In a policing arrangement for an ATM network, every incoming cell is stored in a cell buffer and a virtual path identifier (VPI) contained in the cell is extracted and translated to a corresponding one of a set of threshold values. Policing circuits of a matrix array are connected column by column for transferring a VPI in accordance with a read/write control circuit. Each policing circuit of the first column is uniquely responsive to a VPI of a particular value for storing the extracted VPI into a bridge memory, and this column has a greater number of policing circuits than any of the other columns of the array. In each column of the array, at least one of the policing circuits includes a cell counter for incrementing a cell count value in response to the VPI of every incoming cell and decrementing the cell count in response to a VPI read out of the bridge memory of the policing circuit. The cell count value is compared with the threshold value and a cell is discarded from the cell buffer when the cell count value exceeds the threshold value.