한국경영과학회지 (Journal of the Korean Operations Research and Management Science Society)

  • 제42권1호
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  • Pages.19-28
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  • 2017
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  • 1225-1119(pISSN)
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  • 2733-4759(eISSN)
한국경영과학회 (The Korean Operations Research and Management Science Society)
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3계 마코프 도착과정의 계수과정과 적률근사

Counting Process of MAP(3)s and Moment Fittings

  • 김선교 (아주대학교 경영대학 경영학과)
  • 투고 : 2016.11.07
  • 심사 : 2016.12.16
  • 발행 : 2017.02.28
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초록

Moments of stationary intervals and those of the counting process can be used for moment fittings of the point processes. As for the Markovian arrival processes, the moments of stationary intervals are given as a polynomial function of parameters whereas the moments of the counting process involve exponential terms. Therefore, moment fittings are more complicated with the counting process than with stationary intervals. However, in queueing network analysis, cross-correlation between point processes can be modeled more conveniently with counting processes than with stationary intervals. A Laplace-Stieltjies transform of the stationary intervals of MAP (3)s is recently proposed in minimal number of parameters. We extend the results and present the Laplace transform of the counting process of MAP (3)s. We also show how moments of the counting process such as index of dispersions for counts, IDC, and limiting IDC can be used for moment fittings. Examples of exact MAP (3) moment fittings are also presented on the basis of moments of stationary intervals and those of the counting process.

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참고문헌

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