Wiener-Hopf factorizations for a multidimensional Markov additive process and their applications to reflected processes

Light tail asymptotics in multidimensional reflecting processes for queueing networks

“…The third one is to change the transition probabilities from the interior to the boundary. This has been considered for a reflecting Markov additive process in Miyazawa and Zwart (2009).…”

“…To prevent this difficulty, we may directly consider a multidimensional additive process. This formulation is studied in Miyazawa and Zwart (2009). One needs to generalize the Wiener-Hopf factorization.…”

“…We discuss technical ideas of the Markov additive approach discussed in some recent papers Li et al 2007;Miyazawa 2009a;Miyazawa and Zhao 2004;Miyazawa and Zwart 2009). We start with a useful identity for a general Markov chain, which will be used not only for a Markov additive process but also for the reflecting random walk.…”

“…In its applications, we need to carefully examine for which θ and s it is valid. This is thoroughly considered in Miyazawa and Zwart (2009).…”

“…One is the large deviations technique (see Bertsimas et al 1998;Chang 1995;Dupuis and Ellis 1997;Shwartz and Weiss 1995). Another is the matrix-analytic method due to Neuts (1981), which may be considered as an application of a Markov additive process and WienerHopf factorization (e.g., see Arjas andSpeed 1973 andZwart 2009).…”