### Abstract

Original language | English |
---|---|

Title of host publication | Wiley encyclopedia of operations research and management science |

Editors | J.J. Cochran, L.A. Cox, P. Keskinocak, J.P. Kharoufeh, J.C. Smith |

Place of Publication | Hoboken |

Publisher | Wiley |

Pages | 1-6 |

ISBN (Print) | 978-0-470-40063-0 |

DOIs | |

Publication status | Published - 2011 |

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### Cite this

*Wiley encyclopedia of operations research and management science*(pp. 1-6). Hoboken: Wiley. https://doi.org/10.1002/9780470400531.eorms0722

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic › peer-review

TY - CHAP

T1 - Renewal processes with costs and rewards

AU - Vlasiou, M.

PY - 2011

Y1 - 2011

N2 - 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.

AB - 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.

U2 - 10.1002/9780470400531.eorms0722

DO - 10.1002/9780470400531.eorms0722

M3 - Chapter

SN - 978-0-470-40063-0

SP - 1

EP - 6

BT - Wiley encyclopedia of operations research and management science

A2 - Cochran, J.J.

A2 - Cox, L.A.

A2 - Keskinocak, P.

A2 - Kharoufeh, J.P.

A2 - Smith, J.C.

PB - Wiley

CY - Hoboken

ER -