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Yugoslav Journal of Operations Research
2019, vol. 29, br. 1, str. 133-142
jezik rada: engleski
vrsta rada: neklasifikovan
objavljeno: 28/02/2019
doi: 10.2298/YJOR180418031K
Asymptotic results for the first and second moments and numerical computations in discrete-time bulk-renewal process
(naslov ne postoji na srpskom)
aRoyal Canadian Air Force (RCAF), Ottawa ON., Canada
bAbu Dhabi Mens College, Higher Colleges of Technology, Abu Dhabi, United Arab Emirates

e-adresa: james.kim1@forces.gc.ca, chaudhry-ml@rmc.ca, amans

Sažetak

(ne postoji na srpskom)
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.

Ključne reči

Renewal Theory; Discrete-time; Bulk-renewal Process; Generating Function; Asymptotic Results