A Markov-modulated poisson process (MMPP) is a Poisson process whose rate varies according to an irreducible m-state Markov chain. The MMPP is used in many applications, notably in communications modeling, to describe point processes with fluctuating arrival rates. A statistical procedure is developed for fitting the MMPP. It is implemented for processes having two arrival rates modulated by an alternating exponential or an alternating Erlang renewal process. Its performance is evaluated within the context of queueing theory, where such processes most often arise and is found to be highly satisfactory.