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

- 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 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)

- Bert Zwart, Sem C. Borst, Krzysztof Debicki
- Oper. Res. Lett.
- 2005

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

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)

- Krzysztof Debicki, K. M. Kosinski, Michel Mandjes
- Queueing Syst.
- 2012

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)

- Krzysztof Debicki, K. M. Kosinski, Michel Mandjes
- Queueing Syst.
- 2012

- Krzysztof Debicki, Abdelghafour Es-Saghouani, Michel Mandjes
- Queueing Syst.
- 2009

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)

- Krzysztof Debicki, Miranda van Uitert
- Queueing Syst.
- 2006

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)