Renewal processes with costs and rewards

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

Abstract

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.
Original languageEnglish
Title of host publicationWiley encyclopedia of operations research and management science
EditorsJ.J. Cochran, L.A. Cox, P. Keskinocak, J.P. Kharoufeh, J.C. Smith
Place of PublicationHoboken
PublisherWiley
Pages1-6
ISBN (Print)978-0-470-40063-0
DOIs
Publication statusPublished - 2011

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Renewal Process
Reward
Renewal
Costs
Renewal Reward Process
Theorem
Renewal Theorem
Cycle
Paradox
Counterexample
Inspection
Regularity
Sufficient
Partial
Necessary

Cite this

Vlasiou, M. (2011). Renewal processes with costs and rewards. In J. J. Cochran, L. A. Cox, P. Keskinocak, J. P. Kharoufeh, & J. C. Smith (Eds.), Wiley encyclopedia of operations research and management science (pp. 1-6). Hoboken: Wiley. https://doi.org/10.1002/9780470400531.eorms0722
Vlasiou, M. / Renewal processes with costs and rewards. Wiley encyclopedia of operations research and management science. editor / J.J. Cochran ; L.A. Cox ; P. Keskinocak ; J.P. Kharoufeh ; J.C. Smith. Hoboken : Wiley, 2011. pp. 1-6
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Vlasiou, M 2011, Renewal processes with costs and rewards. in JJ Cochran, LA Cox, P Keskinocak, JP Kharoufeh & JC Smith (eds), Wiley encyclopedia of operations research and management science. Wiley, Hoboken, pp. 1-6. https://doi.org/10.1002/9780470400531.eorms0722

Renewal processes with costs and rewards. / Vlasiou, M.

Wiley encyclopedia of operations research and management science. ed. / J.J. Cochran; L.A. Cox; P. Keskinocak; J.P. Kharoufeh; J.C. Smith. Hoboken : Wiley, 2011. p. 1-6.

Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

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Vlasiou M. Renewal processes with costs and rewards. In Cochran JJ, Cox LA, Keskinocak P, Kharoufeh JP, Smith JC, editors, Wiley encyclopedia of operations research and management science. Hoboken: Wiley. 2011. p. 1-6 https://doi.org/10.1002/9780470400531.eorms0722