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Asymptotics for renewal-reward processes with retrospective reward structure

Authors
Journal
Operations Research Letters
0167-6377
Publisher
Elsevier
Publication Date
Volume
26
Issue
5
Identifiers
DOI: 10.1016/s0167-6377(00)00035-3
Keywords
  • Renewal-Reward Process
  • Retrospective Reward
  • Expected Cumulative Reward
  • Replacement Modelling

Abstract

Abstract Let {(X i,Y i) : i=…,−1,0,1,…} be a doubly infinite renewal-reward process, where {X i : i=…−1,0,1,…} is an i.i.d. sequence of renewal cycle lengths and Y i = g( X i− q , X i− q+1 ,…, X i ) is the lump reward earned at the end of the ith renewal cycle, with some function g : R q+1→ R . Starting with the first renewal cycle (of duration X 1) at the time origin, let C( t) denote the expected cumulative reward earned in (0, t]. In this paper, an asymptotic representation for C of the form C(t)=ξt+η+ o(1), t→∞ , is derived. An application of this result in single item replacement modelling is discussed.

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