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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.
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)
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)
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)
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)