Krzysztof Debicki

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We consider fluid models with infinite buffer size. Let {ZN (t)} be the net input rate to the buffer, where {ZN (t)} is a superposition of N homogeneous alternating on–off flows. Under heavy traffic environment {ZN (t)} converges in distribution to a centred Gaussian process with covariance function of a single flow. The aim of this paper is to prove the(More)
In this paper we present a new representation for the steady state distribution of the workload of the second queue in a two-node tandem network. It involves the difference of two suprema over two adjacent intervals. In case of spectrally-positive Lévy input, this enables us to derive the Laplace transform and Pollaczek-Khintchine representation of the(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 terms(More)
This paper analyzes transient characteristics of Gaussian queues. More specifically, we determine the logarithmic asymptotics of P(Q0 > pB,QTB > qB), where Qt denotes the workload at time t . For any pair (p, q), three regimes can be distinguished: (A) For small values of T , one of the events {Q0 > pB} and {QTB > qB} will essentially imply the other. (B)(More)
We study properties of generalized Pickands constants H that appear in the extreme value theory of Gaussian processes and are de ned via the limit H lim T H T T where H T IE exp maxt T p t Var t and t is a centered Gaussian process with stationary increments We give estimates of the rate of convergence of H T T to H and prove that if n t weakly converges in(More)