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- W4290802910 abstract "In this paper, we study the tail behavior of $max_{ileq N}sup_{s>0}left(W_i(s)+W_A(s)-beta sright)$ as $Ntoinfty$, with $(W_i,ileq N)$ i.i.d. Brownian motions and $W_A$ an independent Brownian motion. This random variable can be seen as the maximum of $N$ mutually dependent Brownian queues, which in turn can be interpreted as the backlog in a Brownian fork-join queue. In previous work, we have shown that this random variable centers around $frac{sigma^2}{2beta}log N$. Here, we analyze the rare-event that this random variable reaches the value $(frac{sigma^2}{2beta}+a)log N$, with $a>0$. It turns out that its probability behaves roughly as a power law with $N$, where the exponent depends on $a$. However, there are three regimes, around a critical point $a^{star}$; namely, $0<a<a^{star}$, $a=a^{star}$, and $a>a^{star}$. The latter regime exhibits a form of asymptotic independence, while the first regime reveals highly irregular behavior with a clear dependence structure among the $N$ suprema, with a nontrivial transition at $a=a^{star}$." @default.
- W4290802910 created "2022-08-12" @default.
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- W4290802910 date "2022-08-09" @default.
- W4290802910 modified "2023-09-27" @default.
- W4290802910 title "Tail Asymptotics for the Delay in a Brownian Fork-Join Queue" @default.
- W4290802910 doi "https://doi.org/10.48550/arxiv.2208.04796" @default.
- W4290802910 hasPublicationYear "2022" @default.
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