A comparative analysis of the successive lumping and the lattice path counting algorithms
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This paper provides a comparison of the successive lumping (SL) methodology developed in Katehakis et al. (2015) with the popular lattice path counting (Mohanty (1979)) in obtaining rate matrices for queueing models, satisfying the specific quasi birth and death structure as in Van Leeuwaarden et al (2009).Abstract:
This paper provides a comparison of the successive lumping (SL) methodology developed in Katehakis et al. (2015) with the popular lattice path counting (Mohanty (1979)) in obtaining rate matrices for queueing models, satisfying the specific quasi birth and death structure as in Van Leeuwaarden et al. (2009) and Van Leeuwaarden and Winands (2006). The two methodologies are compared both in terms of applicability requirements and numerical complexity by analyzing their performance for the same classical queueing models considered in Van Leeuwaarden et al. (2009). The main findings are threefold. First, when both methods are applicable, the SL-based algorithms outperform the lattice path counting algorithm (LPCA). Second, there are important classes of problems (for example, models with (level) nonhomogenous rates or with finite state spaces) for which the SL methodology is applicable and for which the LPCA cannot be used. Third, another main advantage of SL algorithms over lattice path counting is that the former includes a method to compute the steady state distribution using this rate matrix.read more
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References
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Queueing networks with blocking: a bibliography
TL;DR: A first attempt to compile an exhaustive list of related papers in which analytic investigations (exact or approximate) or numerical investigations of queueing networks with blocking have been reported.
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Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes
L. Bright,Peter G. Taylor +1 more
TL;DR: In this paper, the authors considered the problem of computing equilibrium distributions in level dependent quasi-birth-and-death (QBD) processes, which are an extension of the classical QBD process.