Studying an overload system using rotation (Q1582573)

For a Markov process \(\{X(t)\}\) with state space \(\{0,1,\dots, K\}\), the authors define the rotated version by \(Y_t= K-X_t\). This concept is then generalized to a semi-Markov setting where also the state space may be unbounded in one direction and includes boundary modifications as well as supplementary variables similar to phases. The analysis is used in particular to revisit a duality result by \textit{V. Ramaswami} and \textit{M. F. Neuts} [Ann. Probab. 8, 974-985 (1980; Zbl 0449.60066)].