Copula-based parameter estimation for Markov-modulated Poisson Process

Fang Dong, Kui Wu, Venkatesh Srinivasan
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Abstract

Markov-modulated Poisson Process (MMPP) has been extensively studied in random process theory and widely used as a network traffic model. Most methods for estimating MMPP parameters are based on the exact arrival times. Nevertheless, in many applications it is costly to record the exact time of each arrival. Instead, we only record the number of arrivals in fixed-length time slots, which is called arrival count. Since arrival count data does not maintain detailed arrival times, it is non trivial to develop effective methods for MMPP parameter estimation with arrival counts only. Very few existing works deal with this challenge. This paper tackles the above challenge with copula analysis. The theoretical marginal distribution and copula of arrival counts in MMPP are applied to develop a new estimation method, MarCpa, which is a two-step estimation method involving marginal matching followed by copula matching. Our evaluation results demonstrate that the proposed method is fast and accurate.
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基于copula的马尔可夫调制泊松过程参数估计
马尔可夫调制泊松过程(MMPP)在随机过程理论中得到了广泛的研究,并被广泛用作网络流量模型。大多数估计MMPP参数的方法都是基于准确的到达时间。然而,在许多应用程序中,记录每次到达的准确时间是昂贵的。相反,我们只记录固定长度时间段的到达数量,这称为到达计数。由于到达次数数据不包含详细的到达时间,因此开发仅使用到达次数进行MMPP参数估计的有效方法是非简单的。很少有现存的作品处理这一挑战。本文用联结分析法解决了上述问题。利用MMPP中到达次数的理论边际分布和联结,提出了一种新的估计方法MarCpa,即边缘匹配后联结匹配的两步估计方法。评价结果表明,该方法快速、准确。
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