Stochastic monotonicity for stationary recurrence times of first passage heights

Eric V. Denardo*, Eugene A. Feinberg, Offer Kella

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

This paper deals with first passage heights of sums of renewal sequences, random walks, and Levy processes. We prove that the joint age and excess (and therefore, the current life) stationary distributions of these heights are stochastically increasing (in the usual first-order sense) in the passage levels. As a preliminary tool, which is also of independent interest, a new decomposition of the stationary excess distribution, as a convolution of two other distributions, is developed. As a consequence of these results, certain monotonicity results are concluded for ratios involving convex functions. This paper is motivated by problems related to control of queues with removable servers which model single-machine produce-to-order manufacturing systems. Applications to these problems are provided.

Original languageAmerican English
Pages (from-to)326-339
Number of pages14
JournalAnnals of Applied Probability
Volume7
Issue number2
DOIs
StatePublished - May 1997

Keywords

  • Age
  • Convex
  • Current life
  • Excess life
  • Lévy process
  • M/G/1 queue
  • N-policy
  • Renewal sequence
  • Stochastic order

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