Likelihood ratio derivative estimation for finite-time performance measures in generalized semi-Markov processes

Marvin K. Nakayama, Perwez Shahabuddin

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

This paper investigates the likelihood ratio method for estimating derivatives of finite-time performance measures in generalized semi-Markov processes (GSMPs). We develop readily verifiable conditions for the applicability of this method. Our conditions mainly place restrictions on the basic building blocks (i.e., the transition probabilities, the distribution and density functions of the event lifetimes, and the initial distribution) of the GSMP, which is in contrast to the structural conditions needed for infinitesimal perturbation analysis. We explicitly show that our conditions hold in many practical settings, and in particular, for large classes of queueing and reliability models. One intermediate result we obtain in this study, which is of independent value, is to formally show that the random variable representing the number of occurring events in a GSMP in a finite time horizon, has finite exponential moments in a neighborhood of zero.

Original languageEnglish (US)
Pages (from-to)1426-1441
Number of pages16
JournalManagement Science
Volume44
Issue number10
DOIs
StatePublished - Oct 1998

All Science Journal Classification (ASJC) codes

  • Strategy and Management
  • Management Science and Operations Research

Keywords

  • Generalized Semi-Markov Processes
  • Gradient Estimation
  • Simulation

Fingerprint Dive into the research topics of 'Likelihood ratio derivative estimation for finite-time performance measures in generalized semi-Markov processes'. Together they form a unique fingerprint.

Cite this