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Computing stationary expectations in level-dependent QBD processes. (English) Zbl 1273.60089

In this paper the authors discuss a novel method to numerically compute the expectations of additive functionals with respect to the stationary distribution of a quasi-birth-and-death process, i.e., Markov chains with generator which is a block-diagonal matrix. The algorithm is applicable to finite-state space chains but specific issues arising in using the method for truncated infinite state space chains are also discussed.
The presented method is based on matrix-analytic techniques and avoids the explicit computation of the stationary distribution when evaluating the expectation of functionals. In this way the algorithm requires far less computer storage than algorithms calculating the stationary distribution directly but does not incur any losses in speed.
A numerical example of a queuing network is used to illustrate the performance of the method.

MSC:

60J22 Computational methods in Markov chains
60J27 Continuous-time Markov processes on discrete state spaces
60J28 Applications of continuous-time Markov processes on discrete state spaces
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References:

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