Renewal processes with costs and rewards

Onderzoeksoutput: Hoofdstuk in Boek/Rapport/CongresprocedureHoofdstukAcademicpeer review


We review the theory of renewal reward processes, which describes renewal processes that have some cost or reward associated with each cycle. We present a new simplified proof of the renewal reward 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 accrued not 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.
Originele taal-2Engels
TitelWiley encyclopedia of operations research and management science
RedacteurenJ.J. Cochran, L.A. Cox, P. Keskinocak, J.P. Kharoufeh, J.C. Smith
Plaats van productieHoboken
ISBN van geprinte versie978-0-470-40063-0
StatusGepubliceerd - 2011

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  • Citeer dit

    Vlasiou, M. (2011). Renewal processes with costs and rewards. In J. J. Cochran, L. A. Cox, P. Keskinocak, J. P. Kharoufeh, & J. C. Smith (editors), Wiley encyclopedia of operations research and management science (blz. 1-6). Wiley.