A tandem queueing system consisting of a finite number of multi-server stations without buffers is analyzed. The input flow at the tandem is a MAP (Markovian Arrival Process). For any station, besides transit customers, an additional MAP flow of new customers (cross-traffic) arrives at the station directly, not entering the previous stations of the tandem. Customers from this flow aim to be served at the station to which they arrive and all subsequent stations of the tandem. The service times at the servers of the tandem are exponentially distributed with different parameters for different stations.

The output flows from the stations of the tandem is described in terms of MAPs. The simple method for recursive constructing the infinitesimal generator of the multi-dimensional Markov chain that describes the operation of the system, calculating the stationary distributions and loss probabilities associated with the tandem is presented.