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Analysis of Effective Service Time under MMPP Service Interruptions with State Dependent Interruption Periods

机译:具有状态相关中断时间段的MMPP服务中断下的有效服务时间分析

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摘要

A stochastic model is considered where a service time having a generaldistribution is delayed by service interruptions generated by an MMPP(MarkovModulated Poisson Process). More specifically, such interruptions occur accordingto a Poisson process with intensity λi whenever the underlying Markov chain isin state i. The distribution of the interruption period depends on the state of theMarkov chain at the time of the interruption. The matrix Laplace transform of theeffective service time is derived explicitly, where the matrix is formed for the initialstate i of the Markov chain and the state j of the Markov chain upon completionof the service time. The mean and variance are obtained explicitly.
机译:考虑一种随机模型,其中具有通用分布的服务时间由于MMPP(马尔可夫调制泊松过程)产生的服务中断而延迟。更具体地,每当基础马尔可夫链处于状态i时,这种中断就根据强度为λi的泊松过程发生。中断时间的分布取决于中断时马尔可夫链的状态。明确推导有效服务时间的矩阵拉普拉斯变换,其中在服务时间完成后,为马尔可夫链的初始状态i和马尔可夫链的状态j形成矩阵。明确获得均值和方差。

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