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Taylor series expansion approach for epistemic uncertainty propagation in queueing‐inventory models
Author(s) -
Soufit Massinissa,
Ouazine Sofiane,
Abbas Karim
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5120
Subject(s) - taylor series , mathematics , queueing theory , markov chain , series (stratigraphy) , stationary distribution , monte carlo method , multivariate statistics , statistical physics , mathematical optimization , statistics , mathematical analysis , paleontology , physics , biology
In this paper, we provide an uncertainty analysis for queueing‐inventory models, by extending the multivariate Taylor series expansion methodology to such stochastic models. Specifically, we derive a closed‐form expressions for the higher‐order sensitivity of discrete‐time Markov chain stationary distribution with respect to multiple parameter. We establish efficient bound on the remainder term corresponding to the multivariate Taylor series. Additionally, we estimate different quantities of interest of the output measures of the studied queueing‐inventory model. Using the copulas theory, we also include the effect of the dependence structure of parameters. The efficacy of the proposed method is shown with several numerical examples and obtained numerical results are compared with those of Monte Carlo simulation.