Jesus R. Artalejo
ABSTRACT
The literature on queueing systems with state-dependent parameters includes a variety of features, such as finite populations, server vacations, variable service rates, queue length dependence, retrials, and control of the admission upon arrival. The complexity of the stochastic models obtained by combining these non-homogeneous features and the method of stages causes practical difficulties. From the point of view of the numerical implementation, the large dimensionality of the underlying matrix representations is a serious problem that requires attention. Specifically, this is a key aspect if an arbitrary, even infinite number of Markovian arrival processes and phase-type distributions are involved. These considerations on the inherent difficulties associated with the stochastic modeling of block-structured state-dependent (BSDE) Markov chains provide the motivation for our study. In this paper, we briefly present the BSDE approach to construct either a specific part or the whole stochastic system in continuous time, modeling a state-dependent phenomenon operating in the presence of phases. A variant of the approach also holds in discrete time. We focus on the correlation structure and present two measures of correlation between events.
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Index Terms
- Markov chains with block-structured state-dependent events: formulation and correlation analysis
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