An integral equation for the second moment function of a geometric process and its numerical solution

PEKALP M. H., AYDOĞDU H.

NAVAL RESEARCH LOGISTICS, vol.65, no.2, pp.176-184, 2018 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 65 Issue: 2
  • Publication Date: 2018
  • Doi Number: 10.1002/nav.21791
  • Journal Name: NAVAL RESEARCH LOGISTICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.176-184
  • Keywords: geometric process, integral equation, power series, trapezoidal integration rule, variance function, QUASI-RENEWAL PROCESS, COSTS
  • Ankara University Affiliated: Yes

Abstract

In this article, an integral equation satisfied by the second moment function M-2(t) of a geometric process is obtained. The numerical method based on the trapezoidal integration rule proposed by Tang and Lam for the geometric functionM(t) is adapted to solve this integral equation. To illustrate the numerical method, the first interarrival time is assumed to be one of four common lifetime distributions, namely, exponential, gamma, Weibull, and lognormal. In addition to this method, a power series expansion is derived using the integral equation for the second moment function M-2(t), when the first interarrival time has an exponential distribution.