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- Hendrik Baumann, Werner Sandmann
- ICCS
- 2010

We consider the numerical computation of stationary distributions for level dependent quasi-birth-and-death processes. An algorithm based on matrix continued fractions is presented and compared to standard solution techniques. Its computational efficiency and numerical stability is demonstrated by numerical examples.

- Hendrik Baumann, Werner Sandmann
- J. Applied Probability
- 2013

- Hendrik Baumann, Tugrul Dayar, M. Can Orhan, Werner Sandmann
- Perform. Eval.
- 2013

Infinite level-dependent quasi-birth-and-death (LDQBD) processes can be used to model Markovian systems with countably infinite multidimensional state spaces. Recently it has been shown that sums of Kronecker products can be used to represent the nonzero blocks of the transition rate matrix underlying an LDQBD process for models from stochastic chemical… (More)

- Hendrik Baumann, Werner Sandmann
- Computers & OR
- 2012

- Hendrik Baumann, Werner Sandmann
- 2012 20th Euromicro International Conference on…
- 2012

Network flooding is among the most prevalent modes of denial-of-service (DoS) attacks. It can seriously degrade the network operation to the point of being unable to serve any legitimate user as intended, because all resources are occupied with serving malicious attack requests. We model flooding DoS attacks by a three-dimensional continuous-time Markov… (More)

- Hendrik Baumann, Werner Sandmann
- J. Applied Probability
- 2015

We consider long run averages of additive functionals on infinite discrete-state Markov chains, either continuous or discrete in time. Special cases include long run average costs or rewards, stationary moments of the components of ergodic multi-dimensional Markov chains, queueing network performance measures, and many others. By exploiting… (More)

- Hendrik Baumann, Werner Sandmann
- PloS one
- 2016

Stochastic epidemics with open populations of variable population sizes are considered where due to immigration and demographic effects the epidemic does not eventually die out forever. The underlying stochastic processes are ergodic multi-dimensional continuous-time Markov chains that possess unique equilibrium probability distributions. Modeling these… (More)

- Hendrik Baumann
- Journal of Approximation Theory
- 2015

- Hendrik Baumann, Werner Sandmann
- European Journal of Operational Research
- 2017

- Hendrik Baumann
- Journal of Approximation Theory
- 2013

We consider continued fractions in Banach algebras, that is b0 + a1(b1 + a2(b2 + · · ·) −1)−1, where (bn)n∈N0 and (an)n∈N are sequences of elements of some Banach algebra. We prove that b−1 n + anb−1 n ≤ 1 for n = 1, 2, . . . is a sufficient condition for convergence. This result is an exact generalization of the Śleszyński–Pringsheim… (More)

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