This paper addresses a parameter estimation problem of Markovian arrival process (MAP). In network traffic measurement experiments, one often encounters the group data where arrival times for a group are collected as one bin. Although the group data are observed in many situations, nearly all existing estimation methods for MAP are based on nongroup data. This paper proposes a numerical procedure for fitting a MAP and a Markov-modulated Poisson process (MMPP) to group data. The proposed algorithm is based on the expectation-maximization (EM) approach and is a natural but significant extension of the existing EM algorithms to estimate parameters of the MAP and MMPP. Specifically for the MMPP estimation, we provide an efficient approximation based on the proposed EM algorithm. We examine the performance of proposed algorithms via numerical experiments and present an example of traffic analysis with real traffic data.

This paper presents a software reliability assessment tool which is built as a Microsoft Excel AddIn. The tool handles 11 types of software reliability growth models (SRGMs) and easily provides the maximum likelihood estimates (MLEs) from input data on spreadsheets. The tool consists of two components: the user interface written by Visual Basic for Application (VBA) and the dynamic link library (DLL) written by C language. In the DLL, the state-of-the-art parameter estimation algorithms for SRGMs are implemented, which are developed from the EM (expectation-maximization) algorithm. These algorithms enable us to derive the MLEs for any patterns of data.