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In this paper we consider a queue fed by a large number n of independent continuous time Gaussian processes with stationary increments After scaling the bu er exceedance threshold B and the constant… (More)

- Krzysztof Debicki, Tomasz Rolski
- Queueing Syst.
- 1995

A fluid model with infinite buffer is considered. The total net rate is a stationary Gaussian process with mean −c and covariance functionR(t). Let Ψ(x) be the probability that in steady state… (More)

- Krzysztof Debicki, A. B. Dieker, Tomasz Rolski
- Math. Oper. Res.
- 2007

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 periods,… (More)

- Krzysztof Debicki, Zbigniew Palmowski
- Queueing Syst.
- 1999

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… (More)

- Krzysztof Debicki, Michel Mandjes
- Queueing Syst.
- 2004

Highly-aggregated traffic in communication networks is often modeled as fractional Brownian motion (fBm). This is justified by the theoretical result that the sum of a large number of on–off inputs,… (More)