A parametric model is proposed for the cell arrival traffic on the input lines of a switch. The cell stream alternates between active and silent periods, and general distributions are allowed for the lengths of these periods. The traffic is represented by a discrete Markov chain model obtained through a simple moment matching procedure. The cell arrivals at in input port of the switch are typically non-Poisson and exhibit periodicities. The simulation experiments illustrate that each parameter included in the model has a significant impact on the performance of the switch (as measured by cell-loss probabilities, average cell delay, and steady-state queue length distribution).>