ASYMPTOTIC PROPERTIES OF STATIONARY DISTRIBUTIONS IN TWO-STAGE TANDEM QUEUEING SYSTEMS

• Fujimoto Kou

  Tokyo Institute of Technology

• Takahashi Yukio

  Tokyo Institute of Technology

• Makimoto Naoki

  Tokyo Institute of Technology

書誌事項

タイトル別名

• Asymptotic Properties of Stationary Dis

抄録

This paper is concerned with geometric decay properties of the joint queue length distribution p(n_1,n_2) in two-stage tandem queueing system PH/PH/c_1 → /PH/c_2. We prove that, under some conditions, p(n_1,n_2) 〜 C(n_2)η^<n_1> as n_1 → ∞ and p(n_1,n_2) 〜 C^^-(n_1)η^^-^<n_2> as n_2 → ∞. We also obtain the asymptotic form of state probabilities when n_1 is large or when n_2 is large. These results prove a part of the conjecture of a previous paper [1]. The proof is a direct application of a theorem in [7] which proves geometric decay property of the stationary distribution in a quasi-birth-and-death process with a countable number of phases in each level.

収録刊行物

• 日本オペレーションズ・リサーチ学会論文誌

  日本オペレーションズ・リサーチ学会論文誌 41 (1), 118-141, 1998

  公益社団法人 日本オペレーションズ・リサーチ学会

キーワード

• Management Science and Operations Research
• General Decision Sciences

詳細情報

• CRID: 1390001204109866240
• NII論文ID: 110001183830
• NII書誌ID: AA00703935
• DOI: 10.15807/jorsj.41.118
• ISSN: 21888299
• ISSN: 04534514
• NDL書誌ID: 4427676
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I4427676
• Web Site: https://www.jstage.jst.go.jp/article/jorsj/41/1/41_KJ00001201834/_pdf
• 本文言語コード: en
• データソース種別:
  • JaLC
  • NDL
  • Crossref
  • CiNii Articles
• 抄録ライセンスフラグ: 使用不可