Identification of the circulant modulated Poisson process: a time domain approach

In this paper we will discuss a new time domain approach to the traac identiication problem for ATM networks. Our identiication approach for the circulant modulated Poisson process (CMPP) consists of two steps: the identiication of the rst order parameters and the determination of the circulant stochastic matrix which matches the second order statistics of the data. The rst step is composed of two parts. We rst characterise the rst order statistics of a given data sequence by the rst order parameters of a Markov modulated Poisson process (MMPP). These parameters are computed by applying a nonnegative least squares algorithm. In addition, the MMPP parameters are translated into CMPP parameters in order to conform this MMPP description to the restrictions of the circulant modulated Poisson process. The identiication of the circulant transition matrix is based on an unconstrained optimi-sation algorithm in which the circulant matrix structure is exploited. We compare our results to those of Yi and De Moor 4]. Summary Li et al. 1] have indicated that mathematical models can be used to perform several tasks in control mechanisms of ATM networks. The models they propose are measurement based and include the time correlation of traac. Whereas the approach of Li et al. 1, 2, 3] is mainly