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CWI's research has a theme-oriented structure and is grouped into four clusters. Listed below are the names of the clusters and in parentheses their acronyms. ABSTRACT We study stochastic tree fluid networks driven by a multidimensional Lévy process. We are interested in (the joint distribution of) the steady-state content in each of the buffers, the busy(More)
This paper considers a Lévy-driven queue (i.e., a Lévy process reflected at 0), and focuses on the distribution of M (t), that is, the minimal value attained in an interval of length t (where it is assumed that the queue is in stationarity at the beginning of the interval). The first contribution is an explicit characterization of this distribution, in(More)
Let {X(t) : t ∈ [0, ∞)} be a centered Gaussian process with stationary increments and variance function σ 2 X (t). We study the exact asymptotics of P(sup t∈[0,T ] X(t) > u), as u → ∞, where T is an independent of {X(t)} nonnegative Weibullian random variable. As an illustration we work out the asymptotics of supremum distribution of fractional Laplace(More)