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A new matrix-infinite-product-form solution for upper block-Hessenberg Markov chains and its quasi-algorithmic constructibility. ADV APPL PROBAB 2022. [DOI: 10.1017/apr.2022.9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
Abstract
Abstract
This paper presents a new matrix-infinite-product-form (MIP-form) solution for the stationary distribution in upper block-Hessenberg Markov chains (UBH-MCs). The existing MIP-form solution (Masuyama, Queueing Systems92, 2019, pp. 173–200) requires a certain parameter set that satisfies both a Foster–Lyapunov drift condition and a convergence condition. In contrast, the new MIP-form solution requires no such parameter sets and no other conditions. The new MIP-form solution also has ‘quasi-algorithmic constructibility’, which is a newly introduced feature of being constructed by iterating infinitely many times a recursive procedure of finite complexity per iteration. This feature is not found in the other existing solutions for the stationary distribution in general UBH-MCs.
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Kimura T, Masuyama H, Takahashi Y. Subexponential Asymptotics of the Stationary Distributions of GI/G/1-Type Markov Chains. STOCH MODELS 2013. [DOI: 10.1080/15326349.2013.783286] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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