Computing the Matrix G of Multi-Dimensional Markov Chains of M/G/1 Type

Valeriy Naumov () and Konstantin Samouylov
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Valeriy Naumov: Service Innovation Research Institute, Annankatu 8 A, 00120 Helsinki, Finland
Konstantin Samouylov: Institute of Computer Science and Telecommunications, RUDN University, 6 Miklukho-Maklaya St., Moscow 117198, Russia

Mathematics, 2025, vol. 13, issue 8, 1-14

Abstract: We consider M d-M/G/1 processes, which are irreducible discrete-time Markov chains consisting of two components. The first component is a nonnegative integer vector, while the second component indicates the state (or phase) of the external environment. The level of a state is defined by the minimum value in its first component. The matrix G of the process represents the conditional probabilities that, starting from a given state of a certain level, the Markov chain will first reach a lower level in a specific state. This study aims to develop an effective algorithm for computing matrices G for M d-M/G/1 processes.

Keywords: discrete-time Markov chain; Markov chain of M/G/1 type; matrix G; system of nonlinear matrix equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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