The M/M\1 queue in a heavy-tailed random environment
نویسندگان
چکیده
منابع مشابه
Heavy-tailed random matrices
We discuss non-Gaussian random matrices whose elements are random variables with heavy-tailed probability distributions. In probability theory heavy tails of the distributions describe rare but violent events which usually have dominant influence on the statistics. They also completely change universal properties of eigenvalues and eigenvectors of random matrices. We concentrate here on the uni...
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The classic GI=G=1 queueing model of which the tail of the service time and/or the interarrival time distribution behaves as t ?v S(t) for t ! 1, 1 < v < 2 and S(t) a slowly varying function at innnity, is investigated for the case that the traac load a approaches one. Heavy-traac limit theorems are derived for the case that these tails have a similar behaviour at innnity as well as for the cas...
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Take XN to be a symmetric matrix with real independent (modulo the symmetry constraint) equidistributed entries with law P and denote (λ1, · · · , λN) its eigenvalues. Then, Wigner [14] has shown that, if ∫ xdP (x) is finite, N−1 ∑N i=1 δλi/ √ N converges in expectation towards the semi-circle distribution. In this paper, we consider the case where P has a heavy tail and belong to the domain of...
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ژورنال
عنوان ژورنال: Statistica Neerlandica
سال: 2000
ISSN: 0039-0402,1467-9574
DOI: 10.1111/1467-9574.00138