The measuring system stores the obtained identifications for the specific connections for a fixed number of received asynchronous transfer mode cells (Z1,...Zn), via a shift register (15), with interrogation of the memory during the cell cycle time, for identifying the memory locations associated with a specific connection identification. The obtained result is provided as a function of the selected memory locations, combined with the size and position of the interrogated memory range. Pref. a number of interrogations are effected within the cell cycle time, for providing a corresponding number of measuring results.
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