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Extensions of Riordan matrices and Applications to Queueing models

저자 : 진성태

형태사항 : 108 ; 26 cm

일반주기 : 지도교수: 천기상

학위논문사항 : Thesis(doctoral)-- 성균관대학교 일반대학원 : 수학과 2015. 8

발행국 : 대한민국

언어 : 영어

출판년 : 2015

주제어 : extended Riordan matrix, 3-D Riordan array, generalized Riordan array, Queueing theory, transient analysis

소장기관 :

  • 성균관대학교 중앙학술정보관

※ 해당 논문은 저작자의 요청에 따라 [원문보기]가 제공되지 않습니다.

  • 목차
    • Chapter I : Introduction 1
    • Chapter II : Extended Riordan matrices 8
    • 1 Structural properties of Riordan matrices 8
    • 1.1 The ray sequences and the diagonal sums 8
    • 1.2 Equivalence relation on the formal power series 16
    • 1.3 Unified combinatorial interpretation for the equivalence class 25
    • 2 Extending the Riordan matrices to the ring of Laurent series 29
    • 2.1 Extended Riordan matrices 29
    • 2.2 Applications to the combinatorial identity 34
    • Chapter III : Multi-dimensional Riordan arrays 37
    • 1 3-D Riordan arrays and the group structure 37
    • 2 Group extension problems 41
    • 3 Lattice path counting problem on Z3 45
    • Chapter IV : Applications of Riordan arrays to queueing models 48
    • 1 Transient analysis of M/M/1 queueing model 48
    • 1.1 Transient analysis of M/M/1 queue starting with zero customers 48
    • 1.2 Transient analysis of M/M/1 queue starting with h customers 56
    • 2 Transient analysis of M/M/c queueing model 60
    • 2.1 Transient analysis of M/M/c queue starting with zero customers 61
    • 2.2 Transient analysis of M/M/c queue starting with h customers 70
    • 3 Numerical examples for several queueing models 78
    • Reference 86
    • Appendix 90
    • 1 PHP codes generating the Riordan matrices, Online Program 90
    • 2 Mathematica code for the transient solution of M/M/1 queue 94