An application of Markovian arrival process (MAP) to modeling superposed ATM cell streams

First, we propose a new modeling method for superposed ATM traffic by the MMPP(2), which is a special case of the MAP(2). In this new method, we measure the mean and autocorrelation of cell interarrival times, and the histogram of the number of arrivals during measurement windows of fixed size. The MMPP(2) has interarrival times with the second-order hyper-exponential distribution with coefficient of variation c_v > 1. However, superposed traffic is often observed to have c_v < 1. To cover this situation, we extend the MMPP(2) to a MAP(3) by adding a new state with inter-state transition accompanied by an arrival. For the MAP(3) model, we take into account the second moment of the interarrival times. From numerical examples, we observe that both the proposed MMPP(2) and MAP(3) yields very good estimation of the cell loss ratio (CLR) for usual superpositions of voice and/or VBR video sources. However, when we have superpositions from CBR video sources together with other VBR sources, c_v is much less than 1, and the MAP(3) outperform the MMPP(2), as expected. The proposed MAP(3) well characterizes the cell scale component as well as the burst scale component of superposed traffic streams.