUE SYSTEM TRANSIENT BEHAVIOUR AND THE BUSY PERIOD
• Mathematics
• 2009
ABSTRACT This paper main subject is the M  G ∞ queue system transient probabilities study as time functions. It is completely achieved when the time origin is an unoccupied system instant. But such
Extensions of Palm's theorem: a review
This note reviews the transient behavior the M/G/\infty queue with nonhomogeneous Poisson or compound Poisson input and nonstationary service distribution. In the case of nonhomogeneous Poisson
Infinite servers queue systems busy period - a practical case on logistics problems solving
• 2015
With this model it is possible to obtain system performance measures and also to contribute to solve organizing structures’ problems, by minimizing the risks of the organizations inoperative structures, with considerable logistics pernicious consequences for companies.
The busy period of the queueing system M / G /∞
For the queueing system M/G/oo some distributions connected with the associated busy periods are derived. QUEUES WITH UNLIMITED SERVICE
Occupation Study of a Surgery Service through a Queues Model
• Medicine
• 2015
A method to study and evaluate the occupation of a Hospital Surgery Service, with some specificity in its activity, is outlined and it is shown that it is simple, practical and useful and allows a practical management of the service occupation.
Looking to a M|G|∞ system occupation through a Riccati equation
• Journal of Mathematics and Technology,
• 2010
M|G|∞ Queue Busy Period Tail
• Journal of Mathematics and Technology,
• 2010
M|G|∞, System Transient Behavior with Time Origin at the Beginning of a Busy Period Mean and Variance
• Aplimat- Journal of Applied Mathematics,
• 2010