• Dr.Sushant Pandey

Renewal Achievement processes, which describes that have some cost or achievement associated with each cycle. We present a new simplified proof of the renewal theorem that mimics the proof of the elementary renewal theorem and avoids the technicalities in the proof that is presented in most textbooks. Moreover, we mention briefly the extension of the theory to partial rewards, where it is assumed that rewards are not accrued only at renewal epochs but also during the renewal cycle. For this case, we present a counterexample which indicates that the standard conditions for the renewal reward theorem are not sufficient; additional regularity assumptions are necessary. We present a few examples to indicate the usefulness of this theory, where we prove the inspection paradox and Little’s law through the renewal reward theorem.

Renewal Function with Costs and Achievement

"Renewal Function with Costs and Achievement", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.5, Issue 10, page no.498-504, October-2018, Available :http://www.jetir.org/papers/JETIR1810B23.pdf

"Renewal Function with Costs and Achievement", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.5, Issue 10, page no. pp498-504, October-2018, Available at : http://www.jetir.org/papers/JETIR1810B23.pdf