In this paper, we analyze a tandem queueing system consisting of R multi-server stations without buffers. The input flow at the first station is a MAP (Markovian arrival process). The customers from this flow aim to be served at all R stations of the tandem. For any r-th station, besides transit customers proceeding from the (r − 1)-th station, an additional MAP flow of new customers arrives at the r-th station directly, not entering the previous stations of the tandem. Customers from this flow aim to be served at the r-th station and all subsequent stations of the tandem. The service time of any customer arriving at the r-th station is exponentially distributed with the service rate depending of r. We present the recursive scheme for calculating the stationary distributions and the loss probabilities associated with the tandem.