# Extensions of Palm's theorem: a review

@article{Carrillo1991ExtensionsOP, title={Extensions of Palm's theorem: a review}, author={Manuel J. Carrillo}, journal={Management Science}, year={1991}, volume={37}, pages={739-744} }

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 input, the number of customers in the queueing system over time turns out to have a Poisson distribution. The generality of the nonhomogeneity/nonstationarity assumptions and the ease of use of the resulting Poisson distribution broaden the area of applications for Poisson models. These results have…

## 52 Citations

Queueing Systems of INAR(1) Processes with Compound Poisson Arrivals

- Mathematics
- 2015

Integer valued autoregressive processes of order 1 (or INAR(1) processes) that may be interpreted as discrete time G/Geom/∞ queue length processes are considered. The arrivals are assumed to be…

Networks of infinite-server queues with nonstationary Poisson input

- MathematicsQueueing Syst. Theory Appl.
- 1993

A more general Poisson-arrival-location model (PALM) is introduced in which arrivals move independently through a general state space according to a location stochastic process after arrivingaccording to a nonhomogeneous Poisson process.

LAPLACE transform effectiveness in the M/G/oo queue busy period probabilistic study

- Mathematics
- 2019

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…

The Physics of the Mt/G/∞ Queue

- MathematicsOper. Res.
- 1993

It is significant that the well known insensitivity property of the stationary M/G/∞ model does not hold for the nonstationary Mt/G/, and the time-dependent mean function m depends on the service-time distribution beyond its mean.

Study about a Differential Equation in an Infinite Servers Queue System with Poisson Arrivals Busy Cycle Distribution Study

- Mathematics
- 2022

In M|G|∞ queue real life practical applications, the busy period and the busy cycle probabilistic study is of main importance. But it is a very difficult task. In this chapter, we show that by…

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

- Mathematics
- 2021

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 M|M|∞ queue transient probabilities

- Mathematics
- 2018

In the theory and applications of queuing systems, transient probabilities play a key role. Often, due to the difficulty of their calculation they are replaced by the stationary probabilities. In the…

An infinite servers queue systems with poisson and non poisson arrivals busy period simulation

- Mathematics, Computer Science
- 2014

A fortran program to simulate the operation of infinite servers’ queues, in particular about busy period parameters and probability distributions, is presented.

Infinite Servers Queue Systems Busy Period Time Length Distribution and Parameters Study through Computational Simulation

- Mathematics, Computer ScienceArXiv
- 2021

A FORTRAN program to simulate the operation of infinite servers’ queues is presented and some experiences may be performed and the respective results used to conjecture about certain queue systems interesting quantities.

Study of a collection of service time distributions and impact in the respective M|G|8 system busy period parameters

- Mathematics
- 2018

The problems arising when computing the moments of a particular service time distributions collection, for which the M|G|∞ queue system busy period becomes very easy to study, are presented and it is…

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