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A comparative analysis of the successive lumping and the lattice path counting algorithms

Published online by Cambridge University Press:  24 March 2016

Michael N. Katehakis ,
Laurens C. Smit  and
Floske M. Spieksma
Laurens C. Smit
Affiliation:
Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands. Email address: lsmit@math.leidenuniv.nl
Floske M. Spieksma
Affiliation:
Mathematisch Instituut, Universiteit Leiden, Niels Bohrweg 1, 2333 CA Leiden, The Netherlands. Email address: spieksma@math.leidenuniv.nl
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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.

Keywords

Steady state analysisqueueingsuccessive lumping
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 1 , March 2016 , pp. 106 - 120
Copyright
Copyright © Applied Probability Trust 2016 

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