CAJ | 학술논문

本文运用应用概率中的随机占优研究位相型（ PH）分布的随机比较问题，具体给出在一阶、二阶随机占优下比较两个离散PH分布或两个连续PH分布的充分条件及充分必要条件。研究表明，比较两个离散PH分布可变性的条件与比较两个连续PH分布可变性的条件不同，在二阶随机占优意义下比较两个连续PH分布的条件与均值无关，而比较两个离散PH分布的条件与均值有关。本文的结果可用于研究PH分布的最小变异系数问题和可变性问题，也可用于研究带有PH到达间隔或PH服务的排队系统中到达过程或服务时间可变性对系统队长或等待时间的影响。
본문운용응용개솔중적수궤점우연구위상형（ PH）분포적수궤비교문제，구체급출재일계、이계수궤점우하비교량개리산PH분포혹량개련속PH분포적충분조건급충분필요조건。연구표명，비교량개리산PH분포가변성적조건여비교량개련속PH분포가변성적조건불동，재이계수궤점우의의하비교량개련속PH분포적조건여균치무관，이비교량개리산PH분포적조건여균치유관。본문적결과가용우연구PH분포적최소변이계수문제화가변성문제，야가용우연구대유PH도체간격혹PH복무적배대계통중도체과정혹복무시간가변성대계통대장혹등대시간적영향。
In this paper, we analyze stochastic comparison of phase-type(PH)distributions by using stochastic dom-inance in applied probability , sufficient conditions and necessary and sufficient conditions for comparing two phase -type distributions under first and second degree stochastic dominance are provided .We prove that conditions to compare variabilities of two discrete phase-type distributions are different from those comparing variabilities of two continuous phase-type distributions .Conditions comparing two continuous phase-type distributions under second degree stochastic dominance are independent of their means , but conditions comparing two discrete phase-type dis-tributions depend on their means .The results in this article can be applied to the problem for the minimization co-efficient of variation and variabilities of phase-type distributions , and they can also be used to analyze the effect of variability of arrival process or service time on queue length or waiting time in queueing systems .