Open AccessAsymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process
Author(s) -
J James Kim,
L Mohan Chaudhry,
Abdalla Mansur
Publication year - 2019
Publication title -
yugoslav journal of operations research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.221
H-Index - 21
eISSN - 1820-743X
pISSN - 0354-0243
DOI - 10.2298/yjor180418031k
Subject(s) - renewal theory , mathematics , limit (mathematics) , moment (physics) , constant (computer programming) , discrete time and continuous time , computation , term (time) , process (computing) , asymptotic analysis , mathematical analysis , computer science , algorithm , statistics , physics , classical mechanics , quantum mechanics , programming language , operating system
This paper introduces a simplified solution to determine the asymptotic results for the renewal density. It also offers the asymptotic results for the first and second moments of the number of renewals for the discrete-time bulk-renewal process. The methodology adopted makes this study distinguishable compared to those previously published where the constant term in the second moment is generated. In similar studies published in the literature, the constant term is either missing or not clear how it was obtained. The problem was partially solved in the study by Chaudhry and Fisher where they provided a asymptotic results for the non-bulk renewal density and for both the first and second moments using the generating functions. The objective of this work is to extend their results to the bulk-renewal process in discrete-time, including some numerical results, give an elegant derivation of the asymptotic results and derive continuous-time results as a limit of the discrete-time results.