Geodesic
Limit theorems on maximums of Poisson sequences and their applications to queuing theory
Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 2, pp. 446-450

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We consider a sequence of independent Poisson random variables $X_n$ with parameters $\lambda_n$. Asymptotic properties of maximums $Y_n=\max_{1\le i\le n}X_i$ under the dependence on properties of the sequence $\{\lambda_n\}$ are studied. The results obtained are applied to investigating the maximal number of claims in the system $M|G|\infty$ with parameters dependent on time.
Mots-clés : Poisson random variables
Keywords: maximums, limit theorems, almost sure convergence, infinitely linear queuing systems. 
@article{TVP_1999_44_2_a12,
     author = {A. V. Lebedev},
     title = {Limit theorems on maximums of {Poisson} sequences and their applications to queuing theory},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {446--450},
     publisher = {mathdoc},
     volume = {44},
     number = {2},
     year = {1999},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a12/}
}
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A. V. Lebedev. Limit theorems on maximums of Poisson sequences and their applications to queuing theory. Teoriâ veroâtnostej i ee primeneniâ, Tome 44 (1999) no. 2, pp. 446-450. http://geodesic.mathdoc.fr/item/TVP_1999_44_2_a12/