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This paper proposes two improvements of fitting algorithms for Markovian arrival processes (MAPs). The first improvement is to enhance the computation speed of Ryd'en's EM algorithm (1996) for estimating MAP parameters. The second one is to provide an efficient sub-class of MAPs to be appropriate for fitting to real traffic data. More precisely, we propose a traffic modeling based on a hidden Markov model which belongs to a sub-class of MAPs. Such a modeling framework leads to a faster fitting algorithm than the conventional algorithm with general MAPs. In numerical examples, we present the effectiveness of proposed fitting algorithms through a real traffic trace.