On the weak convergence of the ergodic distribution for an inventory model of type (s,S)

Xanıyev T., Atalay K. D.

Hacettepe Journal of Mathematics and Statistics, vol.39, no.4, pp.599-611, 2010 (SCI-Expanded, Scopus, TRDizin) identifier

  • Nəşrin Növü: Article / Article
  • Cild: 39 Say: 4
  • Nəşr tarixi: 2010
  • jurnalın adı: Hacettepe Journal of Mathematics and Statistics
  • Jurnalın baxıldığı indekslər: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Səhifə sayı: pp.599-611
  • Açar sözlər: Asymptotic expansion, Discrete interference of chance, Renewal function, Renewal-reward process, Triangular distribution, Weak convergence
  • Açıq Arxiv Kolleksiyası: Məqalə
  • Adres: Bəli

Qısa məlumat

In this study, a renewal-reward process with a discrete interference of chance is constructed. This process describes in particular a semimarkovian inventory model of type (s,S). The ergodic distribution of this process is expressed by a renewal function, and a second-order approximation for the ergodic distribution of the process is obtained as S - s → ∞ when the interference has a triangular distribution. Then, the weak convergence theorem is proved for the ergodic distribution and the limit distribution is derived. Finally, the accuracy of the approximation formula is tested by the Monte Carlo simulation method.