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An asymptotic approach for a semi‐Markovian inventory model of type (s, S)
Author(s) -
Khaniyev Tahir,
Kokangul Ali,
Aliyev Rovshan
Publication year - 2012
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.1918
Subject(s) - ergodic theory , type (biology) , mathematics , markov process , distribution (mathematics) , order (exchange) , statistical physics , stochastic process , pure mathematics , mathematical economics , combinatorics , mathematical analysis , physics , statistics , economics , ecology , finance , biology
In this study, we constructed a stochastic process ( X ( t )) that expresses a semi‐Markovian inventory model of type ( s , S ) and it is shown that this process is ergodic under some weak conditions. Moreover, we obtained exact and asymptotic expressions for the n th order moments ( n = 1,2,3, … ) of ergodic distribution of the process X ( t ), as S − s → ∞ . Finally, we tested how close the obtained approximation formulas are to the exact expressions. Copyright © 2012 John Wiley & Sons, Ltd.